Time-Dependent Multi-Depot Heterogeneous Vehicle Routing Problem Considering Temporal–Spatial Distance

Aiming at the multi-depot heterogeneous vehicle routing problem under the time-dependent road network and soft time window, considering vehicle fixed cost, time window penalty cost and vehicle transportation cost, an optimization model of time-dependent multi-depot heterogeneous vehicle routing problem is established with the objective of minimizing distribution cost. According to the characteristics of the problem, a hybrid genetic algorithm with variable neighborhood search considering the temporal–spatial distance is designed. Customers are clustered according to the temporal–spatial distance to generate initial solutions, which improves the quality of the algorithm. The depth search capability of the variable neighborhood search algorithm is applied to the local search strategy of the genetic algorithm to enhance the local search capability of the algorithm. An adaptive neighborhood search number strategy and a new acceptance mechanism of simulated annealing are proposed to balance the breadth and depth required for population evolution. The validity of the model and algorithm is verified by several sets of examples of different scales. The research results not only deepen and expand the relevant research on vehicle routing problem, but also provide theoretical basis for logistics enterprises to optimize distribution scheme.