# Multi-Objective Order Scheduling via Reinforcement Learning
## 5 Experiments
### Results on Generated Instances  
Figure 4 illustrates the process of a customer complaint handling system developed by Guangzhou Telecom. Customers call the customer service line to communicate their requirements. These requirements can be divided into four categories: 31% Consulting, 24% Malfunction, 23% Complaint, and 22% Business Process. After generating orders, 21% of orders about business expenses are handled by the intensive process. The remaining work orders are distributed to the ICS (Intensive Customer Service). These order are handled by district branches. Considering the area and maintenance costs, the distance and costs need to be considered to ensure that the single target approach will no longer work for this scenario. To simulate the dispatch data in real applications, we generate a dataset with three objectives: time, cost and distance. First, we trained our method on generated data with a size of \(15\times 15,20\times 20\). The three objective training curves are shown in Figure 5. We generated 100 instances of each  
Figure 4: The figure shows the process of generating and distributing work orders. size (\(10\times 10\), \(15\times 15\), \(20\times 20\)) randomly for ten times, and report the average of three objectives to suggest the effect of optimization. The learning curves of the three objectives are reported below. All of them show the effective optimization process of our algorithm. In order to highlight the significance of our multiple-objective algorithm, We performed testing on different sizes of generated datasets with three objectives, as mentioned above. The results of these three objectives are recorded in the table. We compared our dispatching policy with the deep reinforcement policy proposed by [PERSON] [12] and compared the time objective with a traditional baseline. We tested and verified our method on generated instances of sizes \((10\times 10,\)\(15\times 15,20\times 15,20\times 20,30\times 15,30\times 20)\). The results in Table 1 show an obvious improvement with our method. As Table 1 shows, our algorithm has better behavior on solving multiple-objective problems, while our MORL algorithm improves performance on the cost objective and distance objective. In particular, for datasets of size \(15\times 15,20\times 15,20\times 20\) we reached an approximately 20% reduction in the cost objective, while for datasets of size \(10\times 10,15\times 15,30\times 15,30\times 20\) we reached an approximately 20% reduction in the distance objective, which can ensure the nearest service point to take the job. Furthermore, through comparison with two widely used PDRs, namely, SPT and MWKR, we verified the optimization on the time objective. Above all, even though our method had slightly poorer performance on the time objective compared with single-objective reinforcement learning algorithms, the results show better performance on multiple-objective optimization, which is more suitable for practical applications. In addition, we realized optimization on the time objective. In order to demonstrate the superiority of our algorithm, we compared a model optimized using the convex hull algorithm with a model that was not optimized using the convex hull algorithm; the results are shown below in Table 2. The convex hull algorithm was used to optimize the model, aiming to ensure that the weight vector used in the linearly scalarized value function was maximized, thereby achieving optimal optimization across all objectives. The training curves for the three objectives are shown in Figure 5a-c. Based on our experimental results, we observed that the training curve significantly outperforms the unoptimized algorithm (see the Table 3). This indicates that our optimization strategies effectively improved the performance of the algorithm, increasing the stability and accuracy of model training. In the future, we intend to further investigate and optimize the details of the algorithm in order to achieve even better results.