Learning a Transferable Scheduling Policy for Various Vehicle Routing Problems based on Graph-centric Representation Learning

Inwook Kim, Jinkyoo Park

Keywords: Vehicle Routing Problem, Multiple Traveling Salesmen Problem, Capacitated Vehicle Routing Problem, Reinforcement Learning, Graph Neural Network

Abstract: Reinforcement learning has been used to learn to solve various routing problems. however, most of the algorithm is restricted to finding an optimal routing strategy for only a single vehicle. In addition, the trained policy under a specific target routing problem is not able to solve different types of routing problems with different objectives and constraints. This paper proposes an reinforcement learning approach to solve the min-max capacitated multi vehicle routing problem (mCVRP), the problem seeks to minimize the total completion time for multiple vehicles whose one-time traveling distance is constrained by their fuel levels to serve the geographically distributed customer nodes. The method represents the relationships among vehicles, customers, and fuel stations using relationship-specific graphs to consider their topological relationships and employ graph neural network (GNN) to extract the graph's embedding to be used to make a routing action. We train the proposed model using the random mCVRP instance with different numbers of vehicles, customers, and refueling stations. We then validate that the trained policy solve not only new mCVRP problems with different complexity (weak transferability but also different routing problems (CVRP, mTSP, TSP) with different objectives and constraints (storing transferability).

One-sentence Summary: This study proposes the graph-centric, RL-based transferable scheduler for various vehicle routing problems using graph-centric state presentation (GRLTS) that can solve any types of vehicle routing problems such as mCVRP, mTSP, CVRP, and TSP.

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