论文定稿

bibliography/IEEEabrv.bib

@@ -0,0 +1,447 @@
+
+IEEEabrv.bib
+V1.12 (2007/01/11)
+Copyright (c) 2002-2007 by Michael Shell
+See: http://www.michaelshell.org/
+for current contact information.
+
+BibTeX bibliography string definitions of the ABBREVIATED titles of
+IEEE journals and magazines and online publications.
+
+This file is designed for bibliography styles that require 
+abbreviated titles and is not for use in bibliographies that
+require full-length titles.
+
+Support sites:
+http://www.michaelshell.org/tex/ieeetran/
+http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
+and/or
+http://www.ieee.org/
+
+Special thanks to Laura Hyslop and ken Rawson of IEEE for their help
+in obtaining the information needed to compile this file. Also,
+Volker Kuhlmann and Moritz Borgmann kindly provided some corrections
+and additions.
+
+*************************************************************************
+Legal Notice:
+This code is offered as-is without any warranty either expressed or
+implied; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE! 
+User assumes all risk.
+In no event shall IEEE or any contributor to this code be liable for
+any damages or losses, including, but not limited to, incidental,
+consequential, or any other damages, resulting from the use or misuse
+of any information contained here.
+
+All comments are the opinions of their respective authors and are not
+necessarily endorsed by the IEEE.
+
+This work is distributed under the LaTeX Project Public License (LPPL)
+( http://www.latex-project.org/ ) version 1.3, and may be freely used,
+distributed and modified. A copy of the LPPL, version 1.3, is included
+in the base LaTeX documentation of all distributions of LaTeX released
+2003/12/01 or later.
+Retain all contribution notices and credits.
+** Modified files should be clearly indicated as such, including  **
+** renaming them and changing author support contact information. **
+
+File list of work: IEEEabrv.bib, IEEEfull.bib, IEEEexample.bib,
+                   IEEEtran.bst, IEEEtranS.bst, IEEEtranSA.bst,
+                   IEEEtranN.bst, IEEEtranSN.bst, IEEEtran_bst_HOWTO.pdf
+*************************************************************************
+
+
+USAGE:
+
+\bibliographystyle{mybstfile}
+\bibliography{IEEEabrv,mybibfile}
+
+where the IEEE titles in the .bib database entries use the strings
+defined here. e.g.,
+
+
+   journal = IEEE_J_AC,
+
+
+to yield "{IEEE} Trans. Automat. Contr."
+
+
+IEEE uses abbreviated journal titles in their bibliographies -
+this file is suitable for work that is to be submitted to the IEEE.
+
+
+For work that requires full-length titles, you should use the full
+titles provided in the companion file, IEEEfull.bib.
+
+
+** NOTES **
+
+ 1. Journals have been grouped according to subject in order to make it
+    easier to locate and extract the definitions for related journals - 
+    as most works use references that are confined to a single topic.
+    Magazines are listed in straight alphabetical order.
+
+ 2. String names are closely based on IEEE's own internal acronyms.
+ 
+ 3. Abbreviations follow IEEE's style.
+
+ 4. Older, out-of-print IEEE titles are included (but not including titles
+    dating prior to IEEE's formation from the IRE and AIEE in 1963).
+
+ 5. The following NEW/current journal definitions have been disabled because
+    their abbreviations have not yet been verified:
+    
+    STRING{IEEE_J_CBB        = "{IEEE/ACM} Trans. Comput. Biology Bioinformatics"}
+    STRING{IEEE_J_CJECE      = "Canadian J. Elect. Comput. Eng."}
+    STRING{IEEE_J_DSC        = "{IEEE} Trans. Dependable Secure Comput."}
+    STRING{IEEE_O_DSO        = "{IEEE} Distrib. Syst. Online"}
+    
+ 6. The following OLD journal definitions have been disabled because
+    their abbreviations have not yet been found/verified:
+
+    STRING{IEEE_J_BCTV       = "{IEEE} Trans. Broadcast Television Receivers"}
+    STRING{IEEE_J_EWS        = "{IEEE} Trans. Eng. Writing Speech"}
+
+If you know what the proper abbreviation is for a string in #5 or #6 above,
+email me and I will correct them in the next release.
+
+
+
+
+
+IEEE Journals 
+
+
+
+aerospace and military
+@STRING{IEEE_J_AES        = "{IEEE} Trans. Aerosp. Electron. Syst."}
+@STRING{IEEE_J_ANE        = "{IEEE} Trans. Aerosp. Navig. Electron."}
+@STRING{IEEE_J_ANNE       = "{IEEE} Trans. Aeronaut. Navig. Electron."}
+@STRING{IEEE_J_AS         = "{IEEE} Trans. Aerosp."}
+@STRING{IEEE_J_AIRE       = "{IEEE} Trans. Airborne Electron."}
+@STRING{IEEE_J_MIL        = "{IEEE} Trans. Mil. Electron."}
+
+
+
+autos, transportation and vehicles (non-aerospace)
+@STRING{IEEE_J_ITS        = "{IEEE} Trans. Intell. Transp. Syst."}
+@STRING{IEEE_J_VT         = "{IEEE} Trans. Veh. Technol."}
+@STRING{IEEE_J_VC         = "{IEEE} Trans. Veh. Commun."}
+
+
+
+circuits, signals, systems, audio and controls
+@STRING{IEEE_J_SPL        = "{IEEE} Signal Process. Lett."}
+@STRING{IEEE_J_ASSP       = "{IEEE} Trans. Acoust., Speech, Signal Process."}
+@STRING{IEEE_J_AU         = "{IEEE} Trans. Audio"}
+@STRING{IEEE_J_AUEA       = "{IEEE} Trans. Audio Electroacoust."}
+@STRING{IEEE_J_AC         = "{IEEE} Trans. Autom. Control"}
+@STRING{IEEE_J_CAS        = "{IEEE} Trans. Circuits Syst."}
+@STRING{IEEE_J_CASVT      = "{IEEE} Trans. Circuits Syst. Video Technol."}
+@STRING{IEEE_J_CASI       = "{IEEE} Trans. Circuits Syst. {I}"}
+@STRING{IEEE_J_CASII      = "{IEEE} Trans. Circuits Syst. {II}"}
+in 2004 CASI and CASII renamed part title to CASI_RP and CASII_EB, respectively.
+@STRING{IEEE_J_CASI_RP    = "{IEEE} Trans. Circuits Syst. {I}"}
+@STRING{IEEE_J_CASII_EB   = "{IEEE} Trans. Circuits Syst. {II}"}
+@STRING{IEEE_J_CT         = "{IEEE} Trans. Circuit Theory"}
+@STRING{IEEE_J_CST        = "{IEEE} Trans. Control Syst. Technol."}
+@STRING{IEEE_J_SP         = "{IEEE} Trans. Signal Process."}
+@STRING{IEEE_J_SU         = "{IEEE} Trans. Sonics Ultrason."}
+@STRING{IEEE_J_SAP        = "{IEEE} Trans. Speech Audio Process."}
+@STRING{IEEE_J_UE         = "{IEEE} Trans. Ultrason. Eng."}
+@STRING{IEEE_J_UFFC       = "{IEEE} Trans. Ultrason., Ferroelectr., Freq. Control"}
+
+
+
+communications
+@STRING{IEEE_J_COML       = "{IEEE} Commun. Lett."}
+@STRING{IEEE_J_JSAC       = "{IEEE} J. Sel. Areas Commun."}
+@STRING{IEEE_J_COM        = "{IEEE} Trans. Commun."}
+@STRING{IEEE_J_COMT       = "{IEEE} Trans. Commun. Technol."}
+@STRING{IEEE_J_WCOM       = "{IEEE} Trans. Wireless Commun."}
+
+
+
+components, packaging and manufacturing
+@STRING{IEEE_J_ADVP       = "{IEEE} Trans. Adv. Packag."}
+@STRING{IEEE_J_CHMT       = "{IEEE} Trans. Compon., Hybrids, Manuf. Technol."}
+@STRING{IEEE_J_CPMTA      = "{IEEE} Trans. Compon., Packag., Manuf. Technol. {A}"}
+@STRING{IEEE_J_CPMTB      = "{IEEE} Trans. Compon., Packag., Manuf. Technol. {B}"}
+@STRING{IEEE_J_CPMTC      = "{IEEE} Trans. Compon., Packag., Manuf. Technol. {C}"}
+@STRING{IEEE_J_CAPT       = "{IEEE} Trans. Compon. Packag. Technol."}
+@STRING{IEEE_J_CAPTS      = "{IEEE} Trans. Compon. Packag. Technol."}
+@STRING{IEEE_J_CPART      = "{IEEE} Trans. Compon. Parts"}
+@STRING{IEEE_J_EPM        = "{IEEE} Trans. Electron. Packag. Manuf."}
+@STRING{IEEE_J_MFT        = "{IEEE} Trans. Manuf. Technol."}
+@STRING{IEEE_J_PHP        = "{IEEE} Trans. Parts, Hybrids, Packag."}
+@STRING{IEEE_J_PMP        = "{IEEE} Trans. Parts, Mater., Packag."}
+
+
+
+CAD
+@STRING{IEEE_J_TCAD       = "{IEEE} J. Technol. Comput. Aided Design"}
+@STRING{IEEE_J_CAD        = "{IEEE} Trans. Comput.-Aided Design Integr. Circuits Syst."}
+
+
+
+coding, data, information, knowledge
+@STRING{IEEE_J_IT         = "{IEEE} Trans. Inf. Theory"}
+@STRING{IEEE_J_KDE        = "{IEEE} Trans. Knowl. Data Eng."}
+
+
+
+computers, computation, networking and software
+@STRING{IEEE_J_C          = "{IEEE} Trans. Comput."}
+@STRING{IEEE_J_CAL        = "{IEEE} Comput. Archit. Lett."}
+disabled till definition is verified
+STRING{IEEE_J_DSC         = "{IEEE} Trans. Dependable Secure Comput."}
+@STRING{IEEE_J_ECOMP      = "{IEEE} Trans. Electron. Comput."}
+@STRING{IEEE_J_EVC        = "{IEEE} Trans. Evol. Comput."}
+@STRING{IEEE_J_FUZZ       = "{IEEE} Trans. Fuzzy Syst."}
+@STRING{IEEE_J_IFS        = "{IEEE} Trans. Inf. Forensics Security"}
+@STRING{IEEE_J_MC         = "{IEEE} Trans. Mobile Comput."}
+@STRING{IEEE_J_NET        = "{IEEE/ACM} Trans. Netw."}
+@STRING{IEEE_J_NN         = "{IEEE} Trans. Neural Netw."}
+@STRING{IEEE_J_PDS        = "{IEEE} Trans. Parallel Distrib. Syst."}
+@STRING{IEEE_J_SE         = "{IEEE} Trans. Softw. Eng."}
+
+
+
+computer graphics, imaging, and multimedia
+@STRING{IEEE_J_JDT        = "{IEEE/OSA} J. Display Technol."}
+@STRING{IEEE_J_IP         = "{IEEE} Trans. Image Process."}
+@STRING{IEEE_J_MM         = "{IEEE} Trans. Multimedia"}
+@STRING{IEEE_J_VCG        = "{IEEE} Trans. Vis. Comput. Graphics"}
+
+
+
+cybernetics, ergonomics, robots, man-machine, and automation
+@STRING{IEEE_J_ASE        = "{IEEE} Trans. Autom. Sci. Eng."}
+@STRING{IEEE_J_JRA        = "{IEEE} J. Robot. Autom."}
+@STRING{IEEE_J_HFE        = "{IEEE} Trans. Hum. Factors Electron."}
+@STRING{IEEE_J_MMS        = "{IEEE} Trans. Man-Mach. Syst."}
+@STRING{IEEE_J_PAMI       = "{IEEE} Trans. Pattern Anal. Mach. Intell."}
+in 1989 JRA became RA
+in August 2004, RA split into ASE and RO
+@STRING{IEEE_J_RA         = "{IEEE} Trans. Robot. Autom."}
+@STRING{IEEE_J_RO         = "{IEEE} Trans. Robot."}
+@STRING{IEEE_J_SMC        = "{IEEE} Trans. Syst., Man, Cybern."}
+@STRING{IEEE_J_SMCA       = "{IEEE} Trans. Syst., Man, Cybern. {A}"}
+@STRING{IEEE_J_SMCB       = "{IEEE} Trans. Syst., Man, Cybern. {B}"}
+@STRING{IEEE_J_SMCC       = "{IEEE} Trans. Syst., Man, Cybern. {C}"}
+@STRING{IEEE_J_SSC        = "{IEEE} Trans. Syst. Sci. Cybern."}
+
+
+
+earth, wind, fire and water
+@STRING{IEEE_J_GE         = "{IEEE} Trans. Geosci. Electron."}
+@STRING{IEEE_J_GRS        = "{IEEE} Trans. Geosci. Remote Sens."}
+@STRING{IEEE_J_GRSL       = "{IEEE} Geosci. Remote Sens. Lett."}
+@STRING{IEEE_J_OE         = "{IEEE} J. Ocean. Eng."}
+
+
+
+education, engineering, history, IEEE, professional
+disabled till definition is verified
+STRING{IEEE_J_CJECE       = "Canadian J. Elect. Comput. Eng."}
+@STRING{IEEE_J_PROC       = "Proc. {IEEE}"}
+@STRING{IEEE_J_EDU        = "{IEEE} Trans. Educ."}
+@STRING{IEEE_J_EM         = "{IEEE} Trans. Eng. Manag."}
+disabled till definition is verified
+STRING{IEEE_J_EWS         = "{IEEE} Trans. Eng. Writing Speech"}
+@STRING{IEEE_J_PC         = "{IEEE} Trans. Prof. Commun."}
+
+
+
+electromagnetics, antennas, EMI, magnetics and microwave
+@STRING{IEEE_J_AWPL       = "{IEEE} Antennas Wireless Propag. Lett."}
+@STRING{IEEE_J_MGWL       = "{IEEE} Microw. Guided Wave Lett."}
+IEEE seems to want "Compon." here, not "Comp."
+@STRING{IEEE_J_MWCL       = "{IEEE} Microw. Wireless Compon. Lett."}
+@STRING{IEEE_J_AP         = "{IEEE} Trans. Antennas Propag."}
+@STRING{IEEE_J_EMC        = "{IEEE} Trans. Electromagn. Compat."}
+@STRING{IEEE_J_MAG        = "{IEEE} Trans. Magn."}
+@STRING{IEEE_J_MTT        = "{IEEE} Trans. Microw. Theory Tech."}
+@STRING{IEEE_J_RFI        = "{IEEE} Trans. Radio Freq. Interference"}
+@STRING{IEEE_J_TJMJ       = "{IEEE} Transl. J. Magn. Jpn."}
+
+
+
+energy and power
+@STRING{IEEE_J_EC         = "{IEEE} Trans. Energy Convers."}
+@STRING{IEEE_J_PEL        = "{IEEE} Power Electron. Lett."}
+@STRING{IEEE_J_PWRAS      = "{IEEE} Trans. Power App. Syst."}
+@STRING{IEEE_J_PWRD       = "{IEEE} Trans. Power Del."}
+@STRING{IEEE_J_PWRE       = "{IEEE} Trans. Power Electron."}
+@STRING{IEEE_J_PWRS       = "{IEEE} Trans. Power Syst."}
+
+
+
+industrial, commercial and consumer
+@STRING{IEEE_J_APPIND     = "{IEEE} Trans. Appl. Ind."}
+@STRING{IEEE_J_BC         = "{IEEE} Trans. Broadcast."}
+disabled till definition is verified
+STRING{IEEE_J_BCTV        = "{IEEE} Trans. Broadcast Television Receivers"}
+@STRING{IEEE_J_CE         = "{IEEE} Trans. Consum. Electron."}
+@STRING{IEEE_J_IE         = "{IEEE} Trans. Ind. Electron."}
+@STRING{IEEE_J_IECI       = "{IEEE} Trans. Ind. Electron. Contr. Instrum."}
+@STRING{IEEE_J_IA         = "{IEEE} Trans. Ind. Appl."}
+@STRING{IEEE_J_IGA        = "{IEEE} Trans. Ind. Gen. Appl."}
+@STRING{IEEE_J_IINF       = "{IEEE} Trans. Ind. Informat."}
+@STRING{IEEE_J_PSE        = "{IEEE} J. Product Safety Eng."}
+
+
+
+instrumentation and measurement
+@STRING{IEEE_J_IM         = "{IEEE} Trans. Instrum. Meas."}
+
+
+
+insulation and materials
+@STRING{IEEE_J_JEM        = "{IEEE/TMS} J. Electron. Mater."}
+@STRING{IEEE_J_DEI        = "{IEEE} Trans. Dielectr. Electr. Insul."}
+@STRING{IEEE_J_EI         = "{IEEE} Trans. Electr. Insul."}
+
+
+
+mechanical
+@STRING{IEEE_J_MECH       = "{IEEE/ASME} Trans. Mechatronics"}
+@STRING{IEEE_J_MEMS       = "J. Microelectromech. Syst."}
+
+
+
+medical and biological
+@STRING{IEEE_J_BME        = "{IEEE} Trans. Biomed. Eng."}
+Note: The B-ME journal later dropped the hyphen and became the BME.
+@STRING{IEEE_J_B-ME       = "{IEEE} Trans. Bio-Med. Eng."}
+@STRING{IEEE_J_BMELC      = "{IEEE} Trans. Bio-Med. Electron."}
+disabled till definition is verified
+STRING{IEEE_J_CBB         = "{IEEE/ACM} Trans. Comput. Biology Bioinformatics"}
+@STRING{IEEE_J_ITBM       = "{IEEE} Trans. Inf. Technol. Biomed."}
+@STRING{IEEE_J_ME         = "{IEEE} Trans. Med. Electron."}
+@STRING{IEEE_J_MI         = "{IEEE} Trans. Med. Imag."}
+@STRING{IEEE_J_NB         = "{IEEE} Trans. Nanobiosci."}
+@STRING{IEEE_J_NSRE       = "{IEEE} Trans. Neural Syst. Rehabil. Eng."}
+@STRING{IEEE_J_RE         = "{IEEE} Trans. Rehabil. Eng."}
+
+
+
+ optics, lightwave and photonics
+@STRING{IEEE_J_PTL        = "{IEEE} Photon. Technol. Lett."}
+@STRING{IEEE_J_JLT        = "J. Lightw. Technol."}
+
+
+
+physics, electrons, nanotechnology, nuclear and quantum electronics
+@STRING{IEEE_J_EDL        = "{IEEE} Electron Device Lett."}
+@STRING{IEEE_J_JQE        = "{IEEE} J. Quantum Electron."}
+@STRING{IEEE_J_JSTQE      = "{IEEE} J. Sel. Topics Quantum Electron."}
+@STRING{IEEE_J_ED         = "{IEEE} Trans. Electron Devices"}
+@STRING{IEEE_J_NANO       = "{IEEE} Trans. Nanotechnol."}
+@STRING{IEEE_J_NS         = "{IEEE} Trans. Nucl. Sci."}
+@STRING{IEEE_J_PS         = "{IEEE} Trans. Plasma Sci."}
+
+
+
+reliability
+IEEE seems to want "Mat." here, not "Mater."
+@STRING{IEEE_J_DMR        = "{IEEE} Trans. Device Mater. Rel."}
+@STRING{IEEE_J_R          = "{IEEE} Trans. Rel."}
+
+
+
+semiconductors, superconductors, electrochemical and solid state
+@STRING{IEEE_J_ESSL       = "{IEEE/ECS} Electrochem. Solid-State Lett."}
+@STRING{IEEE_J_JSSC       = "{IEEE} J. Solid-State Circuits"}
+@STRING{IEEE_J_ASC        = "{IEEE} Trans. Appl. Supercond."}
+@STRING{IEEE_J_SM         = "{IEEE} Trans. Semicond. Manuf."}
+
+
+
+sensors
+@STRING{IEEE_J_SENSOR     = "{IEEE} Sensors J."}
+
+
+
+VLSI
+@STRING{IEEE_J_VLSI       = "{IEEE} Trans. {VLSI} Syst."}
+
+
+
+
+
+
+IEEE Magazines 
+
+
+
+@STRING{IEEE_M_AES        = "{IEEE} Aerosp. Electron. Syst. Mag."}
+@STRING{IEEE_M_HIST       = "{IEEE} Ann. Hist. Comput."}
+@STRING{IEEE_M_AP         = "{IEEE} Antennas Propag. Mag."}
+@STRING{IEEE_M_ASSP       = "{IEEE} {ASSP} Mag."}
+@STRING{IEEE_M_CD         = "{IEEE} Circuits Devices Mag."}
+@STRING{IEEE_M_CAS        = "{IEEE} Circuits Syst. Mag."}
+@STRING{IEEE_M_COM        = "{IEEE} Commun. Mag."}
+@STRING{IEEE_M_COMSOC     = "{IEEE} Commun. Soc. Mag."}
+@STRING{IEEE_M_CIM        = "{IEEE} Comput. Intell. Mag."}
+CSEM changed to CSE in 1999
+@STRING{IEEE_M_CSE        = "{IEEE} Comput. Sci. Eng."}
+@STRING{IEEE_M_CSEM       = "{IEEE} Comput. Sci. Eng. Mag."}
+@STRING{IEEE_M_C          = "{IEEE} Computer"}
+@STRING{IEEE_M_CAP        = "{IEEE} Comput. Appl. Power"}
+@STRING{IEEE_M_CGA        = "{IEEE} Comput. Graph. Appl."}
+@STRING{IEEE_M_CONC       = "{IEEE} Concurrency"}
+@STRING{IEEE_M_CS         = "{IEEE} Control Syst. Mag."}
+@STRING{IEEE_M_DTC        = "{IEEE} Des. Test. Comput."}
+@STRING{IEEE_M_EI         = "{IEEE} Electr. Insul. Mag."}
+@STRING{IEEE_M_ETR        = "{IEEE} ElectroTechnol. Rev."}
+@STRING{IEEE_M_EMB        = "{IEEE} Eng. Med. Biol. Mag."}
+@STRING{IEEE_M_EMR        = "{IEEE} Eng. Manag. Rev."}
+@STRING{IEEE_M_EXP        = "{IEEE} Expert"}
+@STRING{IEEE_M_IA         = "{IEEE} Ind. Appl. Mag."}
+@STRING{IEEE_M_IM         = "{IEEE} Instrum. Meas. Mag."}
+@STRING{IEEE_M_IS         = "{IEEE} Intell. Syst."}
+@STRING{IEEE_M_IC         = "{IEEE} Internet Comput."}
+@STRING{IEEE_M_ITP        = "{IEEE} {IT} Prof."}
+@STRING{IEEE_M_MICRO      = "{IEEE} Micro"}
+@STRING{IEEE_M_MW         = "{IEEE} Microw. Mag."}
+@STRING{IEEE_M_MM         = "{IEEE} Multimedia"}
+@STRING{IEEE_M_NET        = "{IEEE} Netw."}
+IEEE's editorial manual lists "Pers. Commun.", 
+but "Personal Commun. Mag." seems to be what is used in the journals
+@STRING{IEEE_M_PCOM       = "{IEEE} Personal Commun. Mag."}
+@STRING{IEEE_M_POT        = "{IEEE} Potentials"}
+CAP and PER merged to form PE in 2003
+@STRING{IEEE_M_PE         = "{IEEE} Power Energy Mag."}
+@STRING{IEEE_M_PER        = "{IEEE} Power Eng. Rev."}
+@STRING{IEEE_M_PVC        = "{IEEE} Pervasive Comput."}
+@STRING{IEEE_M_RA         = "{IEEE} Robot. Autom. Mag."}
+@STRING{IEEE_M_SAP        = "{IEEE} Security Privacy"}
+@STRING{IEEE_M_SP         = "{IEEE} Signal Process. Mag."}
+@STRING{IEEE_M_S          = "{IEEE} Softw."}
+@STRING{IEEE_M_SPECT      = "{IEEE} Spectr."}
+@STRING{IEEE_M_TS         = "{IEEE} Technol. Soc. Mag."}
+@STRING{IEEE_M_VT         = "{IEEE} Veh. Technol. Mag."}
+@STRING{IEEE_M_WC         = "{IEEE} Wireless Commun. Mag."}
+@STRING{IEEE_M_TODAY      = "Today's Engineer"}
+
+
+
+
+
+
+IEEE Online Publications 
+
+
+
+@STRING{IEEE_O_CSTO        = "{IEEE} Commun. Surveys Tuts."}
+disabled till definition is verified
+STRING{IEEE_O_DSO          = "{IEEE} Distrib. Syst. Online"}
+
+
+
+
+
+--
+EOF

bibliography/IEEEfull.bib

@@ -0,0 +1,419 @@
+
+IEEEfull.bib
+V1.12 (2007/01/11)
+Copyright (c) 2002-2007 by Michael Shell
+See: http://www.michaelshell.org/
+for current contact information.
+
+BibTeX bibliography string definitions of the FULL titles of
+IEEE journals and magazines and online publications.
+
+This file is designed for bibliography styles that require 
+full-length titles and is not for use in bibliographies that
+abbreviate titles.
+
+Support sites:
+http://www.michaelshell.org/tex/ieeetran/
+http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
+and/or
+http://www.ieee.org/
+
+Special thanks to Laura Hyslop and ken Rawson of IEEE for their help
+in obtaining the information needed to compile this file. Also,
+Volker Kuhlmann and Moritz Borgmann kindly provided some corrections
+and additions.
+
+*************************************************************************
+Legal Notice:
+This code is offered as-is without any warranty either expressed or
+implied; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE! 
+User assumes all risk.
+In no event shall IEEE or any contributor to this code be liable for
+any damages or losses, including, but not limited to, incidental,
+consequential, or any other damages, resulting from the use or misuse
+of any information contained here.
+
+All comments are the opinions of their respective authors and are not
+necessarily endorsed by the IEEE.
+
+This work is distributed under the LaTeX Project Public License (LPPL)
+( http://www.latex-project.org/ ) version 1.3, and may be freely used,
+distributed and modified. A copy of the LPPL, version 1.3, is included
+in the base LaTeX documentation of all distributions of LaTeX released
+2003/12/01 or later.
+Retain all contribution notices and credits.
+** Modified files should be clearly indicated as such, including  **
+** renaming them and changing author support contact information. **
+
+File list of work: IEEEabrv.bib, IEEEfull.bib, IEEEexample.bib,
+                   IEEEtran.bst, IEEEtranS.bst, IEEEtranSA.bst,
+                   IEEEtranN.bst, IEEEtranSN.bst, IEEEtran_bst_HOWTO.pdf
+*************************************************************************
+
+
+USAGE:
+
+\bibliographystyle{mybstfile}
+\bibliography{IEEEfull,mybibfile}
+
+where the IEEE titles in the .bib database entries use the strings
+defined here. e.g.,
+
+
+   journal = IEEE_J_AC,
+
+
+to yield "{IEEE} Transactions on Automatic Control"
+
+
+WARNING: IEEE uses abbreviated journal titles in their bibliographies!
+Because this file provides the full titles, you should NOT use this file
+for work that is to be submitted to the IEEE.
+
+For IEEE work, you should use the abbreviated titles provided in the
+companion file, IEEEabrv.bib.
+
+
+** NOTES **
+
+ 1. Journals have been grouped according to subject in order to make it
+    easier to locate and extract the definitions for related journals - 
+    as most works use references that are confined to a single topic.
+    Magazines are listed in straight alphabetical order.
+
+ 2. String names are closely based on IEEE's own internal acronyms.
+
+ 3. Older, out-of-print IEEE titles are included (but not including titles
+    dating prior to IEEE's formation from the IRE and AIEE in 1963).
+
+
+
+
+
+
+IEEE Journals 
+
+
+
+aerospace and military
+@STRING{IEEE_J_AES        = "{IEEE} Transactions on Aerospace and Electronic Systems"}
+@STRING{IEEE_J_ANE        = "{IEEE} Transactions on Aerospace and Navigational Electronics"}
+@STRING{IEEE_J_ANNE       = "{IEEE} Transactions on Aeronautical and Navigational Electronics"}
+@STRING{IEEE_J_AS         = "{IEEE} Transactions on Aerospace"}
+@STRING{IEEE_J_AIRE       = "{IEEE} Transactions on Airborne Electronics"}
+@STRING{IEEE_J_MIL        = "{IEEE} Transactions on Military Electronics"}
+
+
+
+autos, transportation and vehicles (non-aerospace)
+@STRING{IEEE_J_ITS        = "{IEEE} Transactions on Intelligent Transportation Systems"}
+@STRING{IEEE_J_VT         = "{IEEE} Transactions on Vehicular Technology"}
+@STRING{IEEE_J_VC         = "{IEEE} Transactions on Vehicular Communications"}
+
+
+
+circuits, signals, systems, audio and controls
+@STRING{IEEE_J_SPL        = "{IEEE} Signal Processing Letters"}
+@STRING{IEEE_J_ASSP       = "{IEEE} Transactions on Acoustics, Speech, and Signal Processing"}
+@STRING{IEEE_J_AU         = "{IEEE} Transactions on Audio"}
+@STRING{IEEE_J_AUEA       = "{IEEE} Transactions on Audio and Electroacoustics"}
+@STRING{IEEE_J_AC         = "{IEEE} Transactions on Automatic Control"}
+@STRING{IEEE_J_CAS        = "{IEEE} Transactions on Circuits and Systems"}
+@STRING{IEEE_J_CASVT      = "{IEEE} Transactions on Circuits and Systems for Video Technology"}
+@STRING{IEEE_J_CASI       = "{IEEE} Transactions on Circuits and Systems---Part {I}: Fundamental Theory and Applications"}
+@STRING{IEEE_J_CASII      = "{IEEE} Transactions on Circuits and Systems---Part {II}: Analog and Digital Signal Processing"}
+in 2004 CASI and CASII renamed part title to CASI_RP and CASII_EB, respectively.
+@STRING{IEEE_J_CASI_RP    = "{IEEE} Transactions on Circuits and Systems---Part {I}: Regular Papers"}
+@STRING{IEEE_J_CASII_EB   = "{IEEE} Transactions on Circuits and Systems---Part {II}: Express Briefs"}
+@STRING{IEEE_J_CT         = "{IEEE} Transactions on Circuit Theory"}
+@STRING{IEEE_J_CST        = "{IEEE} Transactions on Control Systems Technology"}
+@STRING{IEEE_J_SP         = "{IEEE} Transactions on Signal Processing"}
+@STRING{IEEE_J_SU         = "{IEEE} Transactions on Sonics and Ultrasonics"}
+@STRING{IEEE_J_SAP        = "{IEEE} Transactions on Speech and Audio Processing"}
+@STRING{IEEE_J_UE         = "{IEEE} Transactions on Ultrasonics Engineering"}
+@STRING{IEEE_J_UFFC       = "{IEEE} Transactions on Ultrasonics, Ferroelectrics, and Frequency Control"}
+
+
+
+communications
+@STRING{IEEE_J_COML       = "{IEEE} Communications Letters"}
+@STRING{IEEE_J_JSAC       = "{IEEE} Journal on Selected Areas in Communications"}
+@STRING{IEEE_J_COM        = "{IEEE} Transactions on Communications"}
+@STRING{IEEE_J_COMT       = "{IEEE} Transactions on Communication Technology"}
+@STRING{IEEE_J_WCOM       = "{IEEE} Transactions on Wireless Communications"}
+
+
+
+components, packaging and manufacturing
+@STRING{IEEE_J_ADVP       = "{IEEE} Transactions on Advanced Packaging"}
+@STRING{IEEE_J_CHMT       = "{IEEE} Transactions on Components, Hybrids and Manufacturing Technology"}
+@STRING{IEEE_J_CPMTA      = "{IEEE} Transactions on Components, Packaging and Manufacturing Technology---Part {A}"}
+@STRING{IEEE_J_CPMTB      = "{IEEE} Transactions on Components, Packaging and Manufacturing Technology---Part {B}: Advanced Packaging"}
+@STRING{IEEE_J_CPMTC      = "{IEEE} Transactions on Components, Packaging and Manufacturing Technology---Part {C}: Manufacturing"}
+@STRING{IEEE_J_CAPT       = "{IEEE} Transactions on Components and Packaging Technology"}
+@STRING{IEEE_J_CAPTS      = "{IEEE} Transactions on Components and Packaging Technologies"}
+@STRING{IEEE_J_CPART      = "{IEEE} Transactions on Component Parts"}
+@STRING{IEEE_J_EPM        = "{IEEE} Transactions on Electronics Packaging Manufacturing"}
+@STRING{IEEE_J_MFT        = "{IEEE} Transactions on Manufacturing Technology"}
+@STRING{IEEE_J_PHP        = "{IEEE} Transactions on Parts, Hybrids and Packaging"}
+@STRING{IEEE_J_PMP        = "{IEEE} Transactions on Parts, Materials and Packaging"}
+
+
+
+CAD
+@STRING{IEEE_J_TCAD       = "{IEEE} Journal on Technology in Computer Aided Design"}
+@STRING{IEEE_J_CAD        = "{IEEE} Transactions on Computer-Aided Design of Integrated Circuits and Systems"}
+
+
+
+coding, data, information, knowledge
+@STRING{IEEE_J_IT         = "{IEEE} Transactions on Information Theory"}
+@STRING{IEEE_J_KDE        = "{IEEE} Transactions on Knowledge and Data Engineering"}
+
+
+
+computers, computation, networking and software
+@STRING{IEEE_J_C          = "{IEEE} Transactions on Computers"}
+@STRING{IEEE_J_CAL        = "{IEEE} Computer Architecture Letters"}
+@STRING{IEEE_J_DSC        = "{IEEE} Transactions on Dependable and Secure Computing"}
+@STRING{IEEE_J_ECOMP      = "{IEEE} Transactions on Electronic Computers"}
+@STRING{IEEE_J_EVC        = "{IEEE} Transactions on Evolutionary Computation"}
+@STRING{IEEE_J_FUZZ       = "{IEEE} Transactions on Fuzzy Systems"}
+@STRING{IEEE_J_IFS        = "{IEEE} Transactions on Information Forensics and Security"}
+@STRING{IEEE_J_MC         = "{IEEE} Transactions on Mobile Computing"}
+@STRING{IEEE_J_NET        = "{IEEE/ACM} Transactions on Networking"}
+@STRING{IEEE_J_NN         = "{IEEE} Transactions on Neural Networks"}
+@STRING{IEEE_J_PDS        = "{IEEE} Transactions on Parallel and Distributed Systems"}
+@STRING{IEEE_J_SE         = "{IEEE} Transactions on Software Engineering"}
+
+
+
+computer graphics, imaging, and multimedia
+@STRING{IEEE_J_JDT        = "{IEEE/OSA} Journal of Display Technology"}
+@STRING{IEEE_J_IP         = "{IEEE} Transactions on Image Processing"}
+@STRING{IEEE_J_MM         = "{IEEE} Transactions on Multimedia"}
+@STRING{IEEE_J_VCG        = "{IEEE} Transactions on Visualization and Computer Graphics"}
+
+
+
+cybernetics, ergonomics, robots, man-machine, and automation
+@STRING{IEEE_J_ASE        = "{IEEE} Transactions on Automation Science and Engineering"}
+@STRING{IEEE_J_JRA        = "{IEEE} Journal of Robotics and Automation"}
+@STRING{IEEE_J_HFE        = "{IEEE} Transactions on Human Factors in Electronics"}
+@STRING{IEEE_J_MMS        = "{IEEE} Transactions on Man-Machine Systems"}
+@STRING{IEEE_J_PAMI       = "{IEEE} Transactions on Pattern Analysis and Machine Intelligence"}
+in 1989 JRA became RA
+in August 2004, RA split into ASE and RO
+@STRING{IEEE_J_RA         = "{IEEE} Transactions on Robotics and Automation"}
+@STRING{IEEE_J_RO         = "{IEEE} Transactions on Robotics"}
+@STRING{IEEE_J_SMC        = "{IEEE} Transactions on Systems, Man, and Cybernetics"}
+@STRING{IEEE_J_SMCA       = "{IEEE} Transactions on Systems, Man, and Cybernetics---Part {A}: Systems and Humans"}
+@STRING{IEEE_J_SMCB       = "{IEEE} Transactions on Systems, Man, and Cybernetics---Part {B}: Cybernetics"}
+@STRING{IEEE_J_SMCC       = "{IEEE} Transactions on Systems, Man, and Cybernetics---Part {C}: Applications and Reviews"}
+@STRING{IEEE_J_SSC        = "{IEEE} Transactions on Systems Science and Cybernetics"}
+
+
+
+earth, wind, fire and water
+@STRING{IEEE_J_GE         = "{IEEE} Transactions on Geoscience Electronics"}
+@STRING{IEEE_J_GRS        = "{IEEE} Transactions on Geoscience and Remote Sensing"}
+@STRING{IEEE_J_GRSL       = "{IEEE} Geoscience and Remote Sensing Letters"}
+@STRING{IEEE_J_OE         = "{IEEE} Journal of Oceanic Engineering"}
+
+
+
+education, engineering, history, IEEE, professional
+@STRING{IEEE_J_CJECE      = "Canadian Journal of Electrical and Computer Engineering"}
+@STRING{IEEE_J_PROC       = "Proceedings of the {IEEE}"}
+@STRING{IEEE_J_EDU        = "{IEEE} Transactions on Education"}
+@STRING{IEEE_J_EM         = "{IEEE} Transactions on Engineering Management"}
+@STRING{IEEE_J_EWS        = "{IEEE} Transactions on Engineering Writing and Speech"}
+@STRING{IEEE_J_PC         = "{IEEE} Transactions on Professional Communication"}
+
+
+
+electromagnetics, antennas, EMI, magnetics and microwave
+@STRING{IEEE_J_AWPL       = "{IEEE} Antennas and Wireless Propagation Letters"}
+@STRING{IEEE_J_MGWL       = "{IEEE} Microwave and Guided Wave Letters"}
+@STRING{IEEE_J_MWCL       = "{IEEE} Microwave and Wireless Components Letters"}
+@STRING{IEEE_J_AP         = "{IEEE} Transactions on Antennas and Propagation"}
+@STRING{IEEE_J_EMC        = "{IEEE} Transactions on Electromagnetic Compatibility"}
+@STRING{IEEE_J_MAG        = "{IEEE} Transactions on Magnetics"}
+@STRING{IEEE_J_MTT        = "{IEEE} Transactions on Microwave Theory and Techniques"}
+@STRING{IEEE_J_RFI        = "{IEEE} Transactions on Radio Frequency Interference"}
+@STRING{IEEE_J_TJMJ       = "{IEEE} Translation Journal on Magnetics in Japan"}
+
+
+
+energy and power
+@STRING{IEEE_J_EC         = "{IEEE} Transactions on Energy Conversion"}
+@STRING{IEEE_J_PEL        = "{IEEE} Power Electronics Letters"}
+@STRING{IEEE_J_PWRAS      = "{IEEE} Transactions on Power Apparatus and Systems"}
+@STRING{IEEE_J_PWRD       = "{IEEE} Transactions on Power Delivery"}
+@STRING{IEEE_J_PWRE       = "{IEEE} Transactions on Power Electronics"}
+@STRING{IEEE_J_PWRS       = "{IEEE} Transactions on Power Systems"}
+
+
+
+industrial, commercial and consumer
+@STRING{IEEE_J_APPIND     = "{IEEE} Transactions on Applications and Industry"}
+@STRING{IEEE_J_BC         = "{IEEE} Transactions on Broadcasting"}
+@STRING{IEEE_J_BCTV       = "{IEEE} Transactions on Broadcast and Television Receivers"}
+@STRING{IEEE_J_CE         = "{IEEE} Transactions on Consumer Electronics"}
+@STRING{IEEE_J_IE         = "{IEEE} Transactions on Industrial Electronics"}
+@STRING{IEEE_J_IECI       = "{IEEE} Transactions on Industrial Electronics and Control Instrumentation"}
+@STRING{IEEE_J_IA         = "{IEEE} Transactions on Industry Applications"}
+@STRING{IEEE_J_IGA        = "{IEEE} Transactions on Industry and General Applications"}
+@STRING{IEEE_J_IINF       = "{IEEE} Transactions on Industrial Informatics"}
+@STRING{IEEE_J_PSE        = "{IEEE} Journal of Product Safety Engineering"}
+
+
+
+instrumentation and measurement
+@STRING{IEEE_J_IM         = "{IEEE} Transactions on Instrumentation and Measurement"}
+
+
+
+insulation and materials
+@STRING{IEEE_J_JEM        = "{IEEE/TMS} Journal of Electronic Materials"}
+@STRING{IEEE_J_DEI        = "{IEEE} Transactions on Dielectrics and Electrical Insulation"}
+@STRING{IEEE_J_EI         = "{IEEE} Transactions on Electrical Insulation"}
+
+
+
+mechanical
+@STRING{IEEE_J_MECH       = "{IEEE/ASME} Transactions on Mechatronics"}
+@STRING{IEEE_J_MEMS       = "{IEEE/ASME} Journal of Microelectromechanical Systems"}
+
+
+
+medical and biological
+@STRING{IEEE_J_BME        = "{IEEE} Transactions on Biomedical Engineering"}
+Note: The B-ME journal later dropped the hyphen and became the BME.
+@STRING{IEEE_J_B-ME       = "{IEEE} Transactions on Bio-Medical Engineering"}
+@STRING{IEEE_J_BMELC      = "{IEEE} Transactions on Bio-Medical Electronics"}
+@STRING{IEEE_J_CBB        = "{IEEE/ACM} Transactions on Computational Biology and Bioinformatics"}
+@STRING{IEEE_J_ITBM       = "{IEEE} Transactions on Information Technology in Biomedicine"}
+@STRING{IEEE_J_ME         = "{IEEE} Transactions on Medical Electronics"}
+@STRING{IEEE_J_MI         = "{IEEE} Transactions on Medical Imaging"}
+@STRING{IEEE_J_NB         = "{IEEE} Transactions on NanoBioscience"}
+@STRING{IEEE_J_NSRE       = "{IEEE} Transactions on Neural Systems and Rehabilitation Engineering"}
+@STRING{IEEE_J_RE         = "{IEEE} Transactions on Rehabilitation Engineering"}
+
+
+
+optics, lightwave and photonics
+@STRING{IEEE_J_PTL        = "{IEEE} Photonics Technology Letters"}
+@STRING{IEEE_J_JLT        = "{IEEE/OSA} Journal of Lightwave Technology"}
+
+
+
+physics, electrons, nanotechnology, nuclear and quantum electronics
+@STRING{IEEE_J_EDL        = "{IEEE} Electron Device Letters"}
+@STRING{IEEE_J_JQE        = "{IEEE} Journal of Quantum Electronics"}
+@STRING{IEEE_J_JSTQE      = "{IEEE} Journal of Selected Topics in Quantum Electronics"}
+@STRING{IEEE_J_ED         = "{IEEE} Transactions on Electron Devices"}
+@STRING{IEEE_J_NANO       = "{IEEE} Transactions on Nanotechnology"}
+@STRING{IEEE_J_NS         = "{IEEE} Transactions on Nuclear Science"}
+@STRING{IEEE_J_PS         = "{IEEE} Transactions on Plasma Science"}
+
+
+
+reliability
+@STRING{IEEE_J_DMR        = "{IEEE} Transactions on Device and Materials Reliability"}
+@STRING{IEEE_J_R          = "{IEEE} Transactions on Reliability"}
+
+
+
+semiconductors, superconductors, electrochemical and solid state
+@STRING{IEEE_J_ESSL       = "{IEEE/ECS} Electrochemical and Solid-State Letters"}
+@STRING{IEEE_J_JSSC       = "{IEEE} Journal of Solid-State Circuits"}
+@STRING{IEEE_J_ASC        = "{IEEE} Transactions on Applied Superconductivity"}
+@STRING{IEEE_J_SM         = "{IEEE} Transactions on Semiconductor Manufacturing"}
+
+
+
+sensors
+@STRING{IEEE_J_SENSOR     = "{IEEE} Sensors Journal"}
+
+
+
+VLSI
+@STRING{IEEE_J_VLSI       = "{IEEE} Transactions on Very Large Scale Integration ({VLSI}) Systems"}
+
+
+
+
+
+
+IEEE Magazines
+
+
+
+@STRING{IEEE_M_AES        = "{IEEE} Aerospace and Electronics Systems Magazine"}
+@STRING{IEEE_M_HIST       = "{IEEE} Annals of the History of Computing"}
+@STRING{IEEE_M_AP         = "{IEEE} Antennas and Propagation Magazine"}
+@STRING{IEEE_M_ASSP       = "{IEEE} {ASSP} Magazine"}
+@STRING{IEEE_M_CD         = "{IEEE} Circuits and Devices Magazine"}
+@STRING{IEEE_M_CAS        = "{IEEE} Circuits and Systems Magazine"}
+@STRING{IEEE_M_COM        = "{IEEE} Communications Magazine"}
+@STRING{IEEE_M_COMSOC     = "{IEEE} Communications Society Magazine"}
+@STRING{IEEE_M_CIM        = "{IEEE} Computational Intelligence Magazine"}
+CSEM changed to CSE in 1999
+@STRING{IEEE_M_CSE        = "{IEEE} Computing in Science and Engineering"}
+@STRING{IEEE_M_CSEM       = "{IEEE} Computational Science and Engineering Magazine"}
+@STRING{IEEE_M_C          = "{IEEE} Computer"}
+@STRING{IEEE_M_CAP        = "{IEEE} Computer Applications in Power"}
+@STRING{IEEE_M_CGA        = "{IEEE} Computer Graphics and Applications"}
+@STRING{IEEE_M_CONC       = "{IEEE} Concurrency"}
+@STRING{IEEE_M_CS         = "{IEEE} Control Systems Magazine"}
+@STRING{IEEE_M_DTC        = "{IEEE} Design and Test of Computers"}
+@STRING{IEEE_M_EI         = "{IEEE} Electrical Insulation Magazine"}
+@STRING{IEEE_M_ETR        = "{IEEE} ElectroTechnology Review"}
+@STRING{IEEE_M_EMB        = "{IEEE} Engineering in Medicine and Biology Magazine"}
+@STRING{IEEE_M_EMR        = "{IEEE} Engineering Management Review"}
+@STRING{IEEE_M_EXP        = "{IEEE} Expert"}
+@STRING{IEEE_M_IA         = "{IEEE} Industry Applications Magazine"}
+@STRING{IEEE_M_IM         = "{IEEE} Instrumentation and Measurement Magazine"}
+@STRING{IEEE_M_IS         = "{IEEE} Intelligent Systems"}
+@STRING{IEEE_M_IC         = "{IEEE} Internet Computing"}
+@STRING{IEEE_M_ITP        = "{IEEE} {IT} Professional"}
+@STRING{IEEE_M_MICRO      = "{IEEE} Micro"}
+@STRING{IEEE_M_MW         = "{IEEE} Microwave Magazine"}
+@STRING{IEEE_M_MM         = "{IEEE} Multimedia"}
+@STRING{IEEE_M_NET        = "{IEEE} Network"}
+@STRING{IEEE_M_PCOM       = "{IEEE} Personal Communications Magazine"}
+@STRING{IEEE_M_POT        = "{IEEE} Potentials"}
+CAP and PER merged to form PE in 2003
+@STRING{IEEE_M_PE         = "{IEEE} Power and Energy Magazine"}
+@STRING{IEEE_M_PER        = "{IEEE} Power Engineering Review"}
+@STRING{IEEE_M_PVC        = "{IEEE} Pervasive Computing"}
+@STRING{IEEE_M_RA         = "{IEEE} Robotics and Automation Magazine"}
+@STRING{IEEE_M_SAP        = "{IEEE} Security and Privacy"}
+@STRING{IEEE_M_SP         = "{IEEE} Signal Processing Magazine"}
+@STRING{IEEE_M_S          = "{IEEE} Software"}
+@STRING{IEEE_M_SPECT      = "{IEEE} Spectrum"}
+@STRING{IEEE_M_TS         = "{IEEE} Technology and Society Magazine"}
+@STRING{IEEE_M_VT         = "{IEEE} Vehicular Technology Magazine"}
+@STRING{IEEE_M_WC         = "{IEEE} Wireless Communications Magazine"}
+@STRING{IEEE_M_TODAY      = "Today's Engineer"}
+
+
+
+
+
+
+IEEE Online Publications 
+
+
+
+@STRING{IEEE_O_CSTO        = "{IEEE} Communications Surveys and Tutorials"}
+@STRING{IEEE_O_DSO         = "{IEEE} Distributed Systems Online"}
+
+
+
+
+
+--
+EOF

bibliography/README

@@ -0,0 +1,141 @@
+
+January 11, 2007
+
+
+IEEEtran.bst is the official BibTeX style for authors of the Institute of
+Electrical and Electronics Engineers (IEEE) Transactions journals and
+conferences.
+
+It also may have applications for other academic work such as theses and
+technical reports. The alphanumeric and natbib variants extend the
+applicability of the IEEEtran bibstyle family to the natural sciences
+and beyond.
+
+The IEEEtran bibstyle is a very comprehensive BibTeX style which provides
+many features beyond the standard BibTeX styles, including full support
+for references of online documents, patents, periodicals and standards.
+See the provided user manual for detailed usage information.
+
+The latest version of the IEEEtran BibTeX style can be found at CTAN:
+
+http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/bibtex/
+
+as well as within IEEE's site:
+
+http://www.ieee.org/
+
+Note that the packages at IEEE's site do not contain the natbib and
+alphanumeric variants (e.g., IEEEtranN.bst, etc.) as these are not used
+for IEEE related work. These files can be obtained on CTAN.
+
+For helpful tips, answers to frequently asked questions and other support,
+visit the IEEEtran home page at my website:
+
+http://www.michaelshell.org/tex/ieeetran/
+
+
+Enjoy!
+
+Michael Shell
+http://www.michaelshell.org/
+
+*******
+Version 1.12 (2007/01/11) changes:
+
+ 1. Fixed bug with unwanted comma before "et al." when an entry contained
+    more than two author names. Thanks to Pallav Gupta for reporting this.
+
+ 2. Fixed bug with anomalous closing quote in tech reports that have a
+    type, but without a number or address. Thanks to Mehrdad Mirreza for
+    reporting this.
+
+ 3. Use braces in \providecommand in begin.bib to better support
+    latex2html. TeX style length assignments OK with recent versions
+    of latex2html - 1.71 (2002/2/1) or later is strongly recommended.
+    Use of the language field still causes trouble with latex2html.
+    Thanks to Federico Beffa for reporting this.
+
+ 4. Added IEEEtran.bst ID and version comment string to .bbl output.
+
+ 5. Provide a \BIBdecl hook that allows the user to execute commands
+    just prior to the first entry.
+
+ 6. Use default urlstyle (is using url.sty) of "same" rather than rm to
+    better work with a wider variety of bibliography styles.
+
+ 7. Changed month abbreviations from Sept., July and June to Sep., Jul.,
+    and Jun., respectively, as IEEE now does. Thanks to Moritz Borgmann
+    for reporting this.
+
+ 8. Control entry types should not be considered when calculating longest
+    label width.
+
+ 9. Added alias www for electronic/online.
+
+10. Updated full and abbreviated journal name string definitions in
+    IEEEfull.bib and IEEEabrv.bib.
+
+11. New IEEEtranSA.bst, IEEEtranN.bst, and IEEEtranSN.bst variants for
+    alphanumeric citation tags and natbib compatibility.
+
+
+********************************** Files **********************************
+
+README                 - This file.
+
+IEEEtran_bst_HOWTO.pdf - The user manual.
+
+IEEEtran.bst           - The standard IEEEtran BibTeX style file. For use
+                         with IEEE work.
+
+IEEEtranS.bst          - A version of IEEEtran.bst that sorts the entries.
+                         Some IEEE conferences/publications may use/allow
+                         sorted bibliographies.
+
+IEEEtranSA.bst         - Like IEEEtranS.bst, but with alphanumeric citation
+                         tags like alpha.bst. Not for normal IEEE use.
+
+IEEEtranN.bst          - Like IEEEtran.bst, but based on plainnat.bst and
+                         is compatible with Patrick W. Daly's natbib
+                         package. Not for normal IEEE use.
+
+IEEEtranSN.bst         - Sorting version of IEEEtranN.bst. Not for normal
+                         IEEE use
+
+IEEEexample.bib        - An example BibTeX database that contains the
+                         references shown in the user manual.
+
+IEEEabrv.bib           - String definitions for the abbreviated names of
+                         IEEE journals. (For use with IEEE work.)
+                         
+IEEEfull.bib           - String definitions for the full names of IEEE
+                         journals. (Do not use for IEEE work.)
+
+***************************************************************************
+Legal Notice:
+This code is offered as-is without any warranty either expressed or
+implied; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE! 
+User assumes all risk.
+In no event shall IEEE or any contributor to this code be liable for
+any damages or losses, including, but not limited to, incidental,
+consequential, or any other damages, resulting from the use or misuse
+of any information contained here.
+
+All comments are the opinions of their respective authors and are not
+necessarily endorsed by the IEEE.
+
+This work is distributed under the LaTeX Project Public License (LPPL)
+( http://www.latex-project.org/ ) version 1.3, and may be freely used,
+distributed and modified. A copy of the LPPL, version 1.3, is included
+in the base LaTeX documentation of all distributions of LaTeX released
+2003/12/01 or later.
+Retain all contribution notices and credits.
+** Modified files should be clearly indicated as such, including  **
+** renaming them and changing author support contact information. **
+
+File list of work: IEEEtran_bst_HOWTO.pdf, IEEEtran.bst, IEEEtranS.bst,
+                   IEEEtranSA.bst, IEEEtranN.bst, IEEEtranSN.bst,
+                   IEEEexample.bib, IEEEabrv.bib, IEEEfull.bib
+                   
+***************************************************************************

bibliography/Reference.bib

@@ -0,0 +1,538 @@
+%% === assembly line optimization ===
+@article{ayob_optimization_2007,
+	title = {The optimisation of the single surface mount device placement machine in printed circuit board assembly: a survey},
+	pages = {553--569},
+	number = {6},
+	journal = {Int. J. Syst. Sci.},
+	author = {Ayob, Masri and Kendall, Graham},
+	volume = {40},
+	year = {2007},
+	month = {Apr.},
+}
+
+@article{kulak_ga-based_2008,
+	title = {A {GA}-based solution approach for balancing printed circuit board assembly lines},
+	volume = {30},
+	pages = {469--491},
+	number = {3},
+	journal = {OR Spectrum},
+	author = {Kulak, Osman and Yilmaz, Ihsan Onur and G\"{u}nther, Hans-Otto},
+	year = {2008},
+	month = {Jun.},
+}
+
+@article{rong_modeling_2011,
+	title = {Modeling the machine configuration and line-balancing problem of a {PCB} assembly line with modular placement machines},
+	volume = {54},
+	pages = {349--360},
+	number = {1},
+	journal = {Int. J. Adv. Manuf. Tech.},
+	author = {Rong, Aiying and T\'{o}th, Attila and Nevalainen, Olli S. and Knuutila, Timo and Lahdelma, Risto},
+    year = {2011},
+	month = {Apr.}
+}
+
+@article{kodek_optimal_2004,
+	title = {Optimal algorithm for minimizing production cycle time of a printed circuit board assembly line},
+	volume = {42},
+	pages = {5031--5048},
+	number = {23},
+	journal = {Int. J. Prod. Res.},
+	author = {Kodek, D. M. and Krisper, M.},
+    year = {2004},
+	month = {Dec.}
+}
+
+@article{toth_reconfiguring_2010,
+	title = {Reconfiguring flexible machine modules of a {PCB} assembly line},
+	volume = {4},
+	pages = {85--94},
+	number = {1},
+	journal = {Prod. Eng.},
+	author = {T\'{o}th, Attila and Knuutila, Timo and Nevalainen, Olli S.},
+	year = {2010},
+	month = {Feb.},
+}
+
+@article{toth_machine_2018,
+	title = {Machine configuration and workload balancing of modular placement machines in multi-product {PCB} assembly},
+	volume = {31},
+	pages = {815--830},
+	number = {9},
+	journal = {Int. J. Comput. Integ. M.},
+	author = {T\'{o}th, Attila and Knuutila, Timo and Nevalainen, Olli S.},
+	year = {2018},
+	month = {Sep.},
+}
+
+@article{hu_fuzzy_2017,
+	title = {Fuzzy goal programming technique for solving flexible assignment problem in {PCB} assembly line},
+	volume = {38},
+	pages = {423--442},
+	number = {3},
+	journal = {J. Inform. Optim. Sci.},
+	author = {Hu, Kuo-Jen},
+	year = {2017},
+	month = {May.},
+}
+
+@article{emet_workload_2010,
+	title = {Workload balancing in printed circuit board assembly},
+	volume = {50},
+	pages = {1175--1182},
+	number = {9},
+	journal = {Int. J. Adv. Manuf. Tech.},
+	author = {Emet, Stefan and Knuutila, Timo and Alhoniemi, Esa and Maier, Michael and Johnsson, Mika and Nevalainen, Olli S.},
+	year = {2010},
+}
+
+
+@article{lin_component_1999,
+	title = {Component partitioning under demand and capacity uncertainty in printed circuit board assembly},
+	pages = {159--176},
+	author = {Lin, Wei-Liang and Tardif, Valerie},
+	year = {1999},
+	volume = {11},
+	journal = {Int. J. Flex. Manu. Sys.}
+}
+
+@article{hillier_cost_2001,
+	title = {Cost minimization and workload balancing in printed circuit board assembly},
+	volume = {33},
+	pages = {547--557},
+	number = {7},
+	journal = {IIE Trans.},
+	author = {Hillier, Mark S. and Brandeau, Margaret L.},
+	year = {2001},
+	month = {Jul.}
+}
+
+@article{guo_integrated_2012,
+	title = {An integrated allocation method for the {PCB} assembly line balancing problem with nozzle changes},
+	volume = {62},
+	pages = {351--369},
+	number = {1},
+	journal = {Int. J. Adv. Manuf. Tech.},
+	author = {Guo, Shujuan and Takahashi, Katsuhiko and Morikawa, Katsumi and Jin, Zhihong},
+	year = {2012},
+	month = {Sep.},
+}
+
+@article{mumtaz_multi-level_2019,
+	title = {Multi-level planning and scheduling for parallel {PCB} assembly lines using hybrid spider monkey optimization approach},
+	volume = {7},
+	pages = {18685--18700},
+	journal = {{IEEE} Access},
+	author = {Mumtaz, Jabir and Guan, Zailin and Yue, Lei and Wang, Zhengya and Ullah, Saif and Rauf, Mudassar},
+	year = {2019},
+	month = {Dec.}
+}
+
+@inproceedings{zhong_multi-objective_2022,
+	title = {A Multi-Objective Scheduling Optimization Method for {PCB} Assembly Lines Based on the Improved Spider Monkey Algorithm},
+	eventtitle = {International Conference on Advances in Mechanical Engineering},
+	pages = {15},
+	booktitle = {the 2nd ICAME},
+	publisher = {MDPI},
+	author = {Zhong, Jingyan and Chen, Yarong and Mumtaz, Jabir},
+	urldate = {2025-03-03},
+	year = {2022},
+}
+
+@article{mumtaz_hybrid_2020,
+	title = {Hybrid spider monkey optimisation algorithm for multi-level planning and scheduling problems of assembly lines},
+	volume = {58},
+	pages = {6252--6267},
+	number = {20},
+	journal = {Int. J. Prod. Res.},
+	author = {Mumtaz, Jabir and Guan, Zailin and Yue, Lei and Zhang, Li and He, Cong},
+	year = {2020},
+	month = {Oct.},
+}
+
+@article{koskinen_rolling_2019,
+	title = {Rolling horizon production scheduling of multi-model {PCBs} for several assembly lines},
+	volume = {58},
+	pages = {1052--1073},
+	journal = {Int. J. Prod. Res.},
+	author = {Koskinen, Jani and Raduly-Baka, Csaba and Johnsson, Mika and S. Nevalainen, Olli},
+	year = {2019},
+	month = {Apr.},
+}
+
+@inproceedings{he_heuristic_2017,
+	booktitle = {FAIM2017},
+	title = {A heuristic algorithm to balance workloads of high-speed {SMT} machines in a {PCB} assembly line},
+	volume = {11},
+	author = {He, Tian and Li, Debiao and Yoon, Sang Won},
+	year = {2017},
+	pages = {1790--1797},
+}
+
+@article{wu_solution_2010,
+	title = {A solution method for the component allocation problem in printed circuit board assembly},
+	volume = {30},
+	pages = {155--163},
+	number = {2},
+	journal = {Assembly Autom.},
+	author = {Wu, Yongzhong and Ji, Ping},
+	year = {2010},
+	month = {Apr.},
+}
+
+
+@article{toth_divide_2022,
+	title = {A divide and combine method for machine configuration and workload balancing problem in multiple product {PCB} assembly},
+	journal = {Int. J. Adv. Manuf. Technol.},
+	author = {T\'{o}th, Attila and Knuutila, Timo and Nevalainen, Olli S.},
+	year = {2022},
+	month = {Mar.},
+	date = {2022-03-12},
+}
+
+
+@article{chen_improved_2023,
+	title = {An improved spider monkey optimization algorithm for multi-objective planning and scheduling problems of {PCB} assembly line},
+	volume = {229},
+	pages = {120600},
+	journal = {Expert Syst. Appl.},
+	author = {Chen, Yarong and Zhong, Jingyan and Mumtaz, Jabir and Zhou, Shengwei and Zhu, Lixia},
+	year = {2023},
+	month = {Nov.},
+}
+
+
+@article{chen_optimal_2024,
+	title = {The optimal configuration for various placement machines in {PCB} assembly lines},
+	journal = {Ann. Oper. Res.},
+	doi = {10.1007/s10479-024-05828-6},
+	author = {Chen, Tzu-Li and Chen, James C. and Chen, Yin-Yann and Chang, Yu-Jie},
+	year = {2024},
+	volume = {},
+	number = {},
+	pages = {},
+}
+
+
+@article{yan_load_2023,
+	title = {Load Optimization Scheduling of Chip Mounter Based on Hybrid Adaptive Optimization Algorithm},
+	volume = {3},
+	pages = {1--11},
+	number = {1},
+	journal = {Complex Syst. Model. Simul.},
+	author = {Yan, Xuesong and Zuo, Hao and Hu, Chengyu and Gong, Wenyin and Sheng, Victor S.},
+	year = {2023},
+	month = {Dec.},
+}
+
+
+%% === time estimating ===
+@article{vainio_estimating_2010,
+	title = {Estimating printed circuit board assembly times using neural networks},
+	volume = {48},
+	number = {8},
+	pages = {2201-2218},
+	journal = {Int. J. Prod. Res.},
+	author = {Vainio, Frans and Maier, Michael and Knuutila, Timo and Alhoniemi, Esa and Johnsson, Mika and Nevalainen, Olli S},
+    year = {2010},
+	month = {Aug.},
+}
+
+
+@article{vainio_estimating_2015,
+	title = {Estimating the production time of a {PCB} assembly job without solving the optimised machine control},
+	volume = {28},
+	pages = {823--835},
+	number = {8},
+	journal = {Int. J. Comput. Integ. M.},
+	author = {Vainio, Frans and Pahikkala, Tapio and Johnsson, Mika and Nevalainen, Olli S. and Knuutila, Timo},
+	year = {2015},
+}
+
+
+@article{li_predicting_2020,
+	title = {Predicting the printed circuit board cycle time of surface-mount-technology production lines using a symbiotic organism search-based support vector regression ensemble},
+	pages = {7246--7265},
+	journal = {Int. J. Prod. Res.},
+	author = {Li, Debiao and Chen, Siping and Chiong, Raymond and Wang, Liting and Dhakal, Sandeep},
+	year = {2020},
+	volume = {59},
+	number = {23},
+}
+
+# prove to be NP-hard
+@article{ji_genetic_2001,
+	title = {A genetic algorithm of determining cycle time for printed circuit board assembly lines},
+	journal = {Eur. J. Oper. Res.},
+	volume = {128},
+	number = {1},
+	pages = {175-184},
+	year = {2001},
+	author = {P. Ji and M.T. Sze and W.B. Lee},
+}
+
+@ARTICLE{zhang_reinforcement_2024,
+	author = {Zhang, Zikai and Tang, Qiuhua and Chica, Manuel and Li, Zixiang},
+	journal = {IEEE Trans. Cybern.}, 
+	title = {Reinforcement Learning-Based Multiobjective Evolutionary Algorithm for Mixed-Model Multimanned Assembly Line Balancing Under Uncertain Demand}, 
+	year = {2024},
+	volume = {54},
+	number = {5},
+	pages = {2914-2927},
+}
+
+@ARTICLE{wang_discrete_2022,
+	author = {Wang, Kaipu and Li, Xinyu and Gao, Liang and Li, Peigen and Sutherland, John W.},
+	journal = {IEEE Trans. Cybern.}, 
+	title = {A Discrete Artificial Bee Colony Algorithm for Multiobjective Disassembly Line Balancing of End-of-Life Products}, 
+	year = {2022},
+	volume = {52},
+	number = {8},
+	pages = {7415-7426},
+}
+
+@ARTICLE{pan_knowledge_2022,
+	author = {Pan, Zixiao and Lei, Deming and Wang, Ling},
+	journal = {IEEE Trans. Cybern.}, 
+	title = {A Knowledge-Based Two-Population Optimization Algorithm for Distributed Energy-Efficient Parallel Machines Scheduling}, 
+	year = {2022},
+	volume = {52},
+	number = {6},
+	pages = {5051-5063},
+}
+
+@article{choudhury_process_2007,
+	title = {Process planning for circuit card assembly on a series of dual head placement machines},
+	volume = {182},
+	number = {2},
+	journal = {Eur. J. Oper. Res.},
+	author = {Choudhury, Nilanjan D. and Wilhelm, Wilbert E. and Rao, Brijesh and Gott, Jonathan and Khotekar, Nikhilesh},
+	month = {Oct.},
+	year = {2007},
+	pages = {626--639},
+}
+
+
+% ===== single machine optimization =====
+@article{lu_scan_based_2023,
+	title = {A Scan-based Hierarchical Heuristic Optimization Algorithm for {PCB} Assembly Process},
+	journal = {IEEE Trans. Industr. Inform.},
+	author = {Lu, Guangyu and Yu, Xinghu and Sun, Hao and Li, Zhengkai and Qiu, Jianbin and Gao, Huijun},
+	year = {2024},
+	volume = {20},
+	number = {3},
+	pages = {3609-3618},
+}
+
+@article{gao_hierarchical_2021,
+	author = {Gao, Huijun and Li, Zhengkai and Yu, Xinghu and Qiu, Jianbin},
+	year = {2021},
+	month = {Jul.},
+	title = {Hierarchical Multiobjective Heuristic for {PCB} Assembly Optimization in a Beam-Head Surface Mounter},
+	volume = {52},
+	number = {7},
+	pages = {6911--6924},
+	journal = {IEEE Trans. Cybern.},
+}
+
+@article{li_cell_2022,
+	author = {Li, Zhengkai and Yu, Xinghu and Qiu, Jianbin and Gao, Huijun},
+	year = {2022},
+	month = {Mar.},
+	volume = {18},
+	number = {1},
+	pages = {559-570},
+	title = {Cell Division Genetic Algorithm for Component Allocation Optimization in Multi-Functional Placers},
+	journal = {IEEE Trans. Industr. Inform.},
+}
+
+@article{ashayeri_aggregated_2011,
+	author = {Ashayeri, Jalal and Ma, N. and Sotirov, Renata},
+	year = {2011},
+	month = {Jan.},
+	pages = {99--105},
+	title = {An aggregated optimization model for multi-head {SMD} placements},
+	volume = {60},
+	number = {1},
+	journal = {Comput. Ind. Eng.},
+}
+
+@article{geng_mcvrp-based_2019,
+	author = {Guo, Shujuan and Geng, Fei and Takahashi, Katsuhiko and Wang, Xiaohan and Jin, Zhihong},
+	year = {2019},
+	month = {Sep.},
+	pages = {5874--5891},
+	title = {A {MCVRP}-based model for {PCB} assembly optimisation on the beam-type placement machine},
+	volume = {57},
+	number = {18},
+	journal = {Int. J. Prod. Res.},
+}
+
+
+
+@article{chen_cooperative_2023,
+	title = {Cooperative Double-Layer Genetic Programming Hyper-Heuristic for Online Container Terminal Truck Dispatching},
+	volume = {27},
+	pages = {1220--1234},
+	number = {5},
+	journal = {{IEEE} Trans. Evol. Computat.},
+	author = {Chen, Xinan and Bai, Ruibin and Qu, Rong and Dong, Haibo},
+	year = {2023},
+	month = {Oct.},
+}
+
+
+@article{wang_explaining_2024,
+	title = {Explaining Genetic Programming-Evolved Routing Policies for Uncertain Capacitated Arc Routing Problems},
+	volume = {28},
+	number = {4},
+	pages = {918-932},
+	journal = {{IEEE} Trans. Evol. Computat.},
+	author = {Wang, Shaolin and Mei, Yi and Zhang, Mengjie},
+	year = {2024},
+}
+
+
+@article{zhao_estimation_2023,
+	title = {An Estimation of Distribution Algorithm-Based Hyper-Heuristic for the Distributed Assembly Mixed No-Idle Permutation Flowshop Scheduling Problem},
+	volume = {53},
+	pages = {5626--5637},
+	number = {9},
+	journal = {{IEEE} Trans. Syst. Man Cybern, Syst.},
+	author = {Zhao, Fuqing and Zhu, Bo and Wang, Ling},
+	year = {2024},
+}
+
+
+@article{li_pcb_2017,
+	title = {{PCB} assembly optimization in a single gantry high-speed rotary-head collect-and-place machine},
+	pages = {2819-2834},
+	journal = {Int. J. Adv. Manuf. Tech.},
+	author = {Li, Debiao and Yoon, Sang Won},
+	year = {2017},
+	volume = {88},
+}
+
+@misc{gurobi, 
+	author = {Gurobi Optimization, LLC}, 
+	title = {Gurobi Optimizer Reference Manual}, 
+	year = {2022}, 
+	url = {"https://www.gurobi.com"} 
+}
+
+
+%-------------------------------------------------------------------------------------
+%----------------------------------------Types----------------------------------------
+%-------------------------------------------------------------------------------------
+% article
+                %An article from a journal or magazine.
+% book
+                %A book with an explicit publisher.
+% booklet
+                %A work that is printed and bound, but without a named publisher or sponsoring institution.
+% ceedings
+                %An article in a conference proceedings.
+% proceedings
+                %The proceedings of a conference.
+% conference
+                %The same as inproceedings.
+% inbook
+                %A part of a book, which may be a chapter (or section or whatever) and/or a range of pages.
+% incollection
+                %A part of a book having its own title.
+% manual
+                %Technical documentation.
+% mastersthesis
+                %A Master's thesis.
+% misc
+                %Use this type when nothing else fits.
+% phdthesis
+                %A PhD thesis.
+% techreport
+                %A report published by a school or other institution, usually numbered within a series.
+% unpublished
+                %A document having an author and title, but not formally published.
+% collection
+                %A collection of works. The same as proceedings
+% patent
+                %A patent.
+
+%-------------------------------------------------------------------------------------
+%----------------------------------------Fields---------------------------------------
+%-------------------------------------------------------------------------------------
+%address
+                %Usually the address of the publisher or other type of institution.
+%annote
+                %An annotation. It is not used by the standard bibliography styles, but may be used by others that produce an annotated bibliography.
+%author
+                %The name(s) of the author(s), in the format described in the LaTeX book.
+%booktitle
+                %Title of a book, part of which is being cited. See the LaTeX book for how to type titles. For book entries, use the title field instead.
+%chapter
+                %A chapter (or section or whatever) number.
+%crossref
+                %The database key of the entry being cross referenced. Any fields that are missing from the current record are inherited from the field being cross referenced.
+%edition
+                %The edition of a book---for example, ``Second''. This should be an ordinal, and should have the first letter capitalized, as shown here; the standard styles convert to lower case when necessary.
+%editor
+                %Name(s) of editor(s), typed as indicated in the LaTeX book. If there is also an author field, then the editor field gives the editor of the book or collection in which the reference appears.
+%howpublished
+                %How something strange has been published. The first word should be capitalized.
+%institution
+                %The sponsoring institution of a technical report.
+%journal
+                %A journal name. Abbreviations are provided for many journals.
+%key
+                %Used for alphabetizing, cross referencing, and creating a label when the ``author'' information is missing. This field should not be confused with the key that appears in the cite command and at the beginning of the database entry.
+%month
+                %The month in which the work was published or, for an unpublished work, in which it was written. You should use the standard three-letter abbreviation, as described in Appendix B.1.3 of the LaTeX book.
+%note
+                %Any additional information that can help the reader. The first word should be capitalized.
+%number
+                %The number of a journal, magazine, technical report, or of a work in a series. An issue of a journal or magazine is usually identified by its volume and number; the organization that issues a technical report usually gives it a number; and sometimes books are given numbers in a named series.
+%organization
+                %The organization that sponsors a conference or that publishes a manual.
+%pages
+                %One or more page numbers or range of numbers, such as 42--111 or 7,41,73--97 or 43+(the `+' in this last example indicates pages following that don't form a simple range). To make it easier to maintain Scribe-compatible databases, the standard styles convert a single dash (as in 7-33) to the double dash used in TeX to denote number ranges (as in 7--33).
+%publisher
+                %The publisher's name.
+%school
+                %The name of the school where a thesis was written.
+%series
+                %The name of a series or set of books. When citing an entire book, the the title field gives its title and an optional series field gives the name of a series or multi-volume set in which the book is published.
+%title
+                %The work's title, typed as explained in the LaTeX book.
+%type
+                %The type of a technical report---for example, ``Research Note''.
+%volume
+                %The volume of a journal or multi-volume book.
+%year
+                %The year of publication or, for an unpublished work, the year it was written. Generally it should consist of four numerals, such as 1984, although the standard styles can handle any year whose last four nonpunctuation characters are numerals, such as `\hbox{(about 1984)}'.
+%affiliation
+                %The authors affiliation.
+%abstract
+                %An abstract of the work.
+%contents
+                %A Table of Contents
+%copyright
+                %Copyright information.
+%ISBN
+                %The International Standard Book Number.
+%ISSN
+                %The International Standard Serial Number. Used to identify a journal.
+%keywords
+                %Key words used for searching or possibly for annotation.
+%language
+                %The language the document is in.
+%location
+                %A location associated with the entry, such as the city in which a conference took place.
+%LCCN
+                %The Library of Congress Call Number. I've also seen this as lib-congress.
+%mrnumber
+                %The Mathematical Reviews number.
+%price
+                %The price of the document.
+%size
+                %The physical dimensions of a work.
+%URL
+                %The WWW Universal Resource Locator that points to the item being referenced. This often is used for technical reports to point to the ftp site where the postscript source of the report is located.

line-opt-manuscript.tex

@@ -0,0 +1,776 @@
+\documentclass[lettersize,journal]{IEEEtran}
+\usepackage{amsmath,amsfonts}
+\usepackage{algorithmic}
+\usepackage{array}
+\usepackage[caption=false,font=normalsize,labelfont=sf,textfont=sf]{subfig}
+\usepackage{textcomp}
+\usepackage{stfloats}
+\usepackage{url}
+\usepackage{verbatim}
+\usepackage{graphicx}
+\usepackage{tabularray}
+\usepackage{threeparttable}
+\usepackage{tabularx}
+\usepackage{booktabs}
+\usepackage[ruled,linesnumbered]{algorithm2e}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{makecell}
+\usepackage{multirow}
+\usepackage{soul}
+\usepackage[normalem]{ulem}
+\usepackage[thicklines]{cancel}
+\usepackage{xcolor}
+\renewcommand{\CancelColor}{\color{blue}}
+\usepackage[linktocpage=true, hyperindex=true]{hyperref}
+\usepackage[numbers,sort&compress]{natbib}
+\hyphenation{op-tical net-works semi-conduc-tor IEEE-Xplore}
+\def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
+T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
+\usepackage{balance}
+\aboverulesep=0pt
+\belowrulesep=0pt
+\begin{document}
+\title{Hyper-Heuristic Optimization Using Multi-Feature Fusion Estimator for PCB Assembly Lines with Linear-Aligned-Heads Surface Mounters}
+\author{Guangyu Lu, \emph{Graduate Student Member, IEEE}, Huijun Gao, \emph{Fellow, IEEE},  Zhengkai Li, \emph{Member, IEEE}, Xinghu Yu, \emph{Member, IEEE}, Tong Wang, \emph{Senior Member, IEEE}, Jianbin Qiu, \emph{Fellow, IEEE}, and Juan J. Rodr\'{i}guez-Andina, \emph{Fellow, IEEE} \vspace{-1em}
+\thanks{
+    % Manuscript received 22 August 2024; revised 19 November 2024 and 5 March 2025; accepted 18 March 2025. Date of current version 30 March 2025. 
+    This work was supported by the National Key Research and Development Program of China under Grant 2024YFB3409200, the National Natural Science Foundation of China under Grant 62303402, and the New Cornerstone Science Foundation through the XPLORER PRIZE. (\emph{Corresponding author: Huijun Gao.})}
+\thanks{Guangyu Lu, Huijun Gao, Tong Wang, and Jianbin Qiu are with the Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, China (e-mail: 20b904007@stu.hit.edu.cn; hjgao@hit.edu.cn; twang@hit.edu.cn, jbqiu@hit.edu.cn).}
+\thanks{Zhengkai Li is with the Research Institute of Interdisciplinary Intelligent Science, Ningbo University of Technology, Ningbo 315211, China (e-mail: LZK2024@nbut.edu.cn).}
+\thanks{Xinghu Yu is with the Intelligent Control and System Research Center, Yongjiang Laboratory, and also with the Ningbo Institute of Intelligent Equipment Technology Co., Ltd., Ningbo 315201, China (e-mail: 17b304003@stu.hit.edu.cn).}
+\thanks{Juan J. Rodr\'{i}guez-Andina is with the Department of Electronic Technology, University of Vigo, 36310 Vigo, Spain, and also with the Research Institute of Interdisciplinary Intelligent Science, Ningbo University of Technology, Ningbo 315211, China (e-mail: juan.j.r@ieee.org).}
+}
+\markboth{IEEE Transactions on Cybernetics}
+{}
+\maketitle
+\begin{abstract}
+Printed circuit board assembly line scheduling (PCBALS) is a difficult task in the electronic industry for assembly lines using surface mounters, which is critical for production efficiency.
+This is a special type of line optimization problem that uses different allocation techniques, resulting in wide differences in assembly times between machines.
+This article proposes a hyper-heuristic optimizer embedded with a multi-feature fusion ensemble
+estimator (HHO-MFFEE) for PCBALS using linear-aligned-heads surface mounters. The objective and constraints of the problem are discussed, and a min-max integer model for small-scale problems is built. At the hyper-heuristic low level, seven data- and target-driven heuristics are presented for allocating components to different machines. Strategies for duplicated conditions with component types and placement points allocation are proposed to improve the applicability of the algorithm and the quality of the solution. An ensemble assembly time estimator that incorporates the coding of multi-features, including estimated sub-objectives, is proposed for evaluating the quality of the solution. Experimental results show that (1) the gaps between the solution from HHO-MFFEE and the optimal solution of the model are 3.44\%$\sim$7.28\% for small-scale data; (2) the proposed time estimator has higher accuracy than regression and heuristic-based ones, with mean absolute error of 2.01\% and 3.43\% for training and testing data, respectively; and (3) HHO-MFFEE is better than other state-of-the-art algorithms, with average improvement of 7.21\%$\sim$9.47\%.
+\end{abstract}
+\begin{IEEEkeywords}
+PCBA line optimization, hyper-heuristic, component allocation balance, multi-feature fusion time estimator, linear-aligned-heads surface mounter
+\end{IEEEkeywords}
+\section{Introduction}
+\IEEEPARstart{P}{rinted} circuit board (PCB) assembly, the process of automatically mounting various electronic components onto bare boards, is an important phase in the manufacturing of electronic products, determining their overall quality. Surface mounters with linear-aligned heads for improving efficiency are widely deployed in PCB assembly lines. Manufacturers tend to use multiple surface mounters in series to increase productivity. However, they face difficulties in both the schedule of a single machine and the optimization of the entire line. The efficiency of single-machine scheduling affects the search process for line optimization, which in turn decides assembly tasks for single machines. Solving these two coupled optimization problems poses a significant challenge.
+
+A PCB assembly line (Fig.~\ref{line_composition}) consists of automatic equipment, including a loader, screen printer, surface mounters, reflow furnace, automatic optical inspector (AOI), and unloader.
+Screen printer applies solder paste to the surface of PCBs. Surface mounters pick and place components on the PCB pads. Reflow furnace melts solder paste, which has been already pre-positioned on the pads, before cooling it to create a permanent solder. Finally, AOI looks for defects on the PCB to ensure assembly quality.
+Of all the equipment, the screen printer applies solder paste faster, and the reflow furnace puts PCBs continuously through the oven, which usually does not become a bottleneck as it is not affected by the previous process. Inspection equipment can take pictures of multiple placement points simultaneously, and the computation time for detection is negligible.
+In contrast, surface mounters, which need to accurately pick and place hundreds of components, have a direct impact on production efficiency.
+Central to production control is the efficient use of machines, with surface mounters being the bottleneck for assembly efficiency~\cite{ayob_optimization_2007,rong_modeling_2011,kulak_ga-based_2008}.
+
+Surface mounters with linear-aligned heads are widely applied in PCB assembly lines. They consist of a stationary platform, two stationary feeder bases, and a moving gantry with multiple heads. The gantry moves between the PCBs and the base and is fitted with heads assembled with suitable nozzles from an automatic nozzle changer for picking and placing different components. The linear-aligned design of the heads is spaced in integer multiples of the slot intervals so that heads can simultaneously pick up components from the feeders on different slots. Compared with the rotary-head type, the mechanical structure of linear-heads is simple and reliable, with higher pickup efficiency, which can achieve high-speed, high-precision assembly. The applicable types of component packages are also more diversified.
+
+\begin{figure*}
+\centering
+\includegraphics[scale=0.75]{figure/assembly-line.eps}
+\caption{PCB assembly line.}
+\label{line_composition}
+\end{figure*}
+
+PCB assembly line scheduling (PCBALS) focuses on allocating components to multiple surface mounters in a production line to improve assembly efficiency. The search for complex feasible domains, which is an extension of the NP-hard general production line optimization problem, is time-consuming and intricate. The huge solution space requires high-efficiency iterative searching, whereas the long time required for single-machine optimization is inadequate for evaluating each solution. Component allocation for the line and time estimation for a single surface mounter are the main tasks in PCBALS.
+
+Extensive research has been conducted on the PCBALS problem~\cite{rong_modeling_2011, kulak_ga-based_2008, guo_integrated_2012}, and optimization for a single machine has been thoroughly studied~\cite{gao_hierarchical_2021, lu_scan_based_2023}.
+Component allocation has been explored for both model-based~\cite{kodek_optimal_2004,hillier_cost_2001, rong_modeling_2011} and heuristic-based~\cite{toth_reconfiguring_2010,he_heuristic_2017, guo_integrated_2012,yan_load_2023} algorithms. Most time estimators are fitting-based, which progressively evolved from the number of points to other factors solved by heuristics, such as the number of assembly cycles~\cite{rong_modeling_2011}, nozzle changes~\cite{hillier_cost_2001} and feeder utilization~\cite{he_heuristic_2017}.
+However, most research to date has concentrated on the optimization of lines with rotary-heads surface mounters~\cite{kulak_ga-based_2008,guo_integrated_2012,rong_modeling_2011,he_heuristic_2017}, which differs from the structural design with linear-aligned heads.
+
+% proposed method introduction
+Heuristic algorithms have been well studied in the field of assembly lines~\cite{zhang_reinforcement_2024}, disassembly lines~\cite{wang_discrete_2022} and parallel machines optimization~\cite{pan_knowledge_2022}.
+Hyper-heuristic algorithms are a novel optimization framework that combines the advantages of high- and low-level heuristics to adaptively solve a wide range of complex optimization problems. They have been widely applied for route scheduling~\cite{wang_explaining_2024}, truck dispatching~\cite{chen_cooperative_2023}, or flow shop scheduling~\cite{zhao_estimation_2023}, among other problems. The estimation of assembly time has been studied with regression fitting approaches~\cite{wu_solution_2010,vainio_estimating_2015,li_predicting_2020}. Ensemble learning provides strong nonlinear fitting capability, and it can have a high fitting accuracy by designing extracted data features.
+
+% the work that we need to do
+In this article, a hyper-heuristic load balancing algorithm with a multi-feature fusion ensemble estimator (HHO-MFFEE) is proposed for PCB assembly lines. Algorithm design is tailored to the structural characteristics of linear-aligned head surface mounters. The hyper-heuristic framework applies techniques with domain knowledge, which results in improved mechanisms for the search and evaluation process, achieving accurate solution evaluation, efficient search process, and balanced allocation results. Compared to state-of-the-art algorithms and industrial solutions, the proposed HHO-MFFEE achieves higher assembly efficiency.
+The contributions of this article are summarized as follows:
+\begin{enumerate}
+\item A hyper-heuristic optimization method is proposed for linear-aligned-heads surface mounter lines, which can be applied to different scenarios in terms of component-machine constraints, component duplication conditions, or other factors.
+\item A set of data- and target-driven low-level heuristics is presented to search the solution space with high-quality results.
+\item An extraction method for data features is proposed, and the features are fused within a multi-feature ensemble time estimator, which makes the estimation more accurate.
+\item An aggregative grouping algorithm for duplicated component points is proposed to improve the efficiency of PCB assembly lines.
+\end{enumerate}
+
+% paper organization
+The rest of the article is organized as follows. Section~\ref{review_section} reviews related work about PCBALS. Section~\ref{problem_formulate_section} formulates the mathematical model. The HHO-MFFEE is presented in Section~\ref{methodology_section}. Comparative experiments with other state-of-the-art approaches are presented and discussed in Section~\ref{experiment_section}. Finally, Section~\ref{conclusion_section} concludes the article.
+
+\section{Literature Review}\label{review_section}
+% definition & classification
+Many studies have contributed to the optimization of PCB assembly lines. This article targets the single-model case~\cite{toth_machine_2018}, where a single PCB type is manufactured without line changeover. This topic has been studied from modeling and heuristic perspectives, with the sub-problems of component allocation and placement sequence. In~\cite{ji_genetic_2001}, the former has been proven to be NP-complete, being the main research focus.
+% The present work focuses on optimizing search capabilities and time estimation accuracy in PCB assembly lines.
+
+% mathematical model
+Although mathematical modeling can solve problems optimally, it is difficult to obtain mathematical expressions for some real-world applications. Even when this is possible, their implementation may require unacceptably high computational complexity.
+The integrated model for changeable head configuration and component allocation presented in~\cite{rong_modeling_2011} is linearized and includes a partial relaxation form to speed up the searching process. A min-max approximation integer model with setup and assembly times, as well as an efficient branch-and-bound-based optimal algorithm, are introduced in~\cite{kodek_optimal_2004}. As an extension to \cite{kodek_optimal_2004}, a mixed integer model with feeder module usage, precedence, and component duplication constraints is proposed in~\cite{emet_workload_2010}.
+In~\cite{lin_component_1999} and~\cite{hu_fuzzy_2017}, an expected value model and a fuzzy goal model are built to deal with environmental uncertainties, such as demand and machine breakdown, as a tradeoff between optimality and stochasticity.
+
+% meta-heuristic
+Meta-heuristics are commonly applied in PCB assembly line optimization. These include genetic algorithms~\cite{guo_integrated_2012, kulak_ga-based_2008} and hybrid spider monkey optimization (HSMO)~\cite{mumtaz_hybrid_2020, chen_improved_2023}, among others. In~\cite{kulak_ga-based_2008}, a genetic algorithm to identify potential solutions for machine-specific component allocation and placement sequence problems is presented.
+In~\cite{guo_integrated_2012}, a hybrid genetic algorithm is researched, which takes into account a more general scenario of component duplication. The solution is evaluated using a greedy heuristic for assigning nozzles and headsets. An HSMO algorithm is developed in~\cite{mumtaz_hybrid_2020} to solve component allocation and placement sequence problems simultaneously. The problem is refined in~\cite{chen_improved_2023} by incorporating a few extra features to optimize completion time, energy consumption, and maintenance time. A combination of an evolutionary algorithm and mathematical programming to determine the optimal configuration of the type of surface mounters in lines is presented in~\cite{chen_optimal_2024}.
+
+% constructive heuristic
+In addition, constructive heuristics based on intuition and experience are proposed for PCB line optimization.
+In~\cite{toth_reconfiguring_2010}, line assignment of modular surface mounters is divided into three phases: head to module, component to head, and nozzle to head. Heuristics, including random search, brute force, and evolutionary algorithms, are applied in each phase.
+In~\cite{he_heuristic_2017}, a deterministic hierarchical heuristic is presented to solve the problem at a lower level, allowing component duplication for identical machines.
+In~\cite{choudhury_process_2007}, assembly process decisions are decomposed into four related sub-problems, and list-processing algorithms for lines with dual-head surface mounters are proposed.
+
+% multiple PCB cases.
+Research has also been conducted to optimize the line as part of multi-level production planning, consisting of PCB assignment to the line, component allocation to machines, and surface mounter optimization. An HSMO algorithm to simultaneously solve the multi-level problems is presented in~\cite{mumtaz_multi-level_2019}. Hierarchical heuristics are applied in~\cite{koskinen_rolling_2019} to solve the problem through job partition, selection, grouping, load balancing, and scheduling.
+In~\cite{toth_divide_2022}, a graph-based divide-and-combine heuristic method is proposed to divide multiple PCBs within a single product, and then sub-problems are solved with standard solvers and meta-heuristics.
+
+% time estimation
+Component allocation depends on the assembly time of surface mounters, and most research is based on estimators. In~\cite{wu_solution_2010}, assembly time is estimated from the number of component types and placement points using linear regression. A regularized least-squares regression with a novel feature solved using the nearest neighbor heuristic is proposed in~\cite{vainio_estimating_2015}. A supported regression method combined with symbiotic organism search is proposed in~\cite{li_predicting_2020} to improve estimation accuracy. Neural networks (NNs) have the ability to fit arbitrary nonlinear functions. In~\cite{vainio_estimating_2010}, a multi-layer perceptron network estimator is presented considering the component shape and the area of the smallest rectangle around the component.
+
+To summarize, the present research focuses more on rotary-head surface mounter line optimization, which inspires us to further optimize a line consisting of surface mounters with special linear-aligned head structures in terms of search capabilities and time estimation accuracy.
+
+\section{Problem Formulation and Model}\label{problem_formulate_section}
+\subsection{Problem Formulation}
+PCBALS can be regarded as a special type of assembly line optimization, known to be NP-hard. It has a higher decision level and higher complexity compared with single-machine problems. Production optimization of surface mounters can be viewed as a combination of warehouse location, task assignment, and route scheduling problems. There are various combinations of component allocation among different machines. Specifically, each assembly component may be assigned to multi-candidate machines with different processing times, resulting in exponential growth of the number of feasible solutions.
+
+% factor affects line efficiency & constraint
+Among the many factors that influence the efficiency of a PCB assembly line, surface mounters take the longest time to process, thus determining the efficiency of the entire line.
+A variety of interdependent factors influence the assembly efficiency of a single surface mount machine, including the number of cycles, pick-ups, nozzle changes, and placement points~\cite{gao_hierarchical_2021}.
+The result of component allocation affects the above multiple sub-objectives. In terms of available resources, assembly tools limit the upper number of assembly machines for each component type, and the priority limits the assembly sequence.  Due to resource coupling and conflicting sub-objectives, several local optimal solutions may exist in the feasible domain.
+
+Fig.~\ref{line-opt-structure} shows the main tasks and constraints affecting PCB assembly line balancing, namely input, output, constraints, estimator, and optimization tasks. The input is the PCB to be assembled, which includes the component information of the placement point. Constraints can be divided into machine configuration, assembly priority, and available tools. The optimization task consists of two parts: line balancing and assembly process optimization of surface mounter, which have a coupled relationship. The former is generally regarded as the input of the latter, and the latter is used to evaluate the quality of the former solution. In the specific task allocation, the allocation of assembly tools and components for lines determines the head and feeder assignment of each component for surface mounter, which further determines key performance indicators affecting assembly efficiency. Assignment of placement points in load balancing affects the quality of the assembly route scheduling of the surface mounter, which also impacts overall assembly efficiency. The complexity of the assembly tasks makes it difficult to directly get productivity. An estimator evaluates actual assembly time based on the operating process of a single machine and guides line balancing.
+% The PCBALS problem is essentially a combination of two sub-problems: component allocation and time estimation.
+
+\begin{figure}
+    \centering
+    \includegraphics[scale=0.6]{figure/line-opt-structure.eps}
+    \caption{Main tasks and constraints for PCB assembly line optimization.}
+    \label{line-opt-structure}
+\end{figure}
+
+% difficulty in component allocation and time estimation
+Assembly process optimization focuses on performance improvement of individual machines through optimizing feeder configuration, pickup operations, and movement path, among other factors. Meanwhile, assembly line optimization focuses on improving the efficiency of the bottleneck machine. Surface mounter performance directly affects line efficiency, whereas assembly task assignment affects machine utilization rate.
+The large number of combinations for component allocation makes it difficult to get high-quality solutions, and computing effort increases rapidly as problems scale up, needing massive resources even for small-scale data.
+For the unique mechanics of linear-aligned heads, single-machine production simulations with long running time, as well as traditional time estimators with large errors are no longer applicable. In production line optimization, it is necessary to reasonably allocate assembly tasks of each mounter to balance load, which requires accurate and fast estimation of the assembly process of surface mounters.
+\subsection{Integer Programming Model}
+Notations used in the model are listed in Table~\ref{notation_summary_table}.
+\begin{table}
+\caption{Notations of the Model}
+\begin{tabular}{p{1.1cm}<{\centering}p{6.8cm}}
+    \toprule
+    Notation & Description \\
+    \midrule
+    \multicolumn{2}{l}{\textbf{Indices \& Sets}} \\
+    $i \in I$ & Index of component type, $I = \left\{1,2,\cdots \right\}$ \\
+    $j \in J$ & Index of nozzle type, $J = \left\{1,2,\cdots \right\}$ \\
+    $p \in P$ & Index of points, $P = \left\{1,2,\cdots \right\}$ \\
+    $k \in K$ & Index of cycle, $K = \left\{1,2,\cdots \right\}$ \\
+    $s \in S$ & Index of slot, $S = \left\{1,2,\cdots \right\}$ \\
+    $h \in H$ & Index of head, $H = \left\{1,2,\cdots \right\}$ \\
+    $m \in M$ & Index of surface mounter machine, $M = \left\{1,2,\cdots \right\}$ \\
+    $q \in Q$ & Pair Index of assembly priority , $Q = \left\{ \left(i, i^\prime \right) ,\cdots \right\}$, $i \in I$, $i^\prime \in I$, which means component type $i$ is assembled before component type $i^\prime$ \\
+    \multicolumn{2}{l}{\textbf{Parameters}} \\
+    $\phi_{i}$ & Number of placement points of component type $i$ \\
+    $\theta_{i}$ & Number of available feeders of component type $i$ \\
+    $\zeta_{j}$ & Number of available nozzles of type $j$ \\
+    % $\eta_{m}$ & Number of assembly heads for surface mounter $m$ \\
+    $\xi_{ij}$ & $=1$ iff. component type $i$ is compatible with nozzle type $j$ (= 0, otherwise) \\
+    $\eta_{im}$& $=1$ iff. component type $i$ is compatible with machine $m$ (= 0, otherwise) \\
+    $\mu_{ip}$& $=1$ iff. component type $i$ is compatible with point $p$ (= 0, otherwise)  \\
+    $\tau$ & Interval ratio between adjacent heads to adjacent slots \\
+    $T_1 \sim T_5$ & Weights for assembly efficiency-related metrics \\
+    $N$ & A sufficiently large number \\
+    \multicolumn{2}{l}{\textbf{Decision Variables}} \\
+    $g_{km}$ & Binary variable, $=1$ iff. any point is assembled in cycle $k$ of machine $m$ \\
+    % $n _{hm}$ & Number of nozzle change for head $h$ of machine $m$ \\
+    $u_{ikhm}$ & Binary variable, $=1$ iff. component type $i$ is assigned to head $h$ in cycle $k$ of machine $m$ \\
+    $v_{skhm}$ & Binary variable, $=1$ iff. head $h$ picks up components from slot $s$ in cycle $k$ of machine $m$ \\
+    % $w_{jkhm}$ & $=1$ iff. head $h$ is equipped with nozzle $j$ in cycle $k$ of machine $m$ \\
+    $f_{ism}$ & Binary variable, $=1$ iff. component $i$ is assigned to slot $s$ of machine $m$ \\
+    $e_{skm}$ & Binary variable, $=1$ iff. component is picked up when the left-most head aligns to slot $s$ of machine $m$ in cycle $k$ \\
+    $n_{khm}$ & Binary variable, $=1$ iff. head $h$ of machine $m$ changes nozzles between cycles $k$ and $k+1$ \\
+    $r_{im}$ & Binary variable, $=1$ iff. component type $i$ is assembled by machine $m$ \\
+    $w_{km}$ & Integer variable, which indicates slots crossed by the gantry during pick-up in cycle $k$ of machine $m$ \\
+    \bottomrule
+\end{tabular}
+\label{notation_summary_table}
+\end{table}
+In~\cite{lu_scan_based_2023}, an integer model for head task assignment, including the major factors that influence assembly efficiency, is proposed. Based on it, a new approximation model is proposed that assesses assembly line efficiency in terms of weighted metrics.
+\begin{equation}
+\begin{aligned}
+    \min \max_{m \in M} \left( T_1 \cdot \sum_{k \in K} g_{km} + T_2 \cdot \sum_{k \in K \backslash \left\{ \left| K \right| \right\}} \sum_{h \in H} n_{khm} + T_3 \cdot  \right. \\
+    \left.  \sum_{k \in K} w_{km} + T_4 \cdot \sum_{s \in S} \sum_{k \in K} e_{skm}  + T_5 \cdot \sum_{i \in I} \sum_{k \in K} \sum_{h \in H} u_{ikhm} \right)
+    \end{aligned}
+    \label{objective_equation}
+\end{equation}
+
+Objective~\eqref{objective_equation} of the model is to minimize the maximum weighted key assembly metrics among all machines, with different weights $T_1$ for assembly cycle, $T_2$ for nozzle change, $T_3$ for pick-up movement, $T_4$ for pick-up operations, and $T_5$ for placement operations. As described below, Constraints~\eqref{comp_assign_equation}--\eqref{feeder_assign_equation} are related to the configuration of a single surface mounter, whereas Constraints~\eqref{completion_equation}--\eqref{machine_priority_constr} incorporate line optimization factors.
+\begin{equation}
+    \sum_{i \in I} u_{ikhm} \leq g_{km} \quad \forall k \in K, h \in H, m \in M
+    \label{comp_assign_equation}
+\end{equation}
+\begin{equation}
+\begin{aligned}
+    n_{khm} = \sum_{i \in I} \sum_{j \in J} \left| \xi_{ij} \cdot u_{ikhm} - \xi_{ij} \cdot u_{i\left( k + 1 \right)hm} \right| \\ \quad \forall k \in K \backslash \left\{ \left| K \right| \right\}, h \in H, m \in M
+    \end{aligned}
+    \label{nozzle_change_equation}
+\end{equation}
+\begin{equation}
+    \begin{aligned}
+    e_{skm} \leq \sum_{h \in H} v_{\left[s + \left( h - 1 \right) \cdot \tau \right]khm} \leq N \cdot e_{skm} \\ \quad \forall s \in S, k \in K, m \in M
+    \end{aligned}
+    \label{gang_pick_equation}
+\end{equation}
+\begin{equation}
+    \begin{aligned}
+    w_{km} \geq s \cdot e_{skm} - s^\prime \cdot e_{s^\prime km} + N \cdot \left( e_{skm} + e_{s^\prime km} - 2 \right) \\
+    \quad \forall k \in K, m \in M, s \in S, s^\prime \in S
+    \end{aligned}
+    \label{pickup_move_equation}
+\end{equation}
+\begin{equation}
+    \begin{aligned}
+    f_{ism} \leq \sum_{k \in K} \sum_{h \in H} u_{ikhm} \cdot v_{skhm} \leq N \cdot f_{ism} \\ \quad \forall i \in I, s \in S, m \in M
+    \end{aligned}
+    \label{feeder_assign_equation}
+    \end{equation}
+\begin{equation}
+    \sum_{k \in K} \sum_{h \in H}\sum_{m \in M} x_{ikhm} = \phi_{i} \quad \forall i \in I
+    \label{completion_equation}
+\end{equation}
+\begin{equation}
+    \sum_{s \in S} \sum_{m \in M} f_{ism} \leq \theta_{i} \quad \forall i \in I
+    \label{feeder_limit_equation}
+\end{equation}
+\begin{equation}
+    \sum_{m\in M} \max_{k \in K} \sum_{i \in I} \sum_{h \in H} \xi_{ij} \cdot u_{ikhm} \leq \zeta_j \quad \forall j \in j
+    \label{nozzle_limit_equation}
+\end{equation}
+\begin{equation}
+    r_{im} \leq \sum_{k \in K} \sum_{h \in H} x_{ikhm} \leq N \cdot r_{im} \quad \forall i \in I, m \in M
+    \label{line_assign_constr}
+\end{equation}
+    \begin{equation}
+    r_{im} \leq \eta_{im} \quad \forall i \in I, m \in M
+    \label{machine_specific_equation}
+\end{equation}
+\begin{equation}
+\begin{aligned}
+    m - N \cdot \left( 1 -  r_{im} \right) \leq m^{\prime} + N \cdot (1 -  r_{i^\prime m^{\prime}}) \\
+    \quad \forall q = \left(i, i^\prime \right) \in Q, m \in M, m^\prime \in M
+    \end{aligned}
+    \label{line_priority_constr}
+\end{equation}
+\begin{equation}
+    \begin{aligned}
+    \max_{k \in K, h \in H} k \cdot x_{ikhm} + N \cdot \left( r_{im} + r_{i^\prime m} - 2  \right) \leq \min_{k \in K, h \in H}  \\
+    \left\{ k \cdot x_{i^\prime khm} + N \cdot \left( 1 - x_{i^\prime khm}\right) \right\} \; \forall q = \left(i, i^\prime \right) \in Q, m \in M
+    \end{aligned}
+    \label{machine_priority_constr}
+\end{equation}
+
+The cycle of each machine with component assignment is defined in Constraint~\eqref{comp_assign_equation}.
+Constraint~\eqref{nozzle_change_equation} calculates the number of nozzle changes. Constraint~\eqref{gang_pick_equation} converts pick-up slots to the left-most head-aligned one to get the number of simultaneous pick-ups.
+Constraint~\eqref{pickup_move_equation} indicates the number of slots through the pick-up movement.
+Constraint~\eqref{feeder_assign_equation} represents the relationship between component and feeder assignment. More details about the relationship between decision variables and tool constraints of a single machine can be found in~\cite{lu_scan_based_2023}.
+
+Constraint~\eqref{completion_equation} denotes all placement points that are assigned to machines.
+Constraints~\eqref{feeder_limit_equation} and \eqref{nozzle_limit_equation} define the maximum number of machines the component can be assigned to, which is limited by the number of feeders and nozzles.
+Constraint~\eqref{line_assign_constr} indicates the relationship between machine-assigned and head-assigned components. Constraint~\eqref{machine_specific_equation} restricts the components from being assigned to compatible machines. Constraints~\eqref{line_priority_constr} and \eqref{machine_priority_constr} restrict the priority of the assembly process. The former indicates that a component with a high priority cannot be assigned to a machine later than a component with a low priority, whereas the latter restricts the order in which two components are assigned to the same machine.
+
+\section{HHO-MFFEE}\label{methodology_section}
+\subsection{Solution Framework for the HHO-MFFEE Algorithm}
+As shown in Fig.~\ref{solution_framework}, the proposed evolutionary-based HHO-MFFEE is built from low-level heuristics and an estimator. Component division and aggregated-based grouping algorithms are designed for component duplication at the beginning and end of the optimization. Multiple populations with varying component allocation sequences iterate separately to avoid allocation sequence limiting efficiency gains while providing multiple high-quality solutions for further evaluation. The combination and execution order of low-level heuristics are specified in the population-generating code. A multi-feature fusion ensemble time estimator based on fully connected NNs is proposed to calculate the fitness value of each individual, fed with data and estimated sub-objectives. In the iterative process, truncated crossover and mutation operations are conducted on individuals.
+After the evolutionary process is completed, placement points with the same component type are segregated using an aggregated grouping algorithm.
+
+\begin{figure}[htbp]
+    \centering
+    \includegraphics[scale=0.6]{figure/solution_framework.eps}
+    \caption{Flowchart of the proposed HHO-MFFEE algorithm.}
+    \label{solution_framework}
+\end{figure}
+
+\subsection{Low-Level Heuristics for Component Allocation}
+Low-level heuristics (LLHs) are basic compositions of hyper-heuristics. They can be divided into data- and target-driven LLHs. The allocation sequence for components is preset and heuristics are selected based on the allocated components.
+
+Data-driven LLHs are connected to the number of points, component type, and nozzle type, as follows: components are allocated to the machine with minimum assigned placement points (\emph{Minimum Points Heuristic}), component types (\emph{Minimum Component Types Heuristic}), nozzle types (\emph{Minimum Nozzle Types Heuristic}), and minimum ratio of number of component types to nozzle types (\emph{Minimum Ratio Heuristic}), respectively.
+
+Target-driven LLHs are related to assembly efficiency, and key sub-objectives are extracted as a basis for component allocation.
+Instead of specific values, they compare relative values of sub-objectives between surface mounters, which can be evaluated without a specialized procedure. The number of heads assigned to nozzle type $j$ of machine $m$ is denoted as $\gamma_{jm}$, based on the cascade rounding method proposed in~\cite{li_pcb_2017}. The target-driven LLHs are:
+\begin{enumerate}
+    \item \emph{Minimum Cycle Heuristic}, which allocates components to the machine with the minimum cycle without nozzle change, i.e.,
+    \begin{equation}
+        {\arg \min}_{m \in M} \max_{j \in J} \left( \sum_{i \in I} \sum_{k \in K} \sum_{h \in H} \left( \xi_{ij} \cdot u_{ikhm} \right) / \gamma_{jm} \right)
+    \end{equation}
+    \item  \emph{Minimum Nozzle Change Heuristic}, which allocates components to the machine with the minimum probability of nozzle change, reflected in the mean squared error of the points for each head, i.e.
+    \begin{equation}
+    \arg \min_{m \in M} \sigma \left( \left\{ \overbrace{\sum_{i \in I} \sum_{k \in K} \sum_{h \in H} \frac{ \xi_{ij} \cdot u_{ikhm} }{ \gamma_{jm}}}^{\text{ $\gamma_{jm}$ terms in total}} \mid j \in J \right\} \right)
+    \end{equation}
+    where $\sigma\left( \cdot \right)$ denotes the mean square deviation of a set.
+    \item \emph{Minimum Pick-up Heuristic}, which allocates components to the machine with minimum pick-up operations.
+\end{enumerate}
+
+Algorithm~\ref{least_pickup_algorithm} presents a method to estimate the number of pick-ups. A hierarchical greedy heuristic assigns components to heads in decreasing order of the number of points, subject to the number of heads accessible to the nozzle. Assigned points of each component type for machine $m$ are denoted as $\phi^\prime$. Assignment of all attachable heads to each component implies the start of a new cycle, and the number of pick-ups equals the maximum number of points assigned to heads in each cycle.
+
+The number of component feeders and machine requirements restricts allocatable machines. All LLHs are based on a set of feasible surface mounters. The set of assigned surface mounters for each component type cannot exceed available feeders.
+The feasible set is adjusted based on component-assigned mounters. When the number of assigned mounters equals that of available feeders, the indices of assigned mounters are regarded as the new feasible set.
+% Otherwise, the indices of all mounters are regarded as the feasible set.
+Component prioritization needs to be checked first to see if the loop is closed between constraint relationships and, if so, there is no solution. Otherwise, if during component allocation, a newly allocated component breaks the priority constraint, the assigned components that do not satisfy the constraint relationship are replaced and reallocated with the same strategy. The machine with the fewest points among LLHs with the same evaluation value has the highest priority for assembling components.
+\begin{algorithm}
+    \footnotesize
+    \caption{Hierarchical Greedy Head Assignment}
+    \label{least_pickup_algorithm}
+    \SetKwInOut{Input}{Input}\SetKwInOut{Output}{Output}
+    \Input{Nozzle heads $\gamma$, component points $\phi^\prime$}
+    \Output{Number of pick-up operations $\mathcal{O}$}
+    Set a $1 \times \left| J \right| $ vector $\mathcal{L}$, a $1 \times \left| J \right| $ vector $\mathcal{N}$ , and a $1 \times \sum_{i \in I} \phi^\prime_i $ vector $\mathcal{K}$ of all zeros; \\
+    Sort $i \in I $ decreasingly with $\phi^\prime_i$;\\
+    \For {$i \in I$}
+    {
+    $j \leftarrow \sum_{j^\prime \in J} \xi_{ij^\prime} \cdot j^\prime$ ; \tcp{assign nozzle $j$ compatible with component $i$}
+    \If { $\mathcal{N}_j$ $\mathrm{Mod}$ $\gamma_{jm} = 0$ }
+    {
+    $\mathcal{L}_j \leftarrow \mathcal{L}_j + 1 $;  \tcp{nozzle allocation is full and start a new cycle}
+    }
+    \tcc{Update maximum number of allocated points and heads}
+    Set cycle index $c \leftarrow \mathcal{L}_j $,
+    $\mathcal{K}_c \leftarrow \max \left(\mathcal{K}_c, \phi^\prime_i \right)$, $\mathcal{N}_j \leftarrow \mathcal{N}_j + 1$
+    }
+    $\mathcal{O} \leftarrow \sum_{c = 1}^{c =\sum_{i \in I} \phi^\prime_i } \mathcal{K}_c$
+\end{algorithm}
+\subsection{Hyper Heuristic for Line Optimization}
+In the evolutionary-based hyper-heuristic, each individual gene correlates to an LLH denoted as a pattern. It operates in a range of populations with various component allocation sequences and individual genes of different lengths, increasing search diversity. The length of genes is limited to the number of component division groups.
+All individuals are initialized with random lengths and pattern combinations. 
+% If the length of individual genes is less than the number of component groups, the genes are cyclically accessed from the beginning to complete the assignment process. 
+Cyclic access is applied in individuals with short genes.
+Each one of the two genes selects a split point and the crossover operator exchanges gene segments. The mutation operator inserts randomly generated patterns at the split point. Truncated procedures are applied to individuals whose length exceeds the limit value. For each solution, the specific algorithm is executed on the machine with the longest estimated time, reducing single-machine optimizations and increasing solving efficiency.
+% The crossover and mutation operations are depicted in Fig.~\ref{genetic_operation}.
+% \begin{figure}
+% \centering
+% \includegraphics[scale=0.68]{figure/crossover_mutation.eps}
+% \caption{The schematic of crossover and mutation operations.}
+% \label{genetic_operation}
+% \end{figure}
+\subsection{Multi-Feature Fusion Ensemble Time Estimator}
+Ensemble learning with NNs performs well at fitting complex and nonlinear data. Multi-feature of fitting data is related to single-machine optimization. Simulated data are fed to the network to ensure it is sufficiently trained. The complexity of the PCB assembly process makes some properties difficult to uncover. Therefore, a heuristic algorithm is proposed to estimate performance metrics to improve fitting accuracy.
+
+The framework of the estimator is shown in Fig.~\ref{neural-network}. Input coding consists of three parts.
+Basic data are the total number of placement points, component types, nozzle types, and board size. The estimated number of cycles and pick-ups of the preceding section, as well as nozzle change, builds the target feature coding. Nozzle and component types are coded in descending order based on the total number of points as extended parts.
+Grouped components are the object of LLHs allocation, which involves only the type of components and the number of placement points. 
+The independence of point distribution is due to its coding difficulty and relatively small impact on efficiency.
+% This is independent of the point distribution, which is neglected due to its coding difficulty and small impact on efficiency.
+A sufficiently long encoding is used to ensure consistency across diverse data inputs to networks, with redundant bits supplemented by zeros.
+
+\begin{figure}[htbp]
+    \centering
+    \includegraphics[scale=0.5]{figure/neural-network.eps}
+    \caption{Framework of the multi-feature fusion ensemble time estimator.}
+    \label{neural-network}
+\end{figure}
+
+The estimation of nozzle change probability cannot be directly coded. Algorithm~\ref{nozzle_change_heuristic} proposes a computation heuristic for it. Components with the same nozzle type are grouped according to their respective nozzle heads. The group of nozzle $j$ of machine $m$ is denoted as $\mathcal{G}_{jm}$. Nozzle groups are progressively assigned to heads, starting with empty heads and proceeding sequentially to the heads with the fewest points. When the allocation process is complete, the heads with the most and least points are divided equally, which is accepted if the efficiency gain from reducing the number of cycles after equalization outweighs the efficiency loss from increasing nozzle changes. This process is repeated to increase the number of heads of the nozzle with the most head-averaged points, and the total number of nozzle changes is recorded.
+
+\begin{algorithm}
+    \footnotesize
+    \caption{Nozzle Change Computation Heuristic}
+    \label{nozzle_change_heuristic}
+    \SetKwInOut{Input}{Input}\SetKwInOut{Output}{Output}
+    \SetKwProg{Fn}{function}{}{end}
+    \Input{Nozzle heads $\gamma$, component points $\phi$}
+    \Output{Number of nozzle changes $N^{*}$}
+    Set $1 \times \left| H \right|$ vector $\mathcal{T} $ of all zeros, $1 \times \left| H \right|$ vector $\mathcal{N}$, $V \leftarrow 0$, $V^{*} \leftarrow \infty$ and $N^{*} \leftarrow 0$; \\
+    \While{$V \leq V^{*}$} {
+    Set $1 \times \gamma_{jm}$ nozzle group $\mathcal{G}_{jm} $ with $ \sum_{i \in I} \phi_i \cdot \xi_{ij} / \gamma_{jm}$ points for $j \in J$ ; \\
+    \For {$n \in \mathcal{G}_{jm}, j \in J$}
+    {
+        \tcc{assign nozzle groups to heads}
+        $h \leftarrow \arg \min_{h^\prime \in H} \left\{\mathcal{T}_h \right\}$,
+        $\mathcal{N}_h \leftarrow j$, $\mathcal{T}_h \leftarrow \mathcal{T}_h + n$
+    }
+    Set number of cycles $V \leftarrow \max_{h \in H} \mathcal{T}_h$ ;\\
+    \While{\rm{\textbf{true}}} 
+    {
+        \tcc{balance the points of heads}
+        $h^\prime \! \leftarrow \! \arg \max_{h \in H} \mathcal{T}_h$ , $ h^{\prime \prime} \! \leftarrow \! \arg \min_{h \in H} \mathcal{T}_h $ ;\\
+        \If { $\mathcal{N}_{h^{\prime}} = \mathcal{N}_{h^{\prime \prime}}$ }
+        {
+            \textbf{break};
+        }
+        \tcc{compare the weighted metrics}
+        $j^\prime \leftarrow \mathcal{N}_{h^\prime}$, $\mathcal{H}_1 \leftarrow \left\{ h \mid \mathcal{N}_h = j^\prime , h \in H \right\} $,
+        $j^{\prime\prime} \leftarrow \mathcal{N}_{h^{\prime\prime}}$, $\mathcal{H}_2 \leftarrow \left\{ h \mid \mathcal{N}_h = j^{\prime\prime} , h \in H \right\} $;
+        \If {$ T_3 \cdot \left( \mathcal{T}_{h^{\prime}} - \mathcal{T}_{h^{\prime\prime}} \right) > T_2 \cdot \left| \left| \mathcal{H}_2 \right| - \left| \mathcal{H}_1 \right| \right| $ }
+        {
+            \textbf{break};
+        }
+        \tcc{update assignment result}
+        $N \leftarrow \left| \left| \mathcal{H}_2 \right| - \left| \mathcal{H}_1 \right| \right|$, $V \leftarrow V - T_3 \cdot \left( \mathcal{T}_{h^{\prime}} -\mathcal{T}_{h^{\prime\prime}} \right) + T_2 \cdot N $,
+        $\mathcal{T}^\prime \leftarrow \mathcal{T}$; \\
+        \For{$h \in \mathcal{H}_1 \cup \mathcal{H}_2$}
+        {
+            $\mathcal{T}_h \leftarrow \sum_{h^{\prime} \in \mathcal{H}_1 \cup \mathcal{H}_2} \mathcal{T}^{\prime}_{h^{\prime}} / \left( \left| \mathcal{H}_1 \right| + \left| \mathcal{H}_2 \right| \right)$, $\mathcal{N}_h \leftarrow j^{\prime}$;\ \\
+        }
+    }
+    \If { $V < V^{*}$ }
+    {
+        $V^{*} \leftarrow V$, $N^{*} \leftarrow N$, $\gamma_{j^\prime m} \leftarrow \gamma_{j^\prime m} + 1$ ; \tcp{add nozzle groups and re-allocate}
+    }
+    }
+\end{algorithm}
+
+\begin{algorithm}
+    \footnotesize
+    \caption{Duplicated Component Points Allocation Algorithm}
+    \label{cluster_algorithm}
+    \SetKwInOut{Input}{Input}\SetKwInOut{Output}{Output}
+    \Input{Number of feeders $\theta$, component-point compatibility $\mu$, points position $\left(x, y\right)$, machine-component assignment $u$ and $r$}
+    \Output{Machine-allocated points $\overline{\mathcal{P}}$}
+    Set machine-assigned sets $\mathcal{P}_m \leftarrow \varnothing$, number of machine-head assigned points $\mathcal{V}_{ihm} \leftarrow 0$ and head-derivation $\overline{h}_{im} \leftarrow 0$, $\forall i \in I, h \in H, m \in M$ ;\\
+    Set $\rho_h$ as the interval distance between head $h$ and
+    left-most head ;\\
+    % Set machine-head assigned point $\mathcal{V}_{ihm} \leftarrow 0$ ;\\
+    \For{$m \in M$}
+    {
+        \For{$i \in \left\{ i^\prime \mid r_{i^\prime m} > 0, \theta_{i^\prime} = 1, i^\prime \in I \right\}$}
+        {
+            $\mathcal{P}_m \leftarrow \mathcal{P}_m \cup \left\{ p \mid \mu_{ip} = 1, p \in P\right\}$ ; \\
+        }
+        \For{$i\leftarrow \sum_{i^\prime \in I} i^\prime \cdot u_{i^\prime khm}$, $k \in K$, $h \in H$}
+        {
+            $\mathcal{V}_{ihm} \leftarrow \mathcal{V}_{ihm} + 1$, $\overline{h}_{im} \leftarrow \left( 1 - 1 / \sum_{h \in H} \mathcal{V}_{ihm} \right) \cdot \overline{h}_{im} + \left(h - 1\right) / \sum_{h \in H} \mathcal{V}_{ihm}  $\\
+        }
+        Set center points of each machine $\mathcal{X}_m \leftarrow \sum_{p \in \mathcal{P}_m} $
+
+        $ \left(x_p - \sum_{i \in I} \mu_{ip} \cdot \overline{h}_{im}  \right) / \left| \mathcal{P}_m \right| , \mathcal{Y}_m \leftarrow \sum_{p \in \mathcal{P}_m} y_p / \left| \mathcal{P}_m \right| $  ; \\
+    }
+    \While{\rm{\textbf{true}}}
+    {
+        $\overline{\mathcal{X}} \leftarrow \mathcal{X}$, $\overline{\mathcal{Y}} \leftarrow \mathcal{Y}$, $\overline{\mathcal{V}} \leftarrow \mathcal{V}$,
+        $\overline{\mathcal{P}} \leftarrow \mathcal{P}$ ; \\
+        \For {$p \in \left\{ p^\prime \mid p^\prime \in P_i, \theta_i > 1 \right\}, i \in I$}
+        {
+            Set $\left(\hat{m}, \hat{h} \right)  \leftarrow \arg \min_{m \in M, h \in H} \left\{ \left(\overline{\mathcal{X}}_{m} - x_p  + \rho_h \right)^2
+            \right.$ $\left.+ \left(\overline{\mathcal{Y}}_{m} - y_p \right)^2 \mid \overline{\mathcal{V}}_{ihm} > 0  \right\}$ as the allocated machine,
+            $\overline{\mathcal{P}}_{\hat{m}} \leftarrow \overline{\mathcal{P}}_{\hat{m}}\cup \left\{ p \right\} $ ,
+            $\overline{\mathcal{V}}_{i{\hat{h}}{\hat{m}}} \leftarrow \overline{\mathcal{V}}_{i{\hat{h}}{\hat{m}}} - 1$ \;
+            \tcc{update number of assigned points and center
+            of surface mounters}
+            $\overline{\mathcal{X}}_{\hat{m}} \leftarrow \overline{\mathcal{X}}_{\hat{m}} + \left(x_p - \overline{\mathcal{X}}_{\hat{m}} - \rho_{\hat{h}} \right) / \left| \overline{\mathcal{P}}_{\hat{m}} \right|$,
+            $\overline{\mathcal{Y}}_{\hat{m}} \leftarrow \overline{\mathcal{Y}}_{\hat{m}} + \left(y_p - \overline{\mathcal{Y}}_{\hat{m}} \right) / \left| \overline{\mathcal{P}}_{\hat{m}} \right|$;
+        }
+        \If{$\sum_{m \in M}\left( \left| \overline{\mathcal{X}}_m - \mathcal{X}_m  \right| + \left| \overline{\mathcal{Y}}_m - \mathcal{Y}_m \right| \right) < 10^{-3}$}
+        {
+        \textbf{break};
+        }
+    }
+\end{algorithm}
+
+\subsection{Heuristics for Component Duplication}
+Components with multi-available feeders can be assigned to more than one surface mounter, which is called a duplicated condition.
+To deal with this case, in this section the algorithm is improved in two ways. Firstly, components are grouped to meet the needs of distributing multiple machines.
+Equation~\eqref{div-threshold-equation} gives threshold $\hat{\theta}_i$, above which components with more points are to be split.
+\begin{equation}
+    \hat{\theta}_i =  \max \left( \varepsilon \cdot \sum_{i^\prime \in I} \theta_{i^\prime} \cdot \phi_{i} / \sum_{i^\prime \in I} \phi_{i^\prime}, \theta_i \right) \quad \forall i \in I
+    \label{div-threshold-equation}
+\end{equation}
+where $\varepsilon$ regulates the number of groups.
+This grouping strategy balances search efficiency and diversity.
+Besides, the set of feasible surface mounters is updated synchronously in the allocation process.
+
+Secondly, the distribution of points has an impact on assembly efficiency, and an aggregative grouping is proposed in Algorithm~\ref{cluster_algorithm}.
+Component allocation determines the upper number of placement points of each type assigned to each surface mounter.
+The initial aggregated center of each machine is determined by the components with a single feeder.
+Current research~\cite{gao_hierarchical_2021,lu_scan_based_2023} divides surface mounter optimization into head task assignment and pick-and-place sequencing, where the former determines the head-deviation $\overline{h}$ for the alignment of the heads.
+The adjustment of the group center helps to shorten the moving path of the linear head and improve assembly efficiency.
+
+\begin{table}
+    \centering
+    \caption{Hyper-Heuristic and Estimator Parameters}
+    \label{experiment_parameter}
+    \renewcommand\arraystretch{1.2}
+    \begin{tabular}{p{1.5cm}<{\centering}p{4cm}<{\centering}p{1.1cm}<{\centering}}
+    \toprule
+    Method & \makecell[c]{Parameters} & Value \\
+    \midrule
+    \multirow{5}{*}{\shortstack{Hyper\\Heuristic}} & Size of Population  & 10 \\
+    & Threshold Parameter & 1.5 \\
+    & Num. of Individuals in Population & 20 \\
+    & Crossover \& Mutation Rate & 0.6 \& 0.1 \\
+    & Number of Iterations & 50  \\
+    \cmidrule(lr){1-3}
+    \multirow{2}{*}{Estimator} & Learning Rate & $10^{-5}$ \\
+    & Number of Epochs & 8000 \\
+    \bottomrule
+    \end{tabular}
+\end{table}
+
+\section{Comparative Experiments}\label{experiment_section}
+\subsection{Experimental Setup}
+
+Experiments have been carried out using a PC with an Intel(R) Core(TM) i5-14600KF. Table~\ref{experiment_parameter} shows the parameter settings of the hyper-heuristic and estimator.
+Iterations are carried out across populations with ten randomly generated component allocation sequences.
+The multiplier of component grouping is set to 1.5.
+The time estimator is a two-middle-layer fully connected NN with 1,000 neurons per layer and ReLu is used as the activation function. Results are compared for PCB assembly lines \emph{L}1, \emph{L}2, and \emph{L}3, equipped with 2, 3, and 4 surface mounters, respectively. Fifteen PCB data from actual manufacturing lines are used to evaluate the assembly efficiency of the algorithm, with the first five being on a smaller scale, as shown in Table~\ref{pcbdata_parameter}.  As meta-heuristic results are random, the average of the five runs is taken as the result.
+
+Training and testing data for time estimation fitting are randomly generated, and assembly times are obtained from the built-in simulator of the surface mounter, which is accurate for performing optimization and full assembly process simulation.
+The distribution of placement points impacts assembly efficiency. Training data with either sparse or concentrated distribution can reduce the generalization performance of the estimator, which can be refined by fitting randomly generated points with relatively uniform distribution.
+Table~\ref{data_parameter} shows statistical PCB data. Data outliers are detected and removed using the inter-quartile range rule~\cite{li_predicting_2020} with a multiplier of 0.6. Training and testing data have similar distribution characteristics.
+
+\begin{table*}
+    \centering
+    \caption{Statistical PCB data}
+    \label{pcbdata_parameter}
+    \renewcommand\arraystretch{1.2}
+    \begin{tabular}{p{2.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}|p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.5cm}<{\centering}p{0.6cm}<{\centering}}
+    \toprule
+    PCB & 1-1 & 1-2 & 1-3 & 1-4 & 1-5 & 2-1 & 2-2 & 2-3 & 2-4 & 2-5 & 2-6 & 2-7 & 2-8 & 2-9 & 2-10 \\
+    \midrule
+    Num. of Comp. Type & 4 & 4 & 5 & 5 & 5 & 16 & 29 & 7 & 24 & 45 & 7 & 47 & 40 & 10 & 40\\
+    Num. of Nozzle Type & 3 & 3 & 3 & 2 & 2 & 3 & 3 & 3 & 3 & 4 & 4 & 4 & 2 & 3 & 4 \\
+    Number of Points & 28 & 34 & 34 & 30 & 30 & 78 & 165 & 192 & 236 & 209 & 320 & 390 & 546 & 720 & 1510 \\
+    Number of Feeders & 10 & 6 & 8 & 7 & 5 & 19 & 30 & 12 & 28 & 47 & 14 & 54 & 50 & 19 & 40\\
+    \bottomrule
+    \end{tabular}
+\end{table*}
+
+\begin{table}
+    \centering
+    \caption{Parameters of Training and Testing Data}
+    \label{data_parameter}
+    \renewcommand\arraystretch{1.2}
+    \begin{tabular}{p{0.75cm}p{1.6cm}<{\centering}p{1.5cm}<{\centering}p{1.4cm}<{\centering}p{1.4cm}<{\centering}}
+    \toprule
+    \multirow{4}{*}{\makecell[c]{Training\\Sets}} & \# of Samples & Outlier (\%) & Mean & Median \\
+    % \cmidrule{1-5}
+    \cmidrule(lr){2-5}
+    & 2000 & 11.25 & 128.67 & 130.13 \\
+    & Minimum & Maximum & Std. Dev & \\
+    \cmidrule(lr){2-4}
+    & 2.71 & 302.94 & 71.67 & \\
+    \midrule
+    \multirow{4}{*}{\makecell[c]{Testing\\Sets}} & \# of Samples & Outlier (\%) & Mean & Median \\
+    \cmidrule(lr){2-5}
+    & 400 & 10.75 & 126.76 & 127.11 \\
+    & Minimum & Maximum & Std. Dev & \\
+    \cmidrule(lr){2-4}
+    & 3.80 & 311.38 & 72.23 & \\
+    \bottomrule
+    \end{tabular}
+\end{table}
+
+\subsection{Comparison of HHO-MFFEE and Mathematical Model}
+
+Mathematical programming is used to find optimal solutions, but only for small-scale data. In this section, the solutions obtained by HHO-MFFEE are compared with the approximated optimal solutions of the model, which is built by extracting key metrics that affect
+assembly efficiency. The model is validated using the Gurobi solver~\cite{gurobi}. To make the model linear and solvable, it is assumed that enough nozzles are available. In addition, placement priority constraints are ignored. The weights of the model are set using a linear fit to the training data, with $T_1 = 0.041$, $T_2 = 0.326$, $T_3 = 0.870$, $T_4 = 0.159$ and $T_5 = 0.015$. The effect of the layout of points on assembly efficiency is ignored. Table~\ref{model_comparison_table} presents the comparison of the first five data. $T_M$ and $T_H$ represent the weighted performance metrics of the model and the proposed algorithm, respectively. Gap $\delta T = \left( T_H / T_M - 1 \right) \cdot 100 \% $ with respect to the optimal solution of the model is 7.28\%, 6.58\%, and 3.44\% on average in 3 assembly lines. Comparison with the model reveals that the proposed algorithm is close to the optimal solution, with a maximum gap of 12.10\%. The performance of the hyper-heuristic algorithm is comparable to that of the model solution, and its higher solving efficiency makes it possible to apply it to larger-scale data.
+
+\begin{table}
+    \centering
+    \caption{Weighted Key Metrics Indicators of the Mathematical Model and the Proposed  HHO-MFFEE Algorithm}
+    \renewcommand\arraystretch{1.2}
+    \begin{tabular}{p{0.38cm}<{\centering}p{0.38cm}<{\centering}p{0.38cm}<{\centering}p{0.65cm}<{\centering}p{0.38cm}<{\centering}p{0.38cm}<{\centering}p{0.65cm}<{\centering}p{0.38cm}<{\centering}p{0.38cm}<{\centering}p{0.55cm}<{\centering}}
+    \toprule
+    \multirow{2}{*}{Line} & \multicolumn{3}{c}{\emph{L}1} & \multicolumn{3}{c}{\emph{L}2} & \multicolumn{3}{c}{\emph{L}3} \\
+    \cmidrule(lr){2-4} \cmidrule(lr){5-7} \cmidrule(lr){8-10}
+    & $T_M$ & $T_H$ & $\delta T (\%) $  & $T_M$ & $T_H$ & $\delta T(\%)$ & $T_M$ & $T_H$ & $\delta T (\%)$\\
+    \midrule
+    1-1 & 2.585 & 2.626 & 1.59 & 1.758 & 1.837 & 4.49 & 1.676 & 1.813 & 8.17 \\
+    1-2 & 3.286 & 3.672 & 11.75 & 2.785 & 3.122 & 12.10 & 2.473 & 2.514 & 1.66 \\
+    1-3 & 2.719 & 2.998 & 10.26 & 2.218 & 2.445 & 10.23 & 1.947 & 2.054 & 5.50 \\
+    1-4 &2.744 & 3.017 & 9.95 & 2.202 & 2.314 & 5.09 & 2.202 & 2.243 & 1.86 \\
+    1-5 & 2.933 & 3.017 & 2.86 & 2.432 & 2.456 & 0.99 & 2.432 & 2.432 & 0.00 \\
+    \midrule
+    Avg & & & 7.28 & & & 6.58 & & & 3.44 \\
+    \bottomrule
+    \label{model_comparison_table}
+    \end{tabular}
+\end{table}
+
+\subsection{Evaluation of the Proposed Time Estimator}
+The accuracy of the time estimator impacts the search direction for component allocation, as well as the quality of solutions. In this subsection, four different time estimators are compared with the proposed one, which yields $E_1$. $E_2$ refers to the ensemble fitting method using basic parameters, without the target related terms, which is another way of encoding. Results for the heuristic estimators proposed in~\cite{guo_integrated_2012} and~\cite{toth_reconfiguring_2010} are denoted as $E_3$ and $ E_4$, respectively, with coefficients computed using the least squares method. $E_5 $ refers to an ensemble algorithm with symbiotic organism search-based support vector regression (SOS-based SVR)~\cite{li_predicting_2020}.
+
+Mean and maximum absolute errors of training and testing data are listed in Table~\ref{estimator_comparison}. The performance of the fitting method on the testing set is the basis for evaluating the accuracy of the estimators. The two NN-related methods provide better time estimation.
+The proposed estimator encoding method reduces the average absolute error on the testing set from 5.16\% to 3.43\%, compared to simply feeding basic parameters. The number of pick-ups is not incorporated in the two heuristic-based linear regression fittings, resulting in poorly fitted results with mean absolute errors of 9.41\% and 9.44\%, respectively. Despite being effective in the workshop production line of the PCB assembly process, the SOS-based SVR has the lowest fitting accuracy, as it ignores the distinctive properties of each single PCB.
+
+\begin{table}
+    \centering
+    \renewcommand\arraystretch{1.2}
+    \caption{Estimated Accuracy of the Tested Algorithms}
+    \label{estimator_comparison}
+    \begin{tabular}{p{0.8cm}<{\centering}p{3cm}<{\centering}p{0.35cm}<{\centering}p{0.35cm}<{\centering}p{0.35cm}<{\centering}p{0.35cm}<{\centering}p{0.6cm}<{\centering}}
+    \toprule
+    Set & Parameters & $E_1$ & $E_2$ & $E_3$ & $E_4$ & $E_5$ \\
+    \midrule
+    %   \textbf{Training Set} & & & & & \\
+    \multirow{2}{*}{Training} & Mean Absolute Error (\%) & 2.01 & 5.09 & 8.75 & 8.75 & 45.30 \\
+    & Max. Absolute Error (\%) & 18.80 & 21.28 & 37.61 & 37.68 & 214.94 \\
+    \cmidrule(lr){1-7}
+    \multirow{2}{*}{Testing} & Mean Absolute Error (\%) & 3.43 & 5.16 & 9.41 & 9.44 & 45.99 \\
+    & Max. Absolute Error (\%) & 16.57 & 18.65 & 27.65 & 28.82 & 183.98\\
+    \bottomrule
+    \end{tabular}
+\end{table}
+
+\subsection{Comparison of Low-level Heuristics}
+Ten PCBs are used to compare the performances of individual LLHs in \emph{L}2. Table~\ref{llhs_performance_table} shows optimization results of load allocation. $A_p$, $A_n$, $A_c$ and $A_r$ are the data-driven LLHs, i.e., Minimum Points, Minimum Nozzle Types, Minimum Component Types, and Minimum Ratio, respectively. $A_k$, $A_g$ and $A_u$ are the target-driven LLHs, i.e., Minimum Cycle, Minimum Nozzle Change, and Minimum Pick-up, respectively. Both $A_p$ and $A_k$ achieve higher assembly efficiency by more balanced cycles and placement points. Results of LLHs that indirectly affect efficiency or single-objective related have low efficiency. All single-LLHs fail to achieve the hyper-heuristic effect. 
+\begin{table}
+    \centering
+    \caption{Solutions Obtained by Various LLHs}
+    \label{llhs_performance_table}
+    \renewcommand\arraystretch{1.2}
+    \begin{tabular}{p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}}
+    \toprule
+    PCB & $A_p$ & $A_n$ & $A_c$ & $A_r$ & $A_k$ & $A_g$ & $A_u$ \\
+    \midrule
+    2-1 & 10.06  & 10.26  & 9.52  & 9.88  & 9.72  & 9.79  & 10.70   \\
+    2-2 & 15.38  & 18.28  & 16.12  & 19.97  & 14.75  & 17.66  & 16.01   \\
+    2-3 & 20.46  & 20.48  & 20.00  & 23.06  & 20.10  & 22.81  & 19.18   \\
+    2-4 & 18.98  & 25.97  & 19.87  & 26.24  & 21.17  & 27.06  & 22.84   \\
+    2-5 & 22.36  & 28.25  & 26.14  & 29.64  & 21.13  & 32.34  & 22.94   \\
+    2-6 & 28.81  & 35.23  & 28.79  & 38.40  & 28.78  & 33.84  & 27.69   \\
+    2-7 & 46.21  & 45.29  & 40.47  & 51.13  & 42.57  & 45.42  & 43.27   \\
+    2-8 & 52.07  & 59.06  & 50.44  & 59.39  & 51.73  & 63.46  & 49.05    \\
+    2-9 & 66.93  & 67.80  & 65.82  & 84.64  & 65.98  & 68.50  & 65.42 \\
+    2-10 & 135.68  & 143.67  & 143.01  & 168.83  & 139.76  & 146.01  & 149.82 \\
+    \bottomrule
+    \end{tabular}
+\end{table}
+
+\begin{figure}
+    \centering
+    \includegraphics[scale=0.28]{figure/heuristic-ratio.eps}
+    \caption{Ratio of each LLH when using the hyper-heuristic.}
+    \label{heuristic-ratio-figure}
+\end{figure}
+The ratio of each LLH when using the hyper-heuristic is shown in Fig.~\ref{heuristic-ratio-figure}. Balancing the number of placement points among surface mounters is the main task of optimization. The ratio of target-driven operators is higher than that of data-driven ones in the remaining LLHs. Nozzle change-related term $A_g$ occurs less frequently in the assembly process. Thus, for most data, the pickup-related $A_u$ is more relevant in the search process.
+\subsection{Comparison with Other Algorithms}
+The main task of the line optimizer is to allocate components to machines. In this subsection, the proposed algorithm is compared with three state-of-the-art solutions, namely an industrial solver released in 2022 by an advanced manufacturer, the integrated algorithm~\cite{guo_integrated_2012}, and the hybrid algorithm~\cite{toth_reconfiguring_2010}.
+The industrial solver is an optimizer embedded in an integrated production line management tool for surface-mount assembly lines.
+The integrated algorithm is a genetic-based method that provides solutions for PCB assembly lines by designing operators to search the feasible domain.
+The hybrid algorithm combines random search, local search, and evolutionary algorithms, among others. Since the spider monkey algorithm has been widely used in PCB assembly line optimization~\cite{chen_improved_2023,mumtaz_hybrid_2020,zhong_multi-objective_2022}, this section further integrates it into the hybrid framework and improves it based on the coding and searching approaches proposed in~\cite{chen_improved_2023,zhong_multi-objective_2022}.
+The industrial solver provides complete solutions from assembly line balancing to surface mounter optimization, and the rest of the single-machine optimizations are based on the methods proposed in~\cite{lu_scan_based_2023}.
+
+Table~\ref{assembly_time_comparison_table} shows the optimization results of the four tested algorithms. The proposed hyper-heuristic algorithm outperforms the industrial solver, and the hybrid and integrated algorithms by 7.21\%, 8.67\%, and 9.47\%, respectively. In addition, the distribution of the optimization results in three assembly lines are shown in Fig.~\ref{assembly_efficiency_figure}. In algorithms with randomized results, the hyper-heuristic produces a more consistent result. In most cases, the results of a single run of the hyper-heuristic outperform those of the other methods. Even if it produces some weaker solutions, the vast majority of them outperform the best solutions from the other methods.
+\begin{table*}
+    \caption{Assembly Times of the Tested Algorithms}
+    \label{placement_route_table}
+    \centering
+    \renewcommand\arraystretch{1.2}
+    \begin{tabular}{
+    p{0.6cm}<{\centering}
+    p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}
+    p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.85cm}<{\centering}
+    p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.85cm}<{\centering}
+    p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.6cm}<{\centering}p{0.85cm}<{\centering}
+    }
+    \toprule
+    & \multicolumn{3}{c}{Hyper Heuristic} & \multicolumn{4}{c}{Industrial Solver} & \multicolumn{4}{c}{Hybrid Algorithm} & \multicolumn{4}{c}{Integrated Algorithm} \\
+    \cmidrule(lr){2-4} \cmidrule(lr){5-8} \cmidrule(lr){9-12} \cmidrule(lr){13-16}
+    PCB& \emph{L}1 & \emph{L}2 & \emph{L}3 & \emph{L}1 & \emph{L}2 & \emph{L}3 & $\delta$ (\%) & \emph{L}1 & \emph{L}2 & \emph{L}3 & $\delta$ (\%) & \emph{L}1 & \emph{L}2 & \emph{L}3 & $\delta$ (\%)  \\
+    \midrule
+    2-1 & 10.14  & 8.06  & 6.21  & 12.91  & 8.41  & 6.56  & 12.46  & 10.91  & 9.42  & 7.17  & 13.28  & 14.97  & 8.41  & 6.83  & 20.66  \\
+    2-2 & 19.55  & 14.28  & 11.61  & 20.78  & 14.75  & 12.95  & 7.01  & 19.89  & 14.93  & 12.42  & 4.42  & 20.61  & 14.75  & 12.35  & 5.01  \\
+    2-3 & 21.15  & 18.06  & 12.59  & 21.19  & 18.77  & 14.44  & 6.26  & 23.39  & 18.26  & 14.92  & 10.06  & 23.18  & 18.77  & 14.72  & 10.14  \\
+    2-4 & 26.10  & 17.85  & 13.87  & 26.29  & 18.66  & 13.96  & 1.95  & 28.14  & 19.17  & 14.38  & 6.30  & 29.37  & 18.66  & 14.86  & 8.06  \\
+    2-5 & 27.86  & 19.33  & 15.35  & 32.32  & 19.59  & 15.79  & 6.75  & 33.48  & 21.29  & 16.89  & 13.46  & 32.57  & 19.59  & 16.66  & 8.95  \\
+    2-6 & 38.63  & 26.53  & 22.83  & 44.42  & 27.91  & 23.02  & 7.00  & 39.11  & 27.34  & 22.44  & 0.86  & 45.05  & 27.91  & 24.22  & 9.30  \\
+    2-7 & 50.15  & 34.12  & 26.23  & 53.91  & 36.93  & 26.85  & 6.04  & 58.73  & 40.79  & 29.72  & 16.66  & 57.76  & 36.93  & 31.32  & 14.28  \\
+    2-8 & 71.32  & 48.08  & 39.42  & 73.96  & 51.16  & 40.18  & 4.01  & 72.02  & 51.91  & 40.28  & 3.70  & 75.09  & 51.16  & 42.76  & 6.72  \\
+    2-9 & 85.69  & 60.91  & 46.07  & 91.18  & 63.91  & 52.57  & 8.48  & 94.66  & 66.08  & 53.05  & 11.36  & 91.95  & 63.91  & 47.10  & 4.82  \\
+    2-10 & 176.99  & 117.93  & 90.78  & 179.94  & 125.79  & 116.23  & 12.12  & 185.07  & 128.07  & 96.73  & 6.57  & 188.01  & 125.79  & 97.54  & 6.78  \\
+    \midrule
+    Avg & ~ & ~ & ~ & ~ & ~ & ~ & 7.21  & ~ & ~ & ~ & 8.67  & ~ & ~ & ~ & 9.47 \\
+    \bottomrule
+    \label{assembly_time_comparison_table}
+    \end{tabular}
+\end{table*}
+
+\begin{figure*}
+    \begin{minipage}{0.33\linewidth}
+        \vspace{2pt}
+        \centerline{\includegraphics[width=\textwidth]{figure/assembly-efficiency-L01.eps}}
+        \centerline{\emph{L}1}
+    \end{minipage}
+    \begin{minipage}{0.33\linewidth}
+        \vspace{2pt}
+        \centerline{\includegraphics[width=\textwidth]{figure/assembly-efficiency-L02.eps}}
+        \centerline{\emph{L}2}
+    \end{minipage}
+    \begin{minipage}{0.33\linewidth}
+        \vspace{2pt}
+        \centerline{\includegraphics[width=\textwidth]{figure/assembly-efficiency-L03.eps}}
+        \centerline{\emph{L}3}
+    \end{minipage}
+    \caption{Distribution of optimization results of the tested algorithms on three PCB assembly lines.}
+    \label{assembly_efficiency_figure}
+\end{figure*}
+\subsection{Analysis of Solving Efficiency}
+Solving efficiency is one of the most important performance indicators for large-scale combinatorial optimization problems. Solving times for PCBALS using three of the tested algorithms are shown in Table~\ref{solving_time_comparison_table}.
+The industrial solver is not included in the comparison, because it is built into a runtime software package, which includes importing data, optimizing, and outputting results, so its solving times cannot be separated from the rest for fair comparison. The hybrid algorithm consists of relatively basic operators, which allow it to search quickly at the cost of solution quality. The hyper-heuristic and integrated algorithms use a more complex time-fitting approach and account for component duplication, resulting in longer times than that of the hybrid algorithm.
+The proposed HHO-MFFEE is more efficient than the integrated algorithm, and the quality of the solution it provides is higher. Evaluating the quality of the candidate solutions takes a large part of the solving time of the hyper-heuristic.
+PCB2-5 and PCB2-10 are more complex. Single-machine optimization takes longer for PCBs with a larger number of components and nozzle types, resulting in relatively poor solving efficiency.
+By shortening the execution time of surface mounter optimization, efficiency may be further increased.
+\begin{table}
+    \centering
+    \caption{Solving Times of the Tested Algorithms}
+    \renewcommand\arraystretch{1.2}
+    \begin{tabular}{p{0.55cm}<{\centering}p{0.45cm}<{\centering}p{0.45cm}<{\centering}p{0.45cm}<{\centering}<{\centering}p{0.45cm}<{\centering}p{0.45cm}<{\centering}p{0.45cm}<{\centering}p{0.45cm}<{\centering}p{0.45cm}<{\centering}p{0.45cm}<{\centering}}
+    \toprule
+    & \multicolumn{3}{c}{Hyper Heuristic} & \multicolumn{3}{c}{Hybrid Algorithm} & \multicolumn{3}{c}{Integrated Algorithm} \\
+    \cmidrule(lr){2-4} \cmidrule(lr){5-7} \cmidrule(lr){8-10}
+    PCB & \emph{L}1 & \emph{L}2 & \emph{L}3 & \emph{L}1 & \emph{L}2 & \emph{L}3 & \emph{L}1 & \emph{L}2 & \emph{L}3 \\
+    \midrule
+    2-1 & 17.28  & 20.95  & 24.26  & 15.84  & 18.97  & 21.69  & 54.13  & 59.35  & 62.99  \\
+    2-2 & 33.98  & 31.35  & 30.71  & 63.45  & 63.70  & 68.54  & 64.05  & 68.51  & 75.21  \\
+    2-3 & 13.98  & 15.62  & 19.64  & 26.56  & 32.01  & 37.27  & 50.74  & 54.99  & 63.95  \\
+    2-4 & 21.51  & 23.73  & 26.20  & 9.31  & 11.08  & 12.26  & 64.05  & 68.17  & 76.23  \\
+    2-5 & 100.22  & 81.51  & 87.45  & 23.49  & 28.06  & 32.57  & 85.59  & 90.02  & 96.65  \\
+    2-6 & 21.32  & 18.32  & 21.74  & 49.13  & 56.61  & 65.24  & 63.57  & 67.34  & 73.92  \\
+    2-7 & 93.22  & 70.93  & 68.72  & 12.80  & 14.17  & 16.01  & 100.31  & 96.79  & 104.06  \\
+    2-8 & 40.19  & 42.99  & 38.08  & 55.18  & 59.92  & 65.67  & 91.20  & 95.64  & 104.69  \\
+    2-9 & 29.20  & 27.52  & 30.12  & 40.48  & 48.99  & 55.56  & 89.30  & 92.85  & 101.16  \\
+    2-10 & 135.98  & 76.67  & 76.71  & 25.48  & 24.94  & 24.90  & 144.55  & 155.60  & 171.15 \\
+    \bottomrule
+    \label{solving_time_comparison_table}
+    \end{tabular}
+\end{table}
+
+\section{Conclusion}\label{conclusion_section}
+This article presents HHO-MFFEE, a hyper-heuristic optimization method for PCBALS with a multi-feature fusion ensemble time estimator.
+The hyper-heuristic algorithm is implemented using data- and target-driven LLHs. A min-max mathematical model is built covering the major assembly efficiency metrics. In terms of solution quality, the proposed method has comparable performance to the optimal one obtained by the model when dealing with small-scale data. The strategies for component duplication divide components of the same type, balancing assembly time between machines and improving assembly efficiency. An aggregated grouping algorithm assigns placement points to the specific surface mounters. The proposed time estimators have high fitting accuracy, and coding with approximated sub-objectives further enhances fitting accuracy. The combination of the high accuracy of the estimator with the hyper-heuristic search capability for large domains results in high-quality solutions for PCBALS problems. Compared with industrial solutions and other state-of-the-art algorithms, the proposed one achieves higher assembly efficiency and stable results with acceptable solving times.
+
+Future research will focus on load balancing optimization of flexible PCB assembly lines. For high-mix, low-volume PCB production tasks, its efficiency is affected by the configuration adjustments of surface mounters. This involves the optimization of the scheduling of dynamic production tasks, and enhancing the efficiency of the feeder module changeover, among others, which is beneficial to shorten the productive cycle and reduce storage cost, so that small- and medium-batches can achieve profitability comparable to that of mass manufacturing, and improve the efficiency, robustness, and stability of the assembly line.
+
+\footnotesize
+\bibliographystyle{IEEEtran}
+\bibliography{bibliography/Reference}
+\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,keepaspectratio]{author/Guangyu_Lu.pdf}}]{Guangyu Lu} (Graduate Student Member, IEEE) was born in Taiyuan, China, in 1996. He received the B.E. degree in automation from Dalian Maritime University, Dalian, China, in 2019.
+
+He is currently working toward the Ph.D. degree in control science and engineering with the Harbin Institute of Technology, Harbin, China. His research interests include production scheduling and process optimization.
+\end{IEEEbiography}
+\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,keepaspectratio]{author/Huijun_Gao.pdf}}]{Huijun Gao} (Fellow, IEEE)  received the Ph.D. degree in control science and engineering from the Harbin Institute of Technology, Harbin, China, in 2005.
+    
+From 2005 to 2007, he was a Postdoctoral Researcher with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada. Since 2004, he has been with the Harbin Institute of Technology, where he is currently a Chair Professor and the Director of the Research Institute of Intelligent Control and Systems. His research interests include intelligent and robust control, robotics, mechatronics, and their engineering applications.
+
+Dr. Gao was the Vice President of the IEEE Industrial Electronics Society from 2021 to 2024, and a council member of IFAC from 2017 to 2023. He is/was the Editor-in-Chief of IEEE/ASME TRANSACTIONS ON MECHATRONICS, the Co-Editor-in-Chief of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, and an Associate Editor of Automatica, IEEE TRANSACTIONS ON CYBERNETICS, and IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS. He was the recipient of the 2022 Dr.-Ing. Eugene Mittelmann Achievement Award and the 2023 Norbert Wiener Award. He is a member of the Academia Europaea and a Distinguished Lecturer of the IEEE Systems, Man and Cybernetics Society. He has been an ESI Highly Cited Researcher since 2014. 
+
+\end{IEEEbiography}
+\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,keepaspectratio]{author/Zhengkai_Li.pdf}}]{Zhengkai Li} (Member, IEEE) was born in Jinan, China, in 1991. He received the B.E. degree in detection, guidance, and control technology and the M.E. degree in control engineering from Northwestern Polytechnical University, Xi’an, China, in 2013 and 2016, respectively. He also received the Ph.D. degree in control science and engineering from the Harbin Institute of Technology, Harbin, China, in 2022.
+
+He is currently with the Research Institute of Interdisciplinary Intelligent Science, Ningbo University of Technology, Ningbo, China. His current research interests include scheduling and systems optimization.
+\end{IEEEbiography}
+\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,keepaspectratio]{author/Xinghu_Yu.pdf}}]{Xinghu Yu} (Member, IEEE)   was born in Yantai, China, in 1988. He received the M.M. degree in osteopathic medicine from Jinzhou Medical University, Jinzhou, China, in 2016, and the Ph.D. degree in control science and engineering from the Harbin Institute of Technology, Harbin, China, in 2020. 
+    
+He is currently the Chief Executive Officer of Ningbo Institute of Intelligent Equipment Technology Company Ltd., Ningbo, China. He has authored more than 30 technical papers in refereed international journals and conference proceedings, including IEEE Transactions journals, and holds more than 20 invention patents. His research interests include advanced control, intelligent systems, and biomedical image processing.
+
+\end{IEEEbiography}
+\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,keepaspectratio]{author/Tong_Wang.jpg}}]{Tong Wang} (Senior Member, IEEE) received the M.E. degree in control theory and control engineering from the Liaoning University of Technology, Jinzhou, China, in 2013, and the Ph.D. degree in control science and engineering from the Harbin Institute of Technology (HIT), Harbin, China, in 2017.
+
+He is currently an Associate Professor with HIT. His research interests include fuzzy control, stochastic adaptive control, and networked control.
+\end{IEEEbiography}
+\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,keepaspectratio]{author/Jianbin_Qiu.pdf}}]{Jianbin Qiu} (Fellow, IEEE) received the B.Eng. and Ph.D. degrees in Mechanical and Electrical Engineering from the University of Science and Technology of China, Hefei, China, in 2004 and 2009, respectively. He also received the Ph.D. degree in Mechatronics Engineering from the City University of Hong Kong, Kowloon, Hong Kong, in 2009.
+
+He is currently a Full Professor at the School of Astronautics, Harbin Institute of Technology, Harbin, China. He was an Alexander von Humboldt Research Fellow at the Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Duisburg, Germany. His current research interests include intelligent and hybrid control systems, signal processing, and robotics.
+
+Prof. Qiu serves as the Chair of the IEEE Industrial Electronics Society Harbin Chapter, China. He is an Associate Editor of IEEE TRANSACTIONS ON FUZZY SYSTEMS, IEEE TRANSACTIONS ON CYBERNETICS, and IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS.
+\end{IEEEbiography}
+\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,keepaspectratio]{author/Juan_J.Rod-And.jpg}}]{Juan J. Rodr\'{i}guez-Andina} (Fellow, IEEE)  received the M.Sc. degree from the Technical University of Madrid, Madrid, Spain, in 1990, and the Ph.D. degree from the University of Vigo, Vigo, Spain, in 1996, both in electrical engineering.
+
+He is currently a Professor with the Department of Electronic Technology, University of Vigo, and also with the Research Institute of Interdisciplinary Intelligent Science, Ningbo University of Technology, Ningbo, China. From 2010 to 2011, he was on sabbatical leave as a Visiting Professor with the Advanced Diagnosis, Automation, and Control Laboratory, North Carolina State University, Raleigh, NC, USA. From 2015 to 2017, he delivered summer courses at Harbin Institute of Technology, Harbin, China. His research interests include the implementation of complex control and processing algorithms and intelligent sensors in embedded platforms. He has authored more than 180 journal and conference articles and holds several Spanish, European, and U.S. patents.
+
+Prof. Rodr\'{i}guez-Andina is a co-author of the articles awarded the 2023 IEEE Transactions on Industrial Electronics Outstanding Paper Award and the 2017 IEEE Industrial Electronics Magazine Best Paper Award. He received the 2020 Anthony Hornfeck Award from the IEEE Industrial Electronics Society. From 2016 to 2021, he was the Vice President for Conference Activities of the IEEE Industrial Electronics Society. He served as the Editor-in-Chief for IEEE INDUSTRIAL ELECTRONICS MAGAZINE, from 2013 to 2015, and as an Associate Editor for IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, from 2008 to 2018, and IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, from 2011 to 2022. He is currently serving as a Co-Editor-in-Chief for IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and as an Associate Editor for IEEE OPEN JOURNAL OF THE INDUSTRIAL ELECTRONICS SOCIETY.
+\end{IEEEbiography}
+\end{document}