Error analysis of elitist randomized search heuristics

For complicated problems that cannot be solved in polynomial first hitting time (FHT)/running time(RT), a remedy is to perform approximate FHT/TH analysis for given approximation ratio. However, approximate FHT/RT analysis of randomized search heuristics (RSHs) is not flexible enough because polynomial FHT/RT is not always available for any given approximation ratio. In this paper, the error analysis, which focuses on estimation of the expected approximation error of RSHs, is proposed to accommodate the requirement of flexible analysis. By diagonalizing one-step transition matrix of the Markov chain model, a tight estimation of the expected approximation error can be obtained via estimation of the multi-step transition matrix. For both uni-and multi-modal problems, error analysis leads to precise estimations of approximation error instead of asymptotic results on fitness values, which demonstrates its competitiveness to FHT/RT analysis as well as the fixed budget analysis.