Gomez proposes a formal and systematic approach for characterizing stochastic global optimization algorithms. Using it, Gomez formalizes algorithms with a fixed next-population stochastic method, i.e., algorithms defined as stationary Markov processes. These are the cases of standard versions of hill-climbing, parallel hill-climbing, generational genetic, steady-state genetic, and differential evolution algorithms. This paper continues such a systematic formal approach. First, we generalize the sufficient conditions convergence lemma from stationary to non-stationary Markov processes. Second, we develop Markov kernels for some selection schemes. Finally, we formalize both simulated-annealing and evolutionary-strategies using the systematic formal approach.

翻译：Gomez 提出了一种正式和系统化的方法来定性随机全球优化算法。 Gomez 利用它正式确定算法,采用固定的下层人口随机化方法,即固定的Markov 过程的算法。 这些都是山坡攀爬、平行山坡攀爬、代代代遗传、 稳定状态遗传和差异演进算法的标准版本。 本文继续采用这种系统化的正式方法。 首先, 我们从固定状态到非固定状态的Markov 过程的足够条件趋同。 第二, 我们为某些选择计划开发了Markov 内核。 最后, 我们用系统化的正式方法将模拟和进化战略都正式化。