Time-dependent vehicle routing problem with time windows (TDVRPTW) is a pivotal problem in logistics domain. In this study, a special case of TDVRPTW with temporal-spatial distance (TDVRPTW-TSD) is investigated, which objectives are to minimize the total travel time and maximize customer satisfaction while satisfying the vehicle capacity. To address it, an improved multiobjective evolutionary algorithm (IMOEA) is developed. In the proposed algorithm, a hybrid initialization strategy with two efficient heuristics considering temporal-spatial distance is designed to generate high-quality and diverse initial solutions. Then, two crossover operators are devised to broaden the exploration space. Moreover, an efficient local search heuristic combing the adaptive large neighborhood search (ALNS) and the variable neighborhood descent (VND) is developed to improve the exploration capability. Finally, detailed comparisons with several state-of-the-art algorithms are tested on a set of instances, which verify the efficiency and effectiveness of the proposed IMOEA.
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