## 2 Background  
### Vehicle Routing Problem  
With further study of these elements, many VRP models, such as the green VRP (GVRP) and the dynamic VRP (DVRP), have been proposed and investigated. Moreover, depending on the objectives of the VRP, the problems can be categorized into single-objective VRPs and multiobjective VRPs. Many models and algorithms have been proposed for single-objective VRP. [PERSON] [29] et al. constructed a new VRPTW model of multiple distribution centers based on urban rail transportation, and a novel concentration-immune algorithm particle swarm optimization (C-IAPSO). [PERSON] [30] et al. proposed and established a reverse logistics VRP with backhauls (RL-VRPB) for waste packaging recycling route planning. An improved scatter search algorithm (ISS) was proposed, which introduces vehicle residual space recovery capability and the local search strategy. To solve the DVRP, [PERSON] [31] et al. proposed a population-based iterated local search (ILS) algorithm that integrates skewed variable neighborhood descent (SVND), a quality-and-diversity updating strategy and an adaptive multioperator perturbation procedure. [PERSON] [32] et al. proposed a new algorithm by transferring knowledge from useful customer representations that are captured from past solved VRPs. [PERSON] [33] et al. utilized a novel neural network integrated with a heterogeneous attention mechanism to solve the pickup and delivery problem in the VRP problem. [PERSON] [34] et al. proposed a novel bilevel ACO algorithm to solve the capacitated EV routing problem (CEVRP). The algorithm divides the problem into two subproblems: first, an order-first split-second max-min ant system algorithm is proposed to solve problems which ignore the electricity constraint. Second, a new removal heuristic combining a restricted enumeration method is designed to generate the charging schedule in the generated routes to satisfy the electricity constraint. However, these VRP algorithms do not consider the multiobjective characteristics of real problems and lack multidimensional consideration of real problems. Therefore, multiobjective VRPs as well as many variants of multiobjective algorithms have been proposed. [PERSON] [35] et al. proposed a new hybrid search genetic algorithm that combines the SPEA with a resultant local search heuristic to solve the stochastic GVRP, which simultaneously considers economic, environmental, and social aspects. [PERSON] [36] proposed four metaheuristic algorithms that involve combining different multiobjective algorithms to solve routing and scheduling vehicles on a cross-dock, minimizing the total shipping and tardiness costs and minimizing the number of outbound open doors as the objectives. [PERSON] [37] proposed M-NSGA-II, which combines the multifactorial evolutionary algorithm (MFEA) with NSGA-II to solve the VRP in low-carbon intelligent transportation. This approach considers carbon emissions, the number of vehicles, and distribution cost funding. [PERSON] [38] proposed a hybrid multiobjective genetic algorithm to solve the bi-objective overlapped links VRP (OLVRP) for valuable goods transportation, which takes the total cost and risk of routing as objectives. [PERSON] et al. [39] established a five-objective multidepot VRP with time windows (MDVRPTW) and proposed a two-stage MOEA to solve the problem. In stage I, the algorithm focuseson finding extreme solutions and forms a coarse Pareto front. Stage II extends the found solutions for approximating the whole Pareto front. The two-stage strategy provides a new method for balancing convergence and diversity when solving MOPs. Nevertheless, these multiobjective algorithms seldom consider the uncertainty of the real problem, which is an unavoidable problem in practical applications. Uncertainty disrupts problem-solving significantly. With the study of uncertainty problems, researchers have turned to incorporating robustness into VRPs that are insensitive to disturbances and can maintain the optimization performance at an acceptable level under disturbances.