Time-Dependent Route Optimization for Multimodal Hazardous Materials Transport Using Conditional Value-at-Risk Under Uncertainty

Transporting hazardous materials has low accident probabilities but potentially catastrophic consequences, making effective risk management essential in uncertain conditions such as population distribution, weather, traffic, and multimodal scheduling constraints. This study develops a Conditional Value-at-Risk (CVaR)-based optimization model for multimodal hazardous materials transportation that incorporates transportation and transshipment risks, population exposure uncertainty, fixed departure schedules for rail and waterway transport, dual time-window constraints, and limits on the number of transshipments. The model also reflects the decision-maker’s risk aversion and time-varying travel times. To solve this NP-hard problem, an improved chaotic simulated annealing-ant colony optimization (CSAACO) algorithm is proposed. Numerical experiments show that CSAACO outperforms the standard ACO in terms of solution quality and stability. The results demonstrate that the model effectively captures tail risk in dynamic environments and that both the risk aversion coefficient μ and departure time significantly influence route selection. The proposed approach provides an efficient and practical decision-support tool for hazardous materials multimodal transportation planning under uncertainty.