中文摘要：

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—besdl／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。

英文摘要：

This paper studies the soft-capacitated logistics facility location problem that is widely existed in the design and ,nanagement 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 dif- ferential evaluation algorithm to solve the soft-capacitated logistics facility location problem.