  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.
