We build stochastic models for analyzing Jaya and semi-steady-state Jaya algorithms. The analysis shows that for semi-steady-state Jaya (a) the maximum expected value of the number of worst-index updates per generation is a paltry 1.7 regardless of the population size; (b) regardless of the population size, the expectation of the number of best-index updates per generation decreases monotonically with generations; (c) exact upper bounds as well as asymptotics of the expected best-update counts can be obtained for specific distributions; the upper bound is 0.5 for normal and logistic distributions, $\ln 2$ for the uniform distribution, and $e^{-\gamma} \ln 2$ for the exponential distribution, where $\gamma$ is the Euler-Mascheroni constant; the asymptotic is $e^{-\gamma} \ln 2$ for logistic and exponential distributions and $\ln 2$ for the uniform distribution (the asymptotic cannot be obtained analytically for the normal distribution). The models lead to the derivation of computational complexities of Jaya and semi-steady-state Jaya. The theoretical analysis is supported with empirical results on a benchmark suite. The insights provided by our stochastic models should help design new, improved population-based search/optimization heuristics.
翻译:我们为分析Jaya和半稳定状态Jaya算法建立随机模型,分析表明,对于半稳定状态Jaya(a) 半稳定状态Jaya (a) 每一代最坏指数更新数量的最大预期值是微不足道的1.7美元,而不论人口规模大小;(b) 无论人口规模大小,每代最佳指数更新数量的预期值将逐代单数下降;(c) 具体分布可以取得预期最佳数字的精确上限值和抽取值;正常和后勤分配的上限值为0.5美元,统一分配的上限值为2美元,指数分配的上限值为2美元,指数分配的最大预期值为2美元,而美元为2美元,其中美元为美元=伽玛-马舍罗尼常数;(b) 无论人口规模大小,每代人口最佳指数更新的预期值将逐代单数下降;(c) 物流和指数分布的准确上限值为2美元,统一分配的上限值为2美元(正常分配的上限无法通过分析获得分析,统一分布的上限为0.5美元,而统一分配的上限值为$-gammamamama) 模型导致指数化的计算结果。