Estimating Approximation Errors of Elitist Evolutionary Algorithms

Abstract

When evolutionary algorithms (EAs) are unlikely to locate precise global optimal solutions with satisfactory performances, it is important to substitute alternative theoretical routine for the analysis of hitting time/running time. In order to narrow the gap between theories and applications, this paper is dedicated to perform an analysis on approximation error of EAs. First, we proposed a general result on upper bound and lower bound of approximation errors. Then, several case studies are performed to present the routine of error analysis, and theoretical results show the close connections between approximation errors and eigenvalues of transition matrices. The analysis validates applicability of error analysis, demonstrates significance of estimation results, and then, exhibits its potential to be applied for theoretical analysis of elitist EAs.

Error analysis of elitist randomized search heuristics

“…As suggested by He et al [35,36], we investigated performances of random local search (RLS) for the case that the status transition matrices can be computationally diagonalized, and estimated the expected approximation error for arbitrary iteration budget [37]. However, when the bitwise mutation is employed in the (1+1) evolutionary algorithm ((1+1)EA), the transition matrix is a full upper triangular transition matrix, the t-th power of which is theoretically feasible but computationally unavailable.…”