Running Time Analysis of the (1+1)-EA for Robust Linear Optimization
This work addresses a gap in theoretical analysis for evolutionary algorithms applied to robust optimization, which is incremental but provides specific bounds for practitioners in uncertain optimization domains.
The paper analyzes the expected running time of the (1+1)-EA for robust linear optimization problems with cardinality constraints, deriving tight parameter ranges for polynomial-time solutions under deletion-robust and worst-case scenarios.
Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a series of efforts devoted to analyzing the running time of EAs for optimization under uncertainties. Existing studies mainly focus on noisy and dynamic optimization, while another common type of uncertain optimization, i.e., robust optimization, has been rarely touched. In this paper, we analyze the expected running time of the (1+1)-EA solving robust linear optimization problems (i.e., linear problems under robust scenarios) with a cardinality constraint $k$. Two common robust scenarios, i.e., deletion-robust and worst-case, are considered. Particularly, we derive tight ranges of the robust parameter $d$ or budget $k$ allowing the (1+1)-EA to find an optimal solution in polynomial running time, which disclose the potential of EAs for robust optimization.