Stochastic Models of Jaya and Semi-Steady-State Jaya Algorithms

We build stochastic models for analyzing Jaya and semi-steady-state algorithms. The analysis shows that (a) the maximum expected value of number worst-index updates per generation is a paltry 1.7 regardless population size; (b) size, expectation best-index decreases monotonically with generations; (c) exact upper bounds as well asymptotics best-update counts can be obtained specific distributions; bound 0.5 normal logistic distributions, $\ln 2$ uniform distribution, $e^{-\gamma} \ln exponential where $\gamma$ Euler-Mascheroni constant; asymptotic distributions distribution (the cannot analytically distribution). lead to derivation computational complexities Jaya. theoretical supported empirical results on benchmark suite. insights provided by our should help design new, improved population-based search/optimization heuristics.