Abstract

This work proposes a new methodology and mathematical formulation to address the facility layout problem. The goal is to minimise the total material handling cost subjected to production-derived constraints. This cost is a function of the distance that the products should cover within the facility. The first idea is to use the \( {\text{A}}^{ *} \) algorithm to identify the distances between workstations in a more realistic way. \( {\text{A}}^{ *} \) determines the shortest path within the facility that contains obstacles and transportation routes. The second idea is to combine a genetic algorithm and the \( {\text{A}}^{ *} \) algorithm with a homogenous methodology to improve the quality of the facility layouts. In an iterative way, the layout solution space is explored using the genetic algorithm. We study the impacts of the appropriate crossover and mutation operators and the values of the parameters used in this algorithm on the cost of the proposed arrangements. These operators and parameter values are fine-tuned using Monte Carlo simulations. The facility arrangements are all compared and discussed based on their material handling cost associated with the Euclidean distance, rectilinear distance, and \( {\text{A}}^{ *} \) algorithm. Finally, we present a set of conclusions regarding the suggested methodology and discuss our future research goals.

中文翻译：

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考虑障碍的解决设施布局问题的方法：遗传算法与A *搜索结合

摘要

这项工作提出了一种新的方法论和数学公式来解决设施布局问题。目的是使受到生产限制的材料处理总成本最小化。该成本是产品应在设施内覆盖的距离的函数。第一个想法是使用\（{\ text {A}} ^ {* * \ \）算法以一种更现实的方式识别工作站之间的距离。\（{\ text {A}} ^ {* * \）确定设施内包含障碍物和运输路线的最短路径。第二个想法是将遗传算法和\（{\ text {A}} ^ {*} \）采用同质方法的算法，以提高设施布局的质量。以迭代方式，使用遗传算法探索布局解决方案空间。我们研究了适当的交叉和变异算子以及此算法中使用的参数值对拟议安排成本的影响。这些运算符和参数值使用蒙特卡洛模拟进行了微调。所有设施安排都是根据与欧几里得距离，直线距离和\（{\ text {A}} ^ {*} \）算法相关的材料处理成本进行比较和讨论的。最后，我们就建议的方法提出了一系列结论，并讨论了我们未来的研究目标。