A robustness division based multi-population evolutionary algorithm for solving vehicle routing problems with uncertain demand

The vehicle routing problem with uncertain demand (VRPUD) is an extension of capacitated vehicle routing problem (CVRP), where the demand of each customer is unknown when dispatching the vehicles to service customers. Since it is more practical than CVRP, the VRPUD has aroused wide attention. Although the evolutionary algorithms (EAs) have demonstrate its promising performance on solving VRPUD, the most of EAs only consider the robustness of solution after generating offspring, which limit the quality of solutions found by EAs. To this end, in this paper, a robustness division based multi-population evolutionary algorithm (RDMPEA) is developed for VRPUDs, where the robustness is considered before, during and after offspring. Specifically, before generating offspring, the RDMPEA first divides the individuals into different subpopulations according to their robustness level, and only the individuals within the same subpopulation can match each other and generate offspring. During generating offspring, the RDMPEA employs a route based crossover operator to generate offspring, where the routes with higher robustness have a greater probability of being inherited by the offspring. After generating offspring, a dedicated environment selection strategy is applied to survive the individuals with better robustness and travel cost. In the experiments, the proposed RDMPEA is compared to three state-of-the-art heuristic methods tailored for VRPUDs on a variety of instances obtained by using three widely used vehicle routing problem benchmarks. The experimental results indicate that the proposed RDMPEA is superior to three compared algorithms, and can find solutions with better travel cost and robustness.