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Top1 Introduction
Location-routing problem (LRP) includes the location decision and the path decision, which depend on and influence each other. LRP is a NP difficult problem, and the calculation time increases exponentially as the scale of the problem increases. To this end, intelligent optimization algorithm which can give approximate optimal solution in finite computational time has become the main solution of the LRP problem. Watson-Gandy and Dohrn firstly considered warehouse location in the routing problem(Mu Zhou, Yanmeng Wang & Zengshan Tian,et al.2019)(Prodhon C., & Prins C.,2014). Prodhon,Prins, Schneider and Drexl focus on LRP field(Schneider M.,& Drexl M.,2017)(Drexl M., Schneider M.,2015).
The LRP problem has been widely studied, and the relevant researchers have deepened the variant LRPSPD(Location-routing problem with Simultaneous Pickup and Delivery) problem of the LRP problem. The LRPSPD problem also belongs to the NP difficult problem as a branch of the LRP problem, which is an extension of the Mosheiov introduction of the transport salesman location problem in the number of warehouses and vehicle capacity(Qiao J. F.,Li F., & Yang S. X., et al,2020). Karaoglan proposed model of simultaneous pickup and delivery, and solved the problem using hybrid genetic algorithm, branch bound method and heuristic algorithm(Mu Zhou, Yaohua Li, & Yiwen Wang,et al,2021.)(Karaoglan I., Altiparmak F.,& Kara I., et al,2012)(Yu V. F.,& Lin S. W.,2014). Yu put forward an intelligent algorithm combining multi-starting point mountain climbing algorithm and simulated annealing algorithm(Yu V. F., & Lin S. Y.,2016)(Wang X. F.,2014). Wang considered several constraints of service modes, fuzzy time windows, and used TS (tabu search) based heuristic algorithm to solve the problem(Zhang Xiaonan, Fan Houming, & Li Jianfeng,2015). For the positioning-route problem of simultaneous delivery, Zhang Xiaonan designed a variable neighborhood decentralized search algorithm to solve(Sun Qingwei, & Zhang Yang,2017). Sun Qingwei considered the location-path problem of multiple models and simultaneous delivery, and designed an improved GA for solution(Leng Longlong, Zhao Yanwei, & Zhang Chun miao, et al,2019). Leng Longlong proposed a quantum superheuristic algorithm to solve the LRPSPD problem of low carbon and multi-vehicle types(Zhang B., Pan Q., & Gao L., et al,2017).
Based on the LRPSPD problem, this paper considers the cooperation of logistics companies and third-party logistics enterprises, and puts forward a hybrid immune algorithm. Initial solution was generated by greedy clustering algorithm. Besides, the evaluation and rank of antibody was realized by original immune algorithm, and immune operation was improved by neighborhood search algorithm. Taguchi method is used to set the important parameters in the algorithm, and the optimal parameter combination is determined. A set of numerical examples are obtained by using the SN separation method to improve the Prodhon standard database.