  When globally optimal solutions of complicated optimization problems cannot
be located by evolutionary algorithms (EAs) in polynomial expected running
time, the hitting time/running time analysis is not flexible enough to
accommodate the requirement of theoretical study, because sometimes we have no
idea on what approximation ratio is available in polynomial expected running
time. Thus, it is necessary to propose an alternative routine for the
theoretical analysis of EAs. To bridge the gap between theoretical analysis and
algorithm implementation, in this paper we perform an error analysis where
expected approximation error is estimated to evaluate performances of
randomized search heuristics (RSHs). Based on the Markov chain model of RSHs,
the multi-step transition matrix can be computed by diagonalizing the one-step
transition matrix, and a general framework for estimation of expected
approximation errors is proposed. Case studies indicate that the error analysis
works well for both uni- and multi-modal benchmark problems. It leads to
precise estimations of approximation error instead of asymptotic results on
fitness values, which demonstrates its competitiveness to fixed budget
analysis.
