Recently surrogate functions based on the tail inequalities were developed to evaluate the chance constraints in the context of evolutionary computation and several Pareto optimization algorithms using these surrogates were successfully applied in optimizing chance-constrained monotone submodular problems. However, the difference in performance between algorithms using the surrogates and those employing the direct sampling-based evaluation remains unclear. Within the paper, a sampling-based method is proposed to directly evaluate the chance constraint. Furthermore, to address the problems with more challenging settings, an enhanced GSEMO algorithm integrated with an adaptive sliding window, called ASW-GSEMO, is introduced. In the experiments, the ASW-GSEMO employing the sampling-based approach is tested on the chance-constrained version of the maximum coverage problem with different settings. Its results are compared with those from other algorithms using different surrogate functions. The experimental findings indicate that the ASW-GSEMO with the sampling-based evaluation approach outperforms other algorithms, highlighting that the performances of algorithms using different evaluation methods are comparable. Additionally, the behaviors of ASW-GSEMO are visualized to explain the distinctions between it and the algorithms utilizing the surrogate functions.

翻译：近期，基于尾部不等式的代理函数被开发用于评估进化计算中的机会约束，并且利用这些代理函数的多种帕累托优化算法已成功应用于优化机会约束单调子模问题。然而，使用代理函数的算法与采用直接基于采样评估的算法之间的性能差异仍不清楚。本文提出了一种基于采样的方法直接评估机会约束。此外，为了解决更具挑战性的设置问题，引入了一种增强型GSEMO算法，该算法集成了自适应滑动窗口，称为ASW-GSEMO。实验中，采用基于采样方法的ASW-GSEMO在不同设置下对最大覆盖问题的机会约束版本进行了测试。其结果与其他使用不同代理函数的算法的结果进行了比较。实验结果表明，采用基于采样评估方法的ASW-GSEMO优于其他算法，表明使用不同评估方法的算法性能具有可比性。此外，还可视化了ASW-GSEMO的行为，以解释其与使用代理函数的算法之间的区别。