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.

翻译：当在多式预期运行时间中,无法通过演进算法找到复杂的优化问题的全球最佳解决办法时,对时间/运行时间的分析不够灵活,无法满足理论研究的要求,因为有时我们不知道在多式预期运行时间中,可以找到什么近似比率。因此,有必要提出一种替代的常规方法,用于对EA进行理论分析。为了缩小理论分析与算法实施之间的差距,本文件中我们进行了一项错误分析,即估计近似误差,以评价随机搜索超常值的性能。根据RSHs的Markov链模型,多步过渡矩阵可以通过对单步过渡矩阵进行分解来计算,并提出了一个估计预期近似误差的一般框架。案例研究表明,误差分析对单式和多模式基准问题都有效。通过精确估计近似误,而不是对健康值的无序结果,这显示了其对固定预算分析的竞争力。