韦伯型多点设施优化选址的组合算法研究

韦伯型设施选址问题是组合优化领域中的一类重要问题，其核心内容是如何在离散的需求空间域内，寻找到最优决策关注点，即设施点。对于单点设施最优规划问题，由于不存在设置点之间的作用，仅考虑设施点与需求点之间的引力作用问题即可。对于多点设施的最优规划问题，不仅存在着设施点与需求点之间的引力作用问题，而且从资源优化配置的角度，还存在着设施点之间的斥力问题。因此，需要从系统整体优化的角度进行选择规划。目前解决韦伯型设施多点的优化选址问题，一般是通过寻找局部最优解的逐次递阶法来确定最优设施点。但由于该方法没有考虑到设施点间的斥力问题，容易导致设施点间的粘连。针对此问题，提出了一种PGSA．GA组合算法，通过建立模拟植物生长算法得到全局最优解的单点坐标，将其与需求点结合构建遗传算法优化的多目标规划多点设施选址模型求出Pareto最优解，并依此推广到多次选址方案。

Research for combination algorithm of Weber multi-point facilities optimization location

Weber facility location problem is important in the field of combinatorial optimization problems. The core content in the space domain is to find the optimal decision concerns, namely, facility. Because there is no effect between set point in the sin- gle facility optimal planning problems, it only considers the gravitation between the facility and the demand points. However, for optimal planning of multi-facility, not only the problem of the gravitation between the facility and demand points, but also from the perspective of resource optimal configuration, it exists the repulsion between the facility points. Therefore, it is needed to select from the view of system optimization plan. Solving the optimization of the Weber-type facilities for multi-point loca- tion problem is generally through successive hierarchical method to find a local optimal solution to determine the optimal facili- ty. However, since this method does not take into account the repulsion between the facility, it is easy to cause adhesion. In re- sponse to this problem, this article proposes a combination of PGSA-GA algorithm to get global optimal solution of single-point coordinates. Through the establishment of plant growth simulation algorithm, it combines with genetic algorithm for optimiza- tion of multipoint facility location model for multiobjective programming derive Pareto optimal solutions and then extend to sev- eral location plan.