Hybrid multiobjective evolutionary algorithm considering combination timing for multi-type vehicle routing problem with time windows

Abstract

Vehicle routing problem (VRP) has been a classical combinatorial optimization challenge, which has been extensively investigated in recent decades. As a VRP typical variant, multi-type vehicle routing problem with time windows (MT-VRPTW) has been concerned with multiple types of heterogeneous fleets of vehicles, within the delivery time window and limited capacity constraints. For such complicated multiobjective optimization problems, hybrid multiobjective evolutionary algorithm (HMOEA) has become an effective method, however, the research on hybrid algorithms and combination timing is still challenging. This study proposes a hybrid multiobjective evolutionary algorithm based on combination timing (HMOEA-CT) to solve MT-VRPTW with the criteria of minimizing the number of vehicles and wasting time simultaneously. The HMOEA-CT combines a fast convergence in multiple directions (FCMDs)-based global search and a problem-specific difference (PSD)-based local search in different evolutionary stages. The FCMD is assumed to be the global exploration search strategy, which converges faster at the center and edge regions of the Pareto front. The PSD is used to improve the local exploitation search ability by directing poor-performing individuals closer to better-performing individuals. Furthermore, the PSD cooperates with FCMD at the right time according to the different evolutionary stages to improve efficiency. Experimental results on Solomon benchmark problems demonstrate the competitive performance comparison of the HMOEA-CT with traditional multiobjective evolutionary algorithms.