Running time analysis: Convergence-based analysis reduces to switch analysis

Yang Yu, Chao Qian

Abstract: Evolutionary algorithms (EAs) are general purpose optimization tools that can be applied in various situations, therefore, general analysis approaches are appealing for facilitating the analysis of EAs in different problems. Expected running time is a key theoretical issue of evolutionary algorithms (EAs). Several general analysis approaches for the running time analysis of EAs have been proposed and have stimulated the theoretical development. Recently, switch analysis was proposed, which derives the running time of an EA process by comparing it with a simpler EA process. It has been proven that drift analysis and fitness level method are reducible to switch analysis, which means that switch analysis can derive at least as tight results as the two approaches. In this paper, we further prove that another analysis approach, convergence-based analysis, is reducible to switch analysis. We also show in a case study that switch analysis leads to a tighter result than convergence-based analysis.