The purpose of this paper is to present a mathematical model and a new hybrid algorithm for flexible job shop scheduling problem with assembly operations. In this problem, each product is produced by assembling a set of several different parts. At first, the parts are processed in a flexible job shop system, and then at the second stage, the parts are assembled and products are produced.,As the problem is non-deterministic polynomial-time-hard, a new hybrid particle swarm optimization and parallel variable neighborhood search (HPSOPVNS) algorithm is proposed. In this hybrid algorithm, particle swarm optimization (PSO) algorithm is used for global exploration of search space and parallel variable neighborhood search (PVNS) algorithm for local search at vicinity of solutions obtained in each iteration. For parameter tuning of the metaheuristic algorithms, Taguchi approach is used. Also, a statistical test is proposed to compare the ability of metaheuristics at finding the best solution in the medium and large sizes.,Numerical experiments are used to evaluate and validate the performance and effectiveness of HPSOPVNS algorithm with hybrid particle swarm optimization with a variable neighborhood search (HPSOVNS) algorithm, PSO algorithm and hybrid genetic algorithm and Tabu search (HGATS). The computational results show that the HPSOPVNS algorithm achieves better performance than competing algorithms.,Scheduling of manufacturing parts and planning of assembly operations are two steps in production systems that have been studied independently. However, with regard to many manufacturing industries having assembly lines after manufacturing stage, it is necessary to deal with a combination of these problems that is considered in this paper.,This paper proposed a mathematical model and a new hybrid algorithm for flexible job shop scheduling problem with assembly operations.

中文翻译：

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一种新的混合粒子群优化和并行变量邻域搜索算法，用于装配过程柔性作业车间调度

本文的目的是提出一个数学模型和一种新的混合算法，用于解决具有装配操作的柔性作业车间调度问题。在这个问题中，每个产品都是通过组装一组几个不同的零件来生产的。首先在柔性作业车间系统中加工零件，然后在第二阶段组装零件并生产产品。由于问题是非确定性多项式时间困难的，一种新的混合粒子群优化并提出了并行变量邻域搜索（HPSOPVNS）算法。在该混合算法中，粒子群优化 (PSO) 算法用于搜索空间的全局探索，并行变量邻域搜索 (PVNS) 算法用于在每次迭代中获得的解附近的局部搜索。对于元启发式算法的参数调整，使用田口方法。此外，还提出了一种统计测试，以比较元启发式算法在中、大尺寸中寻找最佳解的能力。,数值实验用于评估和验证 HPSOPVNS 算法的性能和有效性，该算法具有可变邻域的混合粒子群优化搜索 (HPSOVNS) 算法、PSO 算法以及混合遗传算法和禁忌搜索 (HGATS)。计算结果表明，HPSOPVNS算法比竞争算法取得了更好的性能。制造零件的调度和装配操作的规划是生产系统中已独立研究的两个步骤。然而，对于许多制造阶段后有装配线的制造业，