论文标题
Jaya和半态状态JAYA算法的随机模型
Stochastic models of Jaya and semi-steady-state Jaya algorithms
论文作者
论文摘要
我们构建了用于分析Jaya和半态状态JAYA算法的随机模型。分析表明，对于半态状态的Jaya（a），每代最差索引更新的最大预期值是一个微不足道的1.7，无论人口大小如何； （b）无论人口规模如何，每一代最佳索引更新数量的期望随几代人的单调减少； （c）对于特定分布，可以获得预期最佳状态计数的确切上限以及渐近学；对于正常和逻辑分布的上限为0.5，均匀分布的$ \ ln 2 $，对于指数分布而言，$ e^{ - γ} \ ln 2 $，其中$γ$是Euler-Mascheroni常数；渐近分布和指数分布的渐近分布是$ e^{ - γ} \ ln 2 $，对于均匀分布的$ \ ln 2 $（对于正态分布，无法分析渐近）。这些模型导致了Jaya和Semi Steaty-State Jaya的计算复杂性的推导。理论分析得到了基准套件的经验结果。我们随机模型提供的见解应有助于设计新的，改进的基于人群的搜索/优化启发式方法。
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 $e^{-γ} \ln 2$ for the exponential distribution, where $γ$ is the Euler-Mascheroni constant; the asymptotic is $e^{-γ} \ln 2$ 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.
