S-CoEA: Subproblems Co-Solving Evolutionary Algorithm for Uncertain Optimization

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.