Solving the Semivectorial Bilevel Hazmat Network Design Problem by a Deconstructive Heuristic Algorithm

The transportation of hazardous materials (hazmat) poses significant risks to urban areas, necessitating careful planning to minimize potential exposure. This study addresses a variant of the Bilevel Hazmat Network Design Problem, introducing an additional objective to balance the usage of certain roads, thereby preventing the overexposure of specific roads and zones within the city. The problem is mathematically formulated as a semivectorial bilevel optimization model, where the leader¿s objective seeks to minimize risk, and the follower optimizes two objectives: minimizing transportation costs and balancing road usage. To address the challenge of determining the follower¿s optimal reaction to the leader¿s decisions, we obtain a Pareto front for the follower¿s objectives. To simplify this process, we make a realistic assumption regarding the follower¿s response and propose a heuristic deconstructive algorithm tailored to the problem¿s complex structure. Computational experiments are conducted on instances derived from real-life case study to evaluate the performance of the proposed approach. The results demonstrate the heuristic¿s effectiveness in designing low-risk networks based on the hazmat flow determined by the follower. Additionally, managerial insights are provided, emphasizing the approach¿s practical applicability to urban hazmat management. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

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