Robust multi-objective vehicle routing problem with time windows for hazardous materials transportation

This work focuses on a hazardous material (HazMat) vehicle routing problem with time windows (VRPTW). Given the multi-objective and uncertainty natures of HazMat transportation, a multi-objective robust VRPTW (MO-RVRPTW) model is proposed, which simultaneously optimise both the number of vehicles and the uncertain transportation risk. An uncertain set containing 32 potential incident scenarios is constructed to model the uncertain parameter. To handle the uncertain multi-objective problem (MOP), this work develops two versions of robust criterion to transform the MO-RVRPTW to its robust counterpart. A hybrid evolutionary algorithm (HEA) is designed to solve the robust counterpart, which integrates a push forward insertion heuristic for initial population construction, a route exchange crossover operator and a multi-component mutation (MCM) operator for generating the better offspring. The MCM is based on three basic local search operators and employs a sequential-move mechanism to improve the effectiveness of the algorithm. The proposed algorithm is tested on classical Solomon instances. Experiment results show that HEA is competitive in terms of convergence and diversity. A deterministic case is employed to justify the proposed robust criterion. In most cases, they can provide a set of robust non-dominated solutions with respect to both pareto optimality and robust optimality.