## Case Study
### Result Study  
After optimization was completed, the optimization curve of the average fitness of the population in 300 iterations was obtained first, and it was compared with the results of the original DE algorithm, as shown in Figure 8. It is evident that our method has a much faster convergence rate compared with the original DE algorithm and produces better variable values that are related to a higher NPV. To be specific, starting from the 30 th iteration, the rate of increase in population fitness of the two methods starts to differ until it reaches the maximum gap at the 50 th iteration. The gap between the two even reaches 20% of the original DE algorithm result. Our method starts to converge and gradually stabilizes around 250 iterations, while the original DE algorithm begins to converge at a relatively low NPV value from 150 iterations. By 300 iterations, both algorithms have stabilized and our algorithm's optimal solution has produced a net present value that is approximately 50% higher than the result of the original DE algorithm. Additionally, it can be observed that the SDEA algorithm, due to its use of Latin hypercube sampling, initially has better objective function values than our algorithm. However, in the later stages, since it primarily focuses on exploring the region around optimal samples and relies on surrogate models that cannot accurately simulate the real simulator, its exploration capability diminishes. As a result, the objective function improvement significantly slows down, and the final convergence results are not as good as those of our algorithm. To further clarify the cause of this difference, we compared the well-deployment maps based on permeability fields. Based on the permeability field, our method for optimal well placement design is illustrated in Figure 9, where the well is placed at the grids with high permeability, indicating its presence in a cave or a fracture. Additionally, the best drilling sequence should prioritize deploying well sites in large, underexploited caves that are far away from old wells in order to maximize the exploration of the remaining oil reserves. As the distant reserves are utilized, new wells can then be deployed to exploit areas with lower permeability or smaller reserves. In contrast, although the well sites are located in high permeability and high saturation regions, well sites designed by the original DE and  
Figure 8: The contrast of the optimization curve of our method with the original DE. SDEA algorithm are located at the edge of caves or fissure bodies and this explains why the NPV of both algorithms is lower compared to our algorithm. Furthermore, we compared the optimization results of well type and injection-production rate and presented them in the form of a heat map, as shown in Figure 10, where positive values represent production wells, negative values represent injection wells, and the final values represent the corresponding rate. The results indicate that our optimization approach adopts a strategy of full production with phase-wise regulation of the production rate to create an asynchronous fluctuation of production rate from these wells, thus activating the flow of residual oil at the corner of the pore. In comparison, the original DE algorithm tends to first replenish energy and then produce at full capacity, which results in a low initial production rate and more dead oil at some pores. Although the strategy proposed by the SDEA algorithm reduces the occurrence of water injection events, the true oil production potential of the reservoir is not fully realized. Finally, due to the utilization of batch parallel technology in our method, our algorithm effectively saves time. As demonstrated by the time consumption comparison, as shown in Figure 11, our method's time consumption is slightly higher than the SDEA algorithm but significantly lower than that of the original DE algorithm and is only one twentieth of the original DE algorithm's calculation time. Figure 10: The optimized well types and corresponding rate.