A tissue P system based evolutionary algorithm for multi-objective VRPTW.

Multi-objective vehicle routing problem with time windows (VRPTW) has important applications in engineering and computer science, and it is a NP-hard problem. In the last decade, numerous new methods for multi-objective VRPTW have sprung up. However, the calculation speed of most algorithms is not fast enough, and on the other hand, these algorithms did not give a complete Pareto optimal front, although their results are excellent. Hence, in this paper, a tissue P system with three cells based MOEA, termed PDVA, is proposed to solve the multi-objective VRPTW. In PDVA, two mechanisms, the discrete glowworm evolution mechanism (DGEM) and the variable neighborhood evolution mechanism (VNEM), are used as sub-algorithms in two cells respectively to balance the exploration and exploitation reasonably. Simultaneously, some special strategies are used to enhance the performance of the proposed algorithm. The following experiments are presented to test the proposed algorithm. First, the influence of the parameters on the performance of the algorithm is investigated. Second, the validity of the algorithm is highlighted when compared to the DGEM-VNEM algorithm. Third, the quality and diversity of the solutions are improved when compared to the other popular algorithms. These results and comparisons on test instances demonstrate the competitiveness of PDVA in solving multi-objective VRPTW in terms of both quantity and speed.