An effective iterated greedy algorithm for PCBs grouping problem to minimize setup times
Introduction
In recent years, with the development of the electronic assembly industry, the research on printed circuit boards (PCBs) assembly process has gained more and more attention. In order to improve the profit of companies and meet customers’ needs, producers always seek a production mechanism that can save as many resources as possible. Typically, in the PCB assembly process, a large number of electronic components are required by a single PCB. An automated placement machine is used to place the needed components to the PCBs. In the actual production process, a setup time always exists for loading and unloading the components from the placement machine. In order to decrease the setups which are caused by the dissimilar operations, PCBs sharing similar components are always grouped together. Here, a concept of PCBs groping problem (PGP) is introduced. For the PGP, a set of similar PCBs that need similar operations are divided into a group, so that a significant decrease in the cost associated with the unnecessary setup times can be achieved. In the real world, the setup operation of transferring one board group to another is also needed. Therefore, in the paper, we take two kinds of setup times into consideration, one is for loading and unloading the components from the placement machine, the other one is for the PCB group transporting. To improve the efficiency of the PCB assembly production as much as possible, it is urgent to reduce the total setup time. Therefore, we take the minimization of the total setup time as the optimization objective in this paper.
Salonen et al. [1] proved that the PGP is a NP-hard problem. Therefore, heuristic and metaheuristic approaches are among the best alternatives to find optimal or near-optimal solutions for the PGP in reasonable computational time. The iterated greedy (IG) algorithm is one of metaheuristics, and it has been proved an effective method for the NP-hard problem. Especially in the scheduling field, Ruiz et al. [2] applied it to solve the distributed permutation flowshop scheduling problem (DPFSP) with the makespan criterion. Pan et al. [3] adapted it to address the same problem with the total flowtime criterion. Given the excellent performance of the IG algorithm shown in the literature, in this paper, we also use it to solve the PGP to minimize the total setup time.
The rest of the paper is organized as follows. In Section 2, the closely related literature is reviewed. Section 3 describes the proposed problem. In Section 4, the proposed IG algorithm for the PGP is presented in details. In Section 5, the design of experiment for the parameter calibration is presented. Section 6 shows the experiments and comparisons. Section 7 concludes the paper and provides an outlook for further study.
In this paper, we provide the five contributions: (1) A mixed integer linear programming (MILP) model for the PGP is set up. (2) Two theorems are proposed to speed up the evolutionary process of solutions. (3) A problem-oriented heuristic is applied to generate an initial solution. (4) A merge operator is proposed to enhance the initial solution. (5) A local search method based on shift and swap operators are used to improve the solution from the destruction and construction phase. (6) An acceptance criterion with probability is used to ensure the ability of escaping from the local optimization.
Section snippets
Literature review
The PGP is a traditional problem in the PCB assembly process. In the literature, there are mainly four major classes [1]: one PCB type and one machine (1-1), multiple PCB types and one machine (M-1), one PCB type and multiple machines (1-M) and multiple PCB types and multiple machines (M-M). The existing literature is mainly about classes M-1 and M-M. Here we list the literature about the two classes as follows. For the situation with M-1, Daskin et al. [4] proposed a heuristic algorithm to
Problem description
The PGP can be described as follows. There are a set of PCBs, , each of which should be assembled with () certain component types according to the electrical design. For a batch of PCBs, a set of component types, , are needed. The component types needed by different PCBs are all from Set . The capacity of the automatic placement machine is a constant, , which refers to the number of different component types that can be loaded simultaneously on the
Proposed IG algorithm for the PGP
The traditional IG algorithm uses a heuristic to create an initial solution, then iterates four phases, i.e., destruction, construction, local search and acceptance criterion, until a termination is met. In the destruction phase, some elements of the current solution are removed, and two partial permutations, and , can be obtained. is used to store the removed elements, and contains the remaining elements of the current permutation. In the construction phase, the elements in are
Calibration for IGP
The IGP has two parameters: (1). the number of the removed jobs in the destruction phase (); (2). the control probability used in the acceptance criterion (). For these parameters, after referring to the related literature and doing some primary experiments, we determine the levels for each parameter as follows: at four levels: 4, 8, 12 and 16; at four levels: 0.0, 0.4, 0.8 and 1.0. As result, we can get a total of different parameter combinations.
To calibrate the presented IGP
Computational evaluation
To test the performance of the IGP algorithm, a computational experiment is carried out. The modern electronic assembly industry is characterized by multi-type and low-volume. By referring to the related literature, we find that the existing test cases for the PGP are all small in size which is not suitable for the actual production environment. In order to adapt to the actual production, by investigating the PCB production industry and referring to the related literature, we set the capacity
Conclusions and future research
The PCBs assembly problem has been a hot issue in recent years, especially in the industrial production field. In the assembly process, all the steps including PCBs grouping problem, PCBs group scheduling problem et al. are equally important. In this paper, we take the PGP into consideration specially, and solve it with an IG algorithm to minimize the total setup time. In the IGP, a problem-oriented heuristic is applied to generate an initial solution, and a merge operator is used to further
CRediT authorship contribution statement
Jiang-Ping Huang: Conceptualization, Software, Investigation, Methodology, Optimization algorithm, Writing – original draft. Quan-Ke Pan: Resources, Optimization algorithm, Writing – review & editing, Supervision. Liang Gao: Resources, Optimization algorithm, Review & editing. Ling Wang: Resources, Optimization algorithm, Review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This research is partially supported by the National Science Foundation of China 61973203, and the National Natural Science Fund for Distinguished Young Scholars of China 51825502, and Shanghai Science and Technology Planning Project, China 21XD1401000, and Shanghai Key Laboratory of Power station Automation Technology, China . Thanks for the support of Cloud computer platform of Shanghai University Computer Center and Prof. Zi-Peng Shan.
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