Learning to Solve Soft-Constrained Vehicle Routing Problems with Lagrangian Relaxation
This addresses the problem of efficiently solving constrained VRPs for logistics and operations research, but it is incremental as it builds on existing RL-based methods with a specific technique.
The paper tackled the challenge of solving soft-constrained Vehicle Routing Problems (VRPs) by proposing a Reinforcement Learning method that incorporates Lagrangian relaxation and constrained policy optimization, demonstrating competitive performance in travel distance, constraint violations, and inference speed on three common VRP types.
Vehicle Routing Problems (VRPs) in real-world applications often come with various constraints, therefore bring additional computational challenges to exact solution methods or heuristic search approaches. The recent idea to learn heuristic move patterns from sample data has become increasingly promising to reduce solution developing costs. However, using learning-based approaches to address more types of constrained VRP remains a challenge. The difficulty lies in controlling for constraint violations while searching for optimal solutions. To overcome this challenge, we propose a Reinforcement Learning based method to solve soft-constrained VRPs by incorporating the Lagrangian relaxation technique and using constrained policy optimization. We apply the method on three common types of VRPs, the Travelling Salesman Problem with Time Windows (TSPTW), the Capacitated VRP (CVRP) and the Capacitated VRP with Time Windows (CVRPTW), to show the generalizability of the proposed method. After comparing to existing RL-based methods and open-source heuristic solvers, we demonstrate its competitive performance in finding solutions with a good balance in travel distance, constraint violations and inference speed.