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

TL;DR

This paper introduces an innovative end-to-end deep reinforcement learning framework for solving complex capacitated location-routing problems, demonstrating superior performance and generalization over existing methods.

Contribution

It is the first to propose an end-to-end learning approach with a novel attention mechanism for CLRPs, reformulating them as a Markov decision process.

Findings

Outperforms traditional and DRL baselines in solution quality

Shows strong generalization on synthetic and benchmark datasets

Effectively handles interdependencies in location and routing decisions

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. To 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.