This paper studies the multi-depot joint distribution vehicle routing problem considering energy consumption with time-dependent networks (MDJDVRP-TDN). Aiming at the multi-depot joint distribution vehicle routing problem where the vehicle travel time depends on the variation characteristics of the road network speed in the distribution area, considering the influence of the road network on the vehicle speed and the relationship between vehicle load and fuel consumption, a multi-depot joint distribution vehicle routing optimization model is established to minimize the sum of vehicle fixed cost, fuel consumption cost and time window penalty cost. Traditional vehicle routing problems are modeled based on symmetric graphs. In this paper, considering the influence of time-dependent networks on routes optimization, modeling is based on asymmetric graphs, which increases the complexity of the problem. A hybrid genetic algorithm with variable neighborhood search (HGAVNS) is designed to solve the model, in which the nearest neighbor insertion method and Logistic mapping equation are used to generate the initial solution firstly, and then five neighborhood structures are designed to improve the algorithm. An adaptive neighborhood search times strategy is used to balance the diversification and depth search of the population. The effectiveness of the designed algorithm is verified through several groups of numerical instances with different scales. The research can enrich the relevant theoretical research of multi-depot vehicle routing problems and provide the theoretical basis for transportation enterprises to formulate reasonable distribution schemes.

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.

Aiming at the dynamic multicompartment refrigerated vehicle routing problem with multigraph based on real-time traffic information, this study, based on the idea of preoptimization followed by real-time adjustment, establishes a two-stage mathematical model with minimizing delivery cost. In the preoptimization phase, this study, based on historical traffic information, designed a hybrid chaotic genetic algorithm with variable neighborhood search (HCGAVNS) to obtain the initial delivery scheme. In the real-time adjustment phase, the order in which customers are served remains the same and a path selection strategy is proposed to solve the problem according to the real-time traffic information of different paths. The validity of the model and the algorithm are verified through the analysis of instances. The research results can enrich the related research on cold chain vehicle routing problem and provide a theoretical basis for logistics companies to optimize their delivery scheme.

Aiming at the dynamic multi-depot multi-compartment refrigerated vehicle routing problem with multi-path based on real-time traffic information, based on the idea of pre-optimization followed by real-time adjustment, a two stages optimization model with the goal of minimizing total cost is established. To solve this problem, this paper designed a hybrid chaotic genetic algorithm with variable neighbourhood search (HCGAVNS) to generate the initial routes. In the real-time adjustment phase, this paper proposed a path selection strategy to update the selected paths. Multiple experiments are constructed to verify the validity of the model and the algorithm. This research has important theoretical and practical significance.