IEEE Trans Cybern. 2022 Oct;52(10):10123-10136. doi: 10.1109/TCYB.2021.3064556. Epub 2022 Sep 19.
Existing techniques on dealing with uncertain optimization problems (UOPs) mostly rely on the preference information of decision makers (DMs) or the knowledge involved in probability distributions on uncertainties. Actually, accurate preferences and distribution information of uncertainties are hard to obtain due to the lack of knowledge. Besides, it is risky to make assumptions on this information to handle uncertainties when DMs do not have sufficient knowledge about the problem. This article attempts to treat UOPs in an a posteriori manner and proposes a subproblem co-solving evolutionary algorithm (EA) for UOPs, namely, S-CoEA. It decomposes a UOP into a series of correlated subproblems by using the proposed decomposition strategy embedded with an original ordered weighted-sum (OWS) operator. These subproblems are formulated in different aggregation forms of sampled function values and represent different preferences on uncertainties. They are co-solved in parallel by using information from neighboring subproblems. The sampling strategy is used to gather the distribution information of uncertain functions and alleviate the detrimental effects of uncertainties. A sample-updating scheme based on historical information is presented to further improve the performance of S-CoEA. The proposed S-CoEA is compared with two state-of-the-art competitors, including the EA with the exponential sampling method (E-sampling) and the population-controlled covariance matrix self-adaptation evolution strategy (pcCMSA-ES). Numerical experiments are conducted on a series of test instances with various characteristics and different strength levels of uncertainties. Experimental results show that S-CoEA outperforms or performs competitively against competitors in the majority of 26 continuous test instances and four test cases of discrete redundancy allocation problems.
现有的不确定优化问题（UOP）处理技术大多依赖决策者（DM）的偏好信息或不确定性概率分布所涉及的知识。实际上，由于知识的缺乏，很难获得准确的偏好和不确定性分布信息。此外，当决策者对问题没有足够的了解时，基于此信息对不确定性进行假设以处理不确定性是有风险的。本文试图从后验的角度处理 UOP，并提出了一种用于 UOP 的子问题协同求解进化算法（EA），即 S-CoEA。它通过使用嵌入原始有序加权和（OWS）算子的提出的分解策略，将 UOP 分解为一系列相关的子问题。这些子问题以不同的抽样函数值聚合形式进行形式化，代表了对不确定性的不同偏好。它们通过使用来自相邻子问题的信息并行协同求解。采样策略用于收集不确定函数的分布信息并减轻不确定性的不利影响。提出了一种基于历史信息的样本更新方案，以进一步提高 S-CoEA 的性能。将提出的 S-CoEA 与两种最先进的竞争对手进行了比较，包括具有指数采样方法（E-sampling）的 EA 和基于种群控制协方差矩阵自适应进化策略（pcCMSA-ES）。在具有各种特征和不同不确定性强度水平的一系列测试实例上进行了数值实验。实验结果表明，在大多数 26 个连续测试实例和 4 个离散冗余分配问题测试案例中，S-CoEA 在大多数情况下优于或与竞争对手竞争。
