A hybrid evolutionary multitask algorithm for the multiobjective vehicle routing problem with time windows

The vehicle routing problem with time windows (VRPTW), as an important logistic problem, has been widely investigated in recent decades. However, it is still a great challenge for most existing approaches to solve multiobjective VRPTWs (MOVRPTWs) with many conflicting objectives. In this study, a hybrid evolutionary multitask algorithm, termed HEMT, is proposed to address MOVRPTWs under the framework of evolutionary multitasking, where multiple MOVRPTWs are optimized simultaneously by leveraging the similarity between them. In particular, HEMT is characterized by three aspects: (1) an exploration stage with knowledge transfer (ESKT) is designed to globally explore the search space by transferring knowledge across different MOVRPTWs; (2) an exploitation stage with knowledge reuse (ESKR) is employed to further promote the quality of solutions by conducting local searches and reusing problem-specific knowledge; and (3) a tradeoff mechanism (TOM) is suggested to adaptively switch the search between ESKT and ESKR. Furthermore, to verify the efficacy of the proposed HEMT, four suites of new multitasking instances are generated based on 45 real-world MOVRPTW benchmarks under different multitask environments. The experimental results show that HEMT not only effectively solves multiple MOVRPTWs simultaneously but also achieves better performances than the traditional single-task counterparts.