张新邦++邢航++李贵栋++汪恭书

摘 要：研究了广泛存在于物流系统设计与管理中的软容量约束的物流设施选址问题，主要决策每个客户需求由哪个设施服务以及每个设施开放的次数，目标为最小化设施开放成本和运输成本之和。为了有效求解该问题，提出了一种改进的差分进化算法，编码方式上采用实数编码策略，较为简单易于实现且能得到较好结果，进化过程采用多种变异算子并进行对比。对以往文献给出的算例采用5种变异算子进行测试，计算结果表明，DE/rand-to-best/1/bin变异算子最好，且所有算子都能得到较好结果，DE算法在软容量约束的设施选址问题上应用具有可行性。

关键词：物流设施选址问题；软容量约束；差分进化；实数编码

中图分类号：F253.9 文献标识码：A

Abstract： This paper studies the soft-capacitated logistics facility location problem that is widely existed in the design and management of logistics system. The problem is to make decision that each customer demand should be serviced by which facility and the open times for each facility so as to minimize the sum of facility opening cost and transportation cost. To solve the problem efficiently， we proposed an improved differential evaluation algorithm. The proposed algorithm uses a real number coding strategy to implement easily， and compares multiple mutation operators in the evolutionary process. We test 5 mutation operators over the instances collected from an existing article. The computational results show that the DE/rand-to-best/1/bin has the best mutation operator， and all other mutation operators can also get better solution for some instances. This verifies that it is feasible to use differential evaluation algorithm to solve the soft-capacitated logistics facility location problem.

Key words： logistics facility location problem； soft-capacitated； differential evaluation； real number coding

0 引 言

设施选址问题是物流与供应链管理领域一类重要的组合优化问题，其在企业选址、网络设施及服务点的分布等众多方面都有应用。自1909年韦伯发表了关于设施选址问题的第一篇论文至今，该类问题备受众多研究者青睐。这一问题受到广泛关注是因为对设施选址问题的研究存在着极为重要的实际意义。选址决策属于长期的，具有战略意义的决策，决策的好坏对于服务方式、服务质量、生产成本等方面都有很大的影响，通常一个较好的设施选址方案会很大程度减少不必要的费用，对一个企业而言，甚至还会极大、长久地影响到其生产经营、市场竞争力甚至企业的发展命运。……