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% !Mode:: "TeX:UTF-8"
\hitsetup{
%******************************
% 注意：
% 1. 配置里面不要出现空行
% 2. 不需要的配置信息可以删除
%******************************
%
%=====
% 秘级
%=====
statesecrets = {公开},
natclassifiedindex = {TP273},
intclassifiedindex = {681.5},
%
%=========
% 中文信息
%=========
ctitlecover={表面组装过程中生产效率提升的关键\\优化方法研究},%放在封面中使用，自由断行
ctitle={表面组装过程中生产效率提升的关键优化方法研究},%放在原创性声明中使用
cxueke = {工学},
csubject = {控制科学与工程},
caffil = {航天学院},
cauthor = {卢光宇},
csupervisor = {高会军~教授},
% 日期自动使用当前时间，若需指定按如下方式修改：
cdate = {2025年4月},
cstudentid = {20B904007},
cstudenttype={学术学位论文},
cnumber = {no9527}, %编号
%（同等学力人员）、（工程硕士）、（工商管理硕士）、
%（高级管理人员工商管理硕士）、（公共管理硕士）、（中职教师）、（高校教师）等
%
%
%=========
% 英文信息
%=========
etitle = {The key optimization method for productivity improvement in surface assembly process},
%esubtitle = {This is the sub title},
exueke = {Engineering},
esubject = {Control Science and Engineering},
eaffil = {School of Aerospace},
esupervisor = {Prof. Huijun Gao},
eauthor = {Guangyu Lu},
eassosupervisor = {},
% 日期自动生成，若需指定按如下方式修改：
edate={April, 2025},
ckeywords={表面组装过程优化；贴片头任务分配；多轴路径规划；组装线负载平衡；启发式优化；数学规划法},
ekeywords={Surface assembly process optimization, placement head task allocation, multi-axis path planning, assembly line load balancing, heuristic optimization, mathematical programming},
}
\begin{cabstract}
表面组装过程优化是电子制造业赋能提效的关键技术，其中涉及的电路板元件组装过程的调度和规划，是综合了仓库选址、任务分配与路径规划的高维组合优化问题，具有多变量、多约束及高耦合性的复杂特性。本文所研究的装配有并列式贴片头的贴片机，因具备组装多种类型元件的能力而得到了广泛的应用。然而，现有研究并未充分考虑组装任务多样性、生产配置差异性及贴片头并列分布结构，导致其适用场景受限、组装效率有待提升。本文根据优化任务主要环节之间的关联性，将其分解为贴片头任务分配、贴装过程路径规划以及组装线负载平衡三个子问题，并分阶段地构建数学规划模型和设计具有普适性的高效表面组装过程优化方法。
首先，本文对组装过程的问题特性和任务分解方法进行了研究，分析了作业完整性、拾取过程一致性和工具适配性等约束条件，提出了基于关键子目标分解的贴片头任务分配模型，其子目标涵盖贴片头的拾贴元件动作、更换吸嘴动作以及组装过程往复运动等环节；在贴片头任务的约束下，进一步构建了多周期的贴装过程路径规划模型。此外，依据关键子目标加权效率评估、生产线中的可用工具和拾贴优先级等约束条件，本文建立了组装生产线的负载平衡模型。分阶段模型可用于求解小规模子问题的最优解，并为解决大规模问题的启发式算法设计提供了参考基准。
在任务分配阶段，本文分别从数学规划法和启发式算法的角度开展了研究，旨在通过优化关键效率指标提升贴片机拾取过程的效率，保证了组装过程整体解的高质量。通过构建基于周期任务集成的整数线性规划模型，实现了解空间的系统搜索。本文提出了递归启发式算法确定模型初始解，并通过限制决策变量的规模和缩小可行域的范围，提升模型的求解效率。同时，一种带有路径预判的启发式策略用于从解集池中筛选解，降低其与后续子问题之间的耦合性。为解决更大规模的问题，提出了基于分层启发式前瞻扫描的贴片头任务分配算法，拆解原问题为供料器-槽位分配和贴片头-元件分配问题，并设计了具有相似搜索架构的分层解决方案。本文从构造吸嘴分配模式出发，设计了最大化拾取过程效率的供料器分配启发式、以及对应的贴片头元件分配算法，综合了拾取可行性、工具可用性以及前瞻性收益等多个方面，平衡了拾取过程的长期与短期收益，适配了不同的生产配置。
在路径规划阶段，本文研究贴装过程的路径规划启发式方法，确保了不同贴片头任务分配约束下解的高质量，提升了贴装过程的效率。本文提出了适用于多轴作业的动态规划路径规划算法，保证了单个周期内解的最优性；为确定贴片头分配的贴装点，提出了多源贪心的动态导向集束搜索策略，将贪心准则应用于多作业区域并行搜索的过程中，增强了解的多样性。动态导向的集束搜索机制通过维持一组非最优的候选解和调整搜索方向，拓宽了搜索范围、提升了解的质量。进一步地，本文提出了基于自适应大邻域搜索的聚合路径重构算法，依据已有解的贴装点分布特征，自适应地调整路径结构，解决了贪心式搜索仅关注当前周期解局部最优的问题，用于在线迭代改进路径规划解。
在负载平衡阶段，本文构建了基于多特征融合集成组装时间估计器的超启发式元件分配算法，通过平衡多台贴片机的工作负载，提高了生产线的组装效率。其中，以集成学习为框架的估计器用于评估解的质量，融合了组装任务的基本参数以及启发式预估的子目标等多维特征，实现了组装时间的快速准确评估。贴片机-元件分配算法由数据驱动和目标驱动的底层算子构成，结合了组装优先级、可用工具等约束。算法在搜索过程中融合多种群策略以增加解的多样性、减少估计器误差对解的影响。此外，本文还结合聚合聚类的分组贴装点分配策略实现多机协同优化。
基于实际生产实例，本文分析了模型的参数灵敏度和复杂度，并在表面组装设备平台上围绕优化目标、运行效率等多项指标进行对比验证，证明了提出算法的有效性。
\end{cabstract}
\begin{eabstract}
Surface assembly optimization is a key technique for empowering and improving efficiency in the electronics manufacturing industry, which involves the production scheduling and planning in the component assembly process of printed circuit boards. It is a high-dimensional combinatorial optimization problem integrating warehouse locating, task allocation, and path planning with the complex characteristics of multi-variable, multi-constraint, and high coupling. The surface mounter with linear-aligned heads is widely employed due to its ability to assemble different types of components. However, the existing studies have not fully considered complex factors such as the diversity of assembly tasks, the difference of production configuration, and the linear-aligned structure of the placement heads, resulting in limited application scenarios and efficiency to be improved. This thesis decomposes the optimization problems into three sub-ones, based on the correlation of the assembly process, namely, head task assignment, path planning of the placement process, and load balancing of the assembly line. The mathematical programming model and an efficient surface assembly process optimization method with general applicability is constructed in stages.
First, we study the characteristics of the assembly process problem, task decomposition methods, and the constraints of the model, such as work completeness, pickup process, and tool consistency constraints. A head task assignment model is proposed based on the decomposition of the key sub-objectives, which include the pick-and-place (PAP) operations, nozzle changing, and reciprocating movement of the placement heads. Moreover, this thesis further builds a multi-cycle path planning model for the placement process under the restrictions of head task assignment. This thesis develops a load balancing model for the assembly line using the weighted value of the key sub-objective as the evaluation metric and combining the machine constraints, assembly priority constraints, etc. The multi-stages models can get the optimal solution of small-scale sub-problems, which provides a reference for the design of heuristic algorithms for larger-scale problems.
In the task assignment stage, this thesis carries out research from the perspectives of mathematical programming and heuristic algorithms, which improve the pick-up process efficiency of the surface mounter by optimizing the key efficiency indicators of the assembly process, so as to ensure the high quality of the overall solution. This thesis proposes an integer linear programming model based on the cyclic task integration to search the solution space systematically. A recursive heuristic algorithm is proposed to determine the initial solution and to improve the efficiency of the model solution by restricting the value range of the decision variables and narrowing the feasible domain. Meanwhile, a heuristic strategy with path estimation is applied to filter solutions from the pool to reduce the coupling with subsequent sub-problems. To solve larger-scale problems, this thesis further proposes a hierarchical heuristic algorithm based on look-forward scanning for head task assignment, which decomposes the problem into feeder-slot and head-component assignment sub-problems. To this end, two hierarchical solutions with a similar search architecture are designed for these sub-problems. This thesis designs a feeder allocation heuristic to maximize the efficiency of the pickup process from the construction of a nozzle allocation pattern, and a corresponding head-component allocation algorithm, which combines the feasibility of the pickup, the tool availability, and the prospective benefits, and balances the long- and short-term benefits of the pickup process, to achieve application in different production configurations.
In the path planning stage, this thesis investigates a placement path planning heuristic algorithm, which ensures the quality of solutions under different head task allocation constraints and thus improves the efficiency of the placement process of the surface mounter.
A dynamic programming-based PAP cycle path planning for multi-axis assembly process algorithm is proposed, which ensures the optimality of the results in each cycle. This thesis proposes a multi-point greedy beam search path planning algorithm with dynamic orientation to determine the allocation of placement points. The strategy effectively enhances the diversity of solutions by searching multiple work regions in parallel and applies the greedy criterion to the placement point allocation for heads. The beam search mechanism broadens the search scope by maintaining a set of non-optimal candidate solutions and adjusting the search direction. Furthermore, an aggregation path reconstruction algorithm based on adaptive large neighborhood search is proposed, which adaptively adjusts the path structure according to the distributed characteristics of the existing solution. It solves the problem that greedy search only focuses on the local optimal solution of the current cycle and realizes the purpose of online improvement of result iteratively.
In the load balancing stage, this thesis proposes a hyper-heuristic component allocation algorithm based on a multifeature fusion ensemble assembly time estimator, which can improve the assembly efficiency by balancing the workload of surface mounters. The assembly time estimator is framed by ensemble learning that integrates the basic parameters of the assembly process as well as the sub-objectives by the heuristic estimation to quickly and accurately evaluate the assembly time, etc. The component allocation algorithm for surface mounters is composed of data- and target-driven low-level operators under constraints such as assembly priority and available tools. In the search process, the algorithm combines multipopulation strategies to increase the diversity of solutions and reduce the influence of estimator errors on the results. In addition, this thesis also combines the aggregated grouping strategy for the placement points to achieve multiple machine co-optimization.
Based on the real-life production examples, this thesis analyses the parameter sensitivity and complexity of the model and conducts comparative experiments of the algorithm centered on the objectives, solving efficiency, etc., with a real surface assembly equipment as the platform, proving the effectiveness of the proposed algorithm.
\end{eabstract}

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\begin{denotation}
\begin{table}[H]
\caption{索引和集合的符号说明}
\vspace{0.5em}\centering\wuhao
\begin{tabular}{m{2.5cm}<{\centering}p{11cm}}
\toprule[1.5pt]
\makecell[c]{符号} & \makecell[c]{描述} \\
\midrule[1pt]
$i \in I$ & 元件索引$i$，元件索引集合$I=\left\lbrace 1, 2, \cdots \right\rbrace $ \\
$j \in J$ & 吸嘴索引$j$，吸嘴索引集合$J=\left\lbrace 1, 2, \cdots \right\rbrace $ \\
$s \in S$ & 供料器基座槽位索引$s$，供料器基座槽位索引集合$S=\left\lbrace 1, 2, \cdots \right\rbrace $ \\
$h \in H $ & 贴片头索引$h$，贴片头索引集合$H=\left\lbrace 1, 2, \cdots \right\rbrace $ \\
$k \in K$ & 拾贴周期/周期组索引，拾贴周期/周期组索引集合$K=\left\lbrace 1, 2, \cdots \right\rbrace $ \\
$m \in M$ & 贴片机索引$m$，贴片机索引集合$M=\left\lbrace 1, 2, \cdots \right\rbrace $ \\
$p \in P$ & 贴装点索引$p$，贴装点索引集合$P=\left\lbrace 1, 2, \cdots \right\rbrace $ \\
$a \in A$ & 移动弧索引$a$，弧索引集合$ A = \left\{ \left(h, h^\prime\right) \mid h \neq h^\prime, h \in H, h^\prime \in H \right\} $ \\
$q \in Q$ & 组装顺序优先级索引$q$，$q = \left( i, i^\prime \right) \in Q, i, i^\prime \in I$，表示元件$i$的拾贴任务需在元件$i^\prime$开始前完成 \\
\bottomrule[1.5pt]
\end{tabular}
\end{table}
\vspace{2em}
\begin{table}[H]
\caption{决策变量的符号说明}
\vspace{0.5em}\centering\wuhao
\begin{tabular}{m{1cm}<{\centering}p{12.5cm}}
\toprule[1.5pt]
\makecell[c]{符号} & \makecell[c]{描述} \\
\midrule[1pt]
$g_{km}$ & $ = 1$时表示贴片机 $m$ 在拾贴周期 $k$ 至少组装一个贴装点，否则为0 \\
$n_{khm}$ & $= 1$时表示贴片机 $m$ 的贴片头 $h$ 在拾贴周期/周期组 $k$ 和 $k + 1$之间发生吸嘴更换，否则为0 \\
$f_{ism}$ & $= 1$时表示贴片机 $m$ 的槽位 $s$分配的元件为 $i$，否则为0 \\
$e_{skm}$ & $= 1$时表示贴片机 $m$ 在拾贴周期/周期组 $k$ 拾取元件时，悬臂的最左侧贴片头所对齐槽位为$s$，否则为0 \\
$x_{ikhm}$ & $= 1$时表示贴片机 $m$ 在拾贴周期/周期组 $k$ 用贴片头 $h$ 拾取 元件$i$，否则为0 \\
$y_{skhm}$ & $= 1$时表示贴片机 $m$ 在拾贴周期/周期组 $k$ 用贴片头 $h$ 从槽位$s$拾取元件，否则为0 \\
$z_{jkhm}$ & $= 1$时表示贴片机 $m$ 在拾贴周期/周期组 $k$ 用贴片头 $h$ 安装吸嘴 $j$，否则为0 \\
$w_{pp^\prime kam}$ & $= 1$时表示贴片机$m$在拾贴周期 $k$ 贴装 点 $p$ 后沿着弧 $a$ 去贴装点 $p^\prime$，否则为0\\
$u_{pkhm}$ & $= 1$时表示贴片机$m$在拾贴周期 $k$用贴片头$h$组装的首个贴装点为点$p$，否则为0\\
$v_{pkhm}$ & $= 1$时表示贴片机$m$在拾贴周期 $k$用贴片头$h$组装的最后贴装点为点$p$，否则为0\\
$r_{im}$ & $= 1$时表示元件$i$被分配到贴片机$m$，否则为0\\
$d_{km}$ & 表示贴片机 $m$ 在拾贴周期 $k$ 拾取元件过程中，悬臂移动所经过的槽位数 \\
$b_{km}$ & 表示贴片机$m$的拾贴周期组$k$中的拾贴周期数 \\
$c_{ikhm}$ & 表示贴片机$m$在拾贴周期组$k$用贴片头$h$拾取的元件$i$的贴装点数 \\
\bottomrule[1.5pt]
\end{tabular}
\end{table}
\begin{table}
\caption{常数参数的符号说明}
\vspace{0.5em}\centering\wuhao
\begin{tabular}{p{1.8cm}<{\centering}m{1.5cm}<{\centering}m{10cm}}
\toprule[1.5pt]
\makecell[c]{类别} &\makecell[c]{符号} & \makecell[c]{描述} \\
\midrule[1pt]
\multirow{4}{*}{时间参数} & $T^{\rm{CY}}$ & 表示贴片头往返于供料器基座和组装电路板之间的平均用时 \\
&$T^{\rm{NZ}}$ & 表示贴片头完成一次吸嘴更换的平均用时 \\
&$T^{\rm{PU}}$ & 表示贴片头完成一次拾取动作的平均用时 \\
&$T^{\rm{PL}}$ & 表示贴片头完成一次贴装动作的平均用时 \\
&$T^{\rm{PM}}$ & 表示贴片头移动过一个槽位的平均用时 \\
\midrule[0.5pt]
\multirow{4}{*}{位置参数} &$X_{p}, Y_{p}$ & 表示贴装点$p$的X坐标和Y坐标 \\
&$X^{\rm{F1}}, Y^{\rm{F1}}$ & 表示最左侧供料器槽位的X坐标和Y坐标 \\
&$F^{\rm{BW}}_{km}$ & 表示贴片机$m$在拾贴周期$k$的第一个取料槽位。 \\
&$F^{\rm{FW}}_{km}$ & 表示贴片机$m$在拾贴周期$k$的最后一个取料槽位 \\
\midrule[0.5pt]
\multirow{6}{*}{距离参数} &$D^{\rm{FW}}_{pkhm}$ &表示贴片机$m$完成从供料器基座拾取元件后贴片头$h$到拾贴周期 $k$ 的第一个贴装点$p$的移动距离 \\
&$D^{\rm{PL}}_{pp^\prime a}$ & 表示贴片头在组装过程中沿着弧 $a$ 从点 $p$ 移动到点 $p^\prime$ 的移动距离 \\
&$D^{\rm{BW}}_{pkhm}$ & 表示贴片机$m$的贴片头$h$从拾贴周期 $k$ 的最后一个贴装点$p$到供料器基座拾取元件的移动距离 \\
&$\rho$ & 表示相邻贴片头的间隔距离 \\
\midrule[0.5pt]
\multirow{3}{*}{匹配参数} &$\mu_{ij}$ & $= 1$时，表示吸嘴$j$可完成元件$i$的拾贴任务，否则为0 \\
&$\xi_{im}$ & $=1$时，表示元件$i$可以被分配给贴片机$m$，否则为0 \\
&$\eta_{ip}$ & $=1$时，表示贴装点 $p$ 对应的元件为 $i$，否则为0 \\
\midrule[0.5pt]
\multirow{5}{*}{其他参数} &$\psi_{i}$ & 表示元件 $i$ 的贴装点数 \\
&$\phi_{i}$ & 表示元件 $i$ 的可用供料器数量 \\
&$\zeta_{j}$ & 表示吸嘴 $j$ 的可用数量 \\
&$\tau$ & 表示相邻贴片头和相邻供料器槽位之间的间隔距离之比 \\
&$N$ & 表示一个足够大的数 \\
\bottomrule[1.5pt]
\end{tabular}
\end{table}
\end{denotation}