## 1 Introduction
These objectives may not be linearly related and cannot be transformed into a single-objective problem with weights. Therefore, there is a limitation in using a single-objective model to solve the VRP. Multiobjective optimization problems (MOPs) are proposed for optimizing multiple objectives which are always mutually exclusive at the same time. In recent decades, researchers have proposed many methods for solving MOPs. Multiobjective evolutionary algorithms (MOEAs) are the mainstream methods for solving MOPs. [PERSON] [13] proposed an enhanced algorithm based on SPEA2 (ESPEA) to solve the pickup vehicle scheduling problem with mixed steel storage (PVSP-MSS) which optimizes the makespan of pickup vehicles and the makespan of steel logistics parks at the same time. [PERSON] [14] proposed an improved hyperplane-assisted evolutionary algorithm (IhpaEA) to solve the distributed hybrid flow shop scheduling problem (DHFS), which takes maximum completion time and energy consumption as objectives. Based on different algorithmic strategies, most MOEAs can be classified into the following categories: (1) based on their dominant relationship, such as the NSGA-II [15], SPEA [1], and PESA-II [16]; (2) based on decomposition, such as the MOEA/D [17], MOEA/D-M2M [18], and RVEA [19]; and (3) based on performance evaluation indicators, such as the IBEA [20], SMSEMOA [21], and DNMOEA/HI [22]. From the above algorithms, Pareto solutions can be obtained. However, for MOPs, the number of Pareto solutions increases as the number of objectives increases. For practical scenarios, not all solutions make sense, especially for uncertain time-based VRPs. Uncertain times require Pareto solutions that are most resistant to uncertain times compared to deter ministic times, and uncertainty in VRPs is rarely considered in these algorithms. To solve this problem, robust optimization has been proposed, where the researcher searches for robust solutions with the strongest resistance to interference. Robust optimization [23] means that the solution and performance results remain relatively unchanged when exposed to uncertain conditions. The solution is usually evaluated using the most unfavorable uncertainty. [PERSON] [24] et al. proposed a new method that sequentially approaches the robust Pareto front (SARPF) from nominal Pareto points to solve MOPs with uncertainties. [PERSON] et al. [25] introduced and discussed existing methods for dealing with different uncertainties and studied the relationships between different categories of uncertainty. [PERSON] [26] et al. introduced and compared the NSGA-II with an improved predator-prey algorithm for the VRPTW with uncertain travel times. [PERSON] [27] et al. used a robust multiobjective optimization optimization evolutionary algorithm (RMOEA) to solve robust multiobjective optimization problems (RMOPs), which consists of two parts: multiobjective optimization using the improved NSGA-II and robust optimization to search for a robust optimal frontier. The robust optimization in this paper is based on Monte Carlo simulation to simulate the practical environment in which the results are approached to the practical situation through a large number of simulation experiments. The number of feasible times of Monte Carlo simulation under the disturbance of uncertainty coefficients is taken as the criterion for assessing the robustness of the solution. In the VRP, the AGV operation time, total travel distance of the AGVs or number of AGVs are often used as objectives. However, the just-in-time (JIT) of the material distribution is often ignored. In addition, the literature discusses the robustness of VRPs, but few papers have combined robustness with JIT problems. JITs pursue just-in-time arrivals, and uncertain times can seriously affect the realization of JIT, so combining JITs with robust optimization can improve the possibility of realizing JITs. To solve the above issues, in this paper, the multiobjective robust VRP model that simultaneously considers uncertainty and JIT strategy is proposed.