Route optimization for urban hazardous materials transportation under time-varying road networks

This paper investigates a time-dependent urban hazardous materials (hazmat) transportation routing optimization problem, where vehicles depart from a distribution center to serve a set of customers. The decision variables include both the travel path and the departure time at each node, with the option for vehicles to wait if necessary. The objective is to minimize both the total transportation risk and cost, which consists of travel costs and overtime penalty costs. To address this, we propose PPO-MOEA/D, a reinforcement-learning-based approximation algorithm that enhances the performance of the conventional MOEA/D. To reduce computational complexity, we introduce a preprocessing strategy for departure-time decision identification and optimization, focusing only on critical nodes. Proximal Policy Optimization (PPO) is utilized to dynamically generate high-quality initial solutions and adaptively select crossover and mutation operators, improving evolutionary efficiency. Extensive experiments on instances with varying scales demonstrate that optimizing departure times significantly reduces transportation risk. Compared to the traditional MOEA/D, PPO-MOEA/D shows superior performance in terms of convergence speed, solution quality, and computational efficiency. Additionally, we analyze the trade-off between computational cost and solution quality across different population sizes and investigate how total transportation risk varies across time periods.