## 1 Introduction  
The vehicle routing problem (VRP) was proposed by [PERSON] and [PERSON] in 1959 [1]; this problem aims to find an optimal route based on constraints and objectives. The problem is widely used in traffic management, logistics transportation, and other fields. This problem has been extensively studied. Several VRP variants have been proposed by applying the VRPs in different environments, such as the capacity-constrained vehicle routing problem (CVRP) and vehicle routing problem with time window (VRPTW). Many researchers have performed systematic literature reviews on the VRP. [PERSON] et al. [2] extracted data and analyzed relevant literature within 2018-2022 to address the problems associated with VRPTW. [PERSON] et al. [3] analyzed the articles which solve VRPs by Learning-Based Optimization (LBO) algorithms from various aspects, evaluated the performance of representative LBO algorithms, summarized the types of problems to which LBO is applicable, and proposed directions for improvement. [PERSON] et al. [4] investigated the contributions related to the green VRP and proposed a classification scheme based on the variants considered in the scientific literature, so as to provide a comprehensive and structured survey of the state of knowledge, as well as to discuss the most important features of the problems and to indicate future directions. [PERSON] et al. [5] provided and categorized a list of VRP datasets. [PERSON] et al. [6] systematically reviewed and analyzed recent research on the VRP from 2001 to 2022, focusing on new and emerging topics in VRPs. Based on the basic VRP, [PERSON] et al. [7] classified VRPs according to their characteristics and practical applications, gave the unified description and mathematical model of each type of problem, and then analyzed the solution methods of each type of VRP. [PERSON] et al. [8] comprehensively analyzed and summarized the literature related to VRPs from 1959 to 2022 by using the knowledge graph, and classified the VRP models and their solutions. However, the complexity of the VRP increases with the additional constraints of real life. The VRP is NP-hard, so finding the optimal solution is difficult. Therefore, the method proposed to solve the VRP aims to find the approximate optimal solution via an efficient computational approach. VRPs for AGVs are solved by using exact algorithms and intelligent evolutionary algorithms. The exact algorithms include the branch-and-bound method, integer linear programming method, and dynamic programming method, which are suitable for solving small-scale VRPs with simple structures. [PERSON] [9] et al. proposed a simulation-based restricted dynamic programming approach to solve the VRP associated with traffic emissions. [PERSON] [10] proposed a branch-and-price algorithm that solves the vehicle routing with demand allocation problem. However, the exact algorithm is prone to falling into a local optimal solution or taking too long to compute when solving large-scale VRPs. In contrast, intelligent evolutionary algorithms can find satisfactory approximate optimal solutions in a limited time when solving large-scale VRPs. Therefore, many experts have improved and designed intelligent evolutionary algorithms. [PERSON] [11] et al. proposed an improved multiobjective genetic algorithm with tabu search (IMOGA-TS), which combines local and global searches with the improvement of solutions at each iteration by TS to solve a collaborative multidepot EV routing problem with time windows and shared charging stations (CMEVRPTW-SCS). [PERSON] [12] proposed a multiobjective genetic algorithm with stochastic partially optimized cyclic shift crossover to solve the multiobjective VRPTW. The multiobjective model is always transformed into a single-objective model by weighting or other conversion methods. In the VRP, the total objective is often composed of multiple objectives with mutual exclusivity, which means that improving the performance of one objective may lead to degradation of the performance of other objectives.