Solving many-objective delivery and pickup vehicle routing problem with time windows with a constrained evolutionary optimization algorithm

Vehicle routing problems (VRP) are a kind of typical combinational optimization problem, particularly in the logistics industry. This paper proposes a constrained evolutionary optimization algorithm, called CEOA, for solving many-objective VRP with simultaneous delivery, pickup, and time windows (VRPSDPTW). Specifically, we first define the weight value vectors based on the constraint satisfaction situation, which can adaptively adjust according to the feedback of population solutions during the search process. Subsequently, based on the feedback from the weight value vectors, the environmental selection strategy is employed to identify promising solutions for both infeasible and feasible situations. Furthermore, considering the data characteristics of the problem at hand, the crossover and mutation operations are tailored to better align with the VRPSDPTW, which is further explained and illustrated in detail regarding solution construction. The experimental results demonstrate the effectiveness of the proposed algorithm for VRPSDPTW in comparison with other state-of-the-art methods.