A Combined Diffusion Model and Reinforcement Learning Approach for Solving the Vehicle Routing Problem With Multiple Soft Time Windows

The Vehicle Routing Problem with Multiple Soft Time Windows (VRPMSTW) is a challenging combinatorial optimization problem where a fleet of vehicles must deliver goods to a set of customers, adhering to time windows while minimizing costs. In this paper, we propose a novel solution approach that combines a Diffusion Model with Reinforcement Learning (RL) to efficiently solve the VRPMSTW. The Diffusion Model generates feasible vehicle routes by denoising a noise distribution, ensuring that constraints such as vehicle capacity, travel distance, and time windows are respected. Subsequently, the RL module fine-tunes these paths by optimizing the objective function, which minimizes the number of vehicles, travel distance, and time window penalties. We evaluate our approach on benchmark datasets and compare it with other state-of-the-art methods. The results demonstrate that our combined model outperforms traditional heuristics, achieving better optimization in terms of the number of vehicles, travel cost, and time window violations. The proposed method provides a promising solution for solving complex real-world vehicle routing problems with soft time window constraints.