An End-to-End Learning Approach for Solving Capacitated Location-Routing Problems

THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICA TION. Abstract--The capacitated location-routing problems (CLRPs) are classical problems in combinatorial optimization, which require simultaneously making location and routing decisions. In CLRPs, the complex constraints and the intricate relationships between various decisions make the problem challenging to solve. With the emergence of deep reinforcement learning (DRL), it has been extensively applied to address the vehicle routing problem and its variants, while the research related to CLRPs still needs to be explored. In this paper, we propose the DRL with heterogeneous query (DRLHQ) to solve CLRP and open CLRP (OCLRP), respectively. We are the first to propose an end-to-end learning approach for CLRPs, following the encoder-decoder structure. In particular, we reformulate the CLRPs as a markov decision process tailored to various decisions, a general modeling framework that can be adapted to other DRL-based methods. T o better handle the interdependency across location and routing decisions, we also introduce a novel heterogeneous querying attention mechanism designed to adapt dynamically to various decision-making stages. Experimental results on both synthetic and benchmark datasets demonstrate superior solution quality and better generalization performance of our proposed approach over representative traditional and DRL-based baselines in solving both CLRP and OCLRP . HE facility location problem (FLP) and vehicle routing problem (VRP) are two critical combinatorial optimization problems (COPs) in transportation and logistics, which are traditionally addressed sequentially. However, planning the routes after facility location may lead to suboptimal solutions due to the interdependencies across various decisions [1], [2]. Therefore, the capacitated location-routing problems (CLRPs) [3] are proposed to simultaneously make location and routing decisions. The CLRPs are one of the most classical topics in the community of operations research and have extensive applications such as supply-chain management [4], emergency management [5], and disaster relief [6]. This work was supported by the National Key Research and Development Program of China No.2022ZD0119703; in part by the National Natural Science Foundations of China (NSFC) under Grant 62273044 and 62022015; in part by the National Natural Science Foundation of China National Science Fund for Distinguished Y oung Scholars under Grant 62025301; in part by the National Natural Science Foundation of China Basic Science Center Program under Grant 62088101. In CLRPs, depots and vehicles are subject to the maximum capacity constraints, and the depots are considered heterogeneous due to distinct capacities and opening costs. Meanwhile, we also study the open CLRP (OCLRP) [7], a variant of CLRP, by considering open-ended routes.