Balancing Multi-Manned Assembly Lines With Walking Workers: Problem Definition, Mathematical Formulation, and an Electromagnetic Field Optimisation Algorithm

Assembly lines are widely used in industrial environments that produce standardised products in high volumes. Multi-manned assembly line is a special version of them that allows simultaneous operation of more than one worker at the same workstation. These lines are widely used in large-sized product manufacturing since they have many advantages over the simple one. This article has dealt with multi-manned assembly line balancing problem with walking workers for minimising the number of workers and workstations as the first and second objectives, respectively. A linear mixed-integer programming formulation of the problem has been firstly addressed after the problem definition is given. Besides that, a metaheuristic based on electromagnetic field optimisation algorithm has been improved. In addition to the classical electromagnetic field optimisation algorithm, a regeneration strategy has been applied to enhance diversification. A particle swarm optimisation algorithm from assembly line balancing literature has been modified to compare with the proposed algorithm. A group of test instances from many precedence diagrams were generated for evaluating the performances of all solution methods. Deviations from lower bound values of the number of workers/workstations and the number of optimal solutions obtained by these methods are concerned as performance criteria. The results obtained by the proposed programming formulations have been also compared with the solutions obtained by the traditional mathematical model of the multi-manned assembly line. Through the experimental results, the performance of the metaheuristic has been found very satisfactory according to the number of obtained optimal solutions and deviations from lower bound values.

装配线广泛应用于大批量生产标准化产品的工业场景中。多工位多人装配线（multi-manned assembly line）作为其特殊变体，支持同一工作站内多名工人同步开展作业。相较于传统单人工位装配线，此类装配线具备多重优势，因此被广泛应用于大型产品制造领域。
本文针对配备移动作业工人的多工位多人装配线平衡问题展开研究，以最小化工人数量与工作站数量分别作为第一、第二优化目标。在明确问题定义后，本文首先构建了该问题的线性混合整数规划模型。此外，本文对基于电磁场优化算法（electromagnetic field optimisation algorithm）的元启发式算法进行了改进：相较于经典电磁场优化算法，本文引入再生策略以提升算法的搜索多样性。为与本文提出的改进算法进行对比，本文对装配线平衡领域已有的粒子群优化（Particle Swarm Optimisation, PSO）算法进行了适配性修改。
本文基于多种优先约束关系图生成了一组测试算例，用于评估所有求解方法的性能，以工人数量、工作站数量的下界偏差以及各方法求得的最优解数量作为性能评价指标。
本文还将所提出的规划模型求解结果与传统多工位多人装配线数学模型的求解结果进行了对比。
实验结果表明，从最优解数量与下界偏差两方面来看，本文改进的元启发式算法性能表现优异。