Multiobjective Vehicle Routing Optimization with Time Windows: A Hybrid Approach Using Deep Reinforcement Learning and NSGA-II

This paper proposes a weight-aware deep reinforcement learning (WADRL) approach designed to address the multiobjective vehicle routing problem with time windows (MOVRPTW), aiming to use a single deep reinforcement learning (DRL) model to solve the entire multiobjective optimization problem. The Non-dominated sorting genetic algorithm-II (NSGA-II) method is then employed to optimize the outcomes produced by the WADRL, thereby mitigating the limitations of both approaches. Firstly, we design an MOVRPTW model to balance the minimization of travel cost and the maximization of customer satisfaction. Subsequently, we present a novel DRL framework that incorporates a transformer-based policy network. This network is composed of an encoder module, a weight embedding module where the weights of the objective functions are incorporated, and a decoder module. NSGA-II is then utilized to optimize the solutions generated by WADRL. Finally, extensive experimental results demonstrate that our method outperforms the existing and traditional methods. Due to the numerous constraints in VRPTW, generating initial solutions of the NSGA-II algorithm can be time-consuming. However, using solutions generated by the WADRL as initial solutions for NSGA-II significantly reduces the time required for generating initial solutions. Meanwhile, the NSGA-II algorithm can enhance the quality of solutions generated by WADRL, resulting in solutions with better scalability. Notably, the weight-aware strategy significantly reduces the training time of DRL while achieving better results, enabling a single DRL model to solve the entire multiobjective optimization problem.