In this paper, a binary integer programming model of an unbiased capability-based distributed layout (UBCB-DL) problem without demand and process flow information is first developed. Then, it is extended to a mixed-integer program for a biased capability-based distributed layout (BCB-DL) problem where the demand information and processing requirements of several parts are taken into account. Since the complex nature of the problems, a recently proposed new generation metaheuristic optimizer namely, weighted superposition attraction (WSA) algorithm is also applied. In order to show validity and practicality of the proposed WSA algorithm and compare its performance with the proposed mathematical programs, a real-life case study is presented. The computational experiments have shown that both of the proposed binary integer program and WSA algorithm are able to find alternative optimal solutions for the UBCB-DL problem under reasonable computation times. However, just a feasible solution with 5.93% optimality gap is found by the proposed mixed-integer program for the BCB-DL problem under 24-hour running time limit. Fortunately, its optimal solution is achieved by the proposed WSA algorithm. Consequently, the proposed WSA algorithm provided the most effective solutions for both UBCB-DL and BCB-DL problems under shortest computation times.

在本文中，首先建立了一个没有需求和过程流信息的，基于无偏能力的分布式布局（UBCB-DL）问题的二进制整数编程模型。然后，将其扩展到混合整数程序，以解决基于偏差功能的分布式布局（BCB-DL）问题，其中考虑了多个零件的需求信息和处理要求。由于问题的复杂性，最近提出的新一代元启发式优化器，即加权叠加吸引力（WSA）算法也被应用。为了显示所提出的WSA算法的有效性和实用性，并将其性能与所提出的数学程序进行比较，提出了一个实际案例研究。计算实验表明，所提出的二进制整数程序和WSA算法都能够在合理的计算时间内找到UBCB-DL问题的替代最优解。然而，对于24小时运行时间限制下的BCB-DL问题，所提出的混合整数程序只能找到一种可行的解决方案，其最佳缺口为5.93％。幸运的是，它的最佳解决方案是通过提出的WSA算法实现的。因此，本文提出的WSA算法在最短的计算时间下为UBCB-DL和BCB-DL问题提供了最有效的解决方案。在24小时的运行时间限制下，针对BCB-DL问题的拟议混合整数程序发现了93％的最佳差距。幸运的是，它的最佳解决方案是通过提出的WSA算法实现的。因此，本文提出的WSA算法在最短的计算时间下为UBCB-DL和BCB-DL问题提供了最有效的解决方案。在24小时的运行时间限制下，针对BCB-DL问题的拟议混合整数程序发现了93％的最佳差距。幸运的是，它的最佳解决方案是通过提出的WSA算法实现的。因此，本文提出的WSA算法在最短的计算时间下为UBCB-DL和BCB-DL问题提供了最有效的解决方案。