Modeling and evolutionary algorithm for solving a multi-depot mixed vehicle routing problem with uncertain travel times

This paper deals with a multi-depot mixed vehicle routing problem under uncertain travel times (MDMVRP-UT), where there are several different depots and a number of identical vehicles. A vehicle can come back to any of the depots after its service is completed. A light-robust-optimization model is set up to control the total travel time within a preset value and to minimize the total travel time as much as possible. Then an effective evolutionary algorithm (EA) is proposed to solve the light-robust-optimization model. In the proposed EA, two constructive heuristics, namely a random customer sequence-based heuristic and a minimum spanning tree-based heuristic, are presented according to the problem-specific knowledge to generate a high-quality initial population with a certain level of diversity. A destruction and construction-based reproduction operator is provided to give birth to high-quality feasible offspring. A pairwise interchange based local search method is proposed to enhance the local exploitation capability. A hybrid selection operator and a population updating method are employed to remain the diversity of the population. The effectiveness of the proposed EA is verified by comprehensive experiments based on the well-known benchmark instances in the literature.