Theoretical analyses of evolution strategies are indispensable for gaining a deep understanding of their inner workings. For constrained problems, rather simple problems are of interest in the current research. This work presents a theoretical analysis of a multi-recombinative evolution strategy with cumulative step size adaptation applied to a conically constrained linear optimization problem. The state of the strategy is modeled by random variables and a stochastic iterative mapping is introduced. For the analytical treatment, fluctuations are neglected and the mean value iterative system is considered. Nonlinear difference equations are derived based on one-generation progress rates. Based on that, expressions for the steady state of the mean value iterative system are derived. By comparison with real algorithm runs, it is shown that for the considered assumptions, the theoretical derivations are able to predict the dynamics and the steady state values of the real runs.

中文翻译：

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(μ/μI,λ)-CSA-ES 与投影修复应用于圆锥约束问题的分析

进化策略的理论分析对于深入了解其内部运作是必不可少的。对于受约束的问题，目前的研究对相当简单的问题感兴趣。这项工作提出了多重组进化策略的理论分析，该策略具有应用于圆锥约束线性优化问题的累积步长自适应。该策略的状态由随机变量建模，并引入了随机迭代映射。对于解析处理，忽略波动并考虑均值迭代系统。非线性差分方程是基于一代进展率推导出来的。在此基础上，推导出均值迭代系统的稳态表达式。通过与真实算法运行的比较，