## 4 The Proposed AC-NSGA-III Algorithm
### Operator Design
#### 4.2.1 IRC Coding
Figure 9: Experimental results. (**a**) Total customer waiting time; (**b**) Order timeout rate. In Figure 10, as the standard deviation of meal preparation time increases, the standard deviation of total customer waiting time under Model-Unc is much smaller than that under model-C. When the standard deviation of meal preparation time of restaurants is 1.2, the scheduling scheme solved by Model-Unc reduces the standard deviation of total customer waiting time by 38.1% compared with model-C. The experimental results of the order timeout rate are similar, thus they will not be described here. * Comparison of order combination patterns. The solution of the MO-RPDRP model is a three-dimensional Pareto front. In order to enable the Pareto front to be located on a two-dimensional plane, the look-forward objective dimension is removed in the following experiments. In this experiment, the model considers the look-forward objective. In this experiment, the rolling scheduling with a large number of remaining unfinished orders is taken as an example. It makes the comparative effect of Pareto frontier more obvious under different order combination modes. Figure 11 shows the change of the number of remaining unfinished orders under each rolling schedule of model-1 (four examples). In each group of examples, the 7 th and 8 th rolling scheduling have the largest number of remaining orders, so they are selected as examples. Figure 12 takes A1 as an example; it shows Pareto frontiers of three order modes under model-1. It can be seen from the figure that the Pareto frontier of the model in AC strategy is significantly better than the other two. * Comparison of look-forward optimization effects. The model considering the look-forward objective is denoted as model-1. A model that does not consider the look-forward objective is denoted as model-2. Taking A1 as an example, to compare the solutions of mode-1 and mode-2, the orders of the 4 th, 7 th, 11 th, and 15 th rolling scheduling are selected as experimental examples. The solution extracted from the Pareto frontier obtained by mode-1 is represented as solu-1. The solution extracted from the Pareto frontier obtained by mode-2 is represented as solu-2. The experimental results are shown in the figure below. In Figure 13, on the fourth rolling scheduling, the solutions extracted from Pareto front of model-2 dominate the solutions extracted from Pareto front of model-1. With the increasing of rolling schedule times, the scheduling after-effect of look-forward objective increases gradually. Pareto frontier obtained by model-1 considering look-forward objective is significantly better than Pareto frontier obtained by model-2 without look-forward objective. The solutions extracted from the Pareto front of model-2 no longer dominate the solutions extracted from the Pareto front of model-1. * Comparison of advantages of scheduling methods When the experiment is completed, the four scheduling methods are compared comprehensively. The results are shown in Table 4. The experimental data clearly show that

Figure 12: Superiority comparison of order combination mode. Figure 13: Superiority comparison of look-forward process. the proposed scheduling method shows significant advantages in objective function 1 and objective function 2. ## 6 Conclusions

In this paper, we considered the uncertainty of the meal preparation time and the AGV route optimization problem was addressed. Based on the realistic constraints, such as order node access sequence restrictions and vehicle volume, a MO-RPDRP model integrating an AC strategy and node sequence is developed. In the model, customer waiting time and order timeout rate are taken into account. Meanwhile, an improved NSGA-III algorithm is designed. In the numerical experiment, the actual survey data of a regional delivery enterprise during the peak hours are taken as examples.