中图分类号：F224.3 文献标志码：A

Salp swarm algorithm for solving the two-echelon location routing problem with simultaneous pickup and delivery

ZHANG Wenmei， ZHANG Huizhen， HAI Sheshe （Business School， University of Shanghai for Science and Technology，Shanghai 2Ooo93，China）

Abstract： In a two-echelon logistics network， to simultaneously meet the pickup and delivery requirements of each customer， a mixed integer programming model was established to minimize the costs associated with distribution center location， vehicle activation and vehicle transportation. An improved salp swarm algorithm was designed based on the specific characteristics of the model to solve this problem. The greedy clustering algorithm was employed to generate the initial solutions. An adaptive weighting strategy， adjusting food source quantity strategy， elite retention strategy and various search operators were introduced. The constructed model and algorithm were verified through testing instances of different customer sizes，and the original salp swarm algorithm， genetic algorithm， immune algorithm， grey wolf optimizer， and whale optimization algorithm were used for solving the problem. A comparative analysis of the operation results of each algorithm verified the feasibility of the constructed model and the effectiveness of the improved algorithm.

Keywords： location routing problem; two-echelon; simultaneous pickup and delivery; improved salp swarm algorithm

选址路径问题（location routingproblem，LRP）是交通运输以及运筹优化领域的重要研究内容之一，需同时考虑两方面的决策问题：设施选址问题（facilitylocationproblem，FLP）和车辆路径问题（vehicle routing problem，VRP）[1]。随着互联网的发展以及全球经济一体化的深入推进，企业物流运作范围日益扩大，物流系统亦呈现出多层级的演进态势。因此，众多学者在标准选址路径问题的基础上提出构建双层级选址路径问题（two-echelonlocation routingproblem，2E-LRP），双层级物流网络设计逐渐成为研究热点，对现代物流行业的发展具有重要意义。

20世纪80年代，Jacobsen等[2第一次正式提出2E-LRP，此后，众多学者对双层级选址路径问题进行了模型优化及拓展。Cuda等[3对双层级选址路径问题、双层级车辆路径问题以及多车型路径规划问题中的相关文献进行介绍和调查，得出城市物流和多式联运系统是双层级物流网络中较为关注的研究内容。Pichka等4将第三方物流企业纳入供应链配送系统，提出了开放式的双层级选址路径 问 题（two-echelon open location routingproblem，2E-OLRP），从而增强了2E-LRP问题的现实意义。Nikbakhsh等[5]考虑物流企业服务客户满意度的因素，以最小化成本为目标建立了带时间窗的双层级选址路径问题（two-echelonlocationrouting problem with time window， 2E-LRPTW）模型。除上述研究，关于2E-LRP的变体及扩展还包括：多资源的和多产品的2E-LRP（2E-LRPwithmultisources and multiproducts）[、绿色低碳的 2E-LRP（ low carbon two-echelon location routingproblem，LC2E-LRP）[7]等。

实际交易时，客户除了送货需求外，往往还存在取货需求，标准的LRP仅能满足客户的送货需求而无法满足客户的取货需求，这导致LRP模型已经不再符合当今物流行业的实际情况。因此，研究者们提出了同时取送货的选址路径问题（location routing problem with simultaneous pickupanddelivery，LRPSPD）。……