Stochastic models of Jaya and semi-steady-state Jaya algorithms

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.

Semi-steady-state Jaya Algorithm

The Jaya algorithm is arguably one of the fastest-emerging metaheuristics amongst the newest members of the evolutionary computation family. The present paper proposes a new, improved Jaya algorithm by modifying the update strategies of the best and the worst members in the population. Simulation results on a twelve-function benchmark test-suite as well as a real-world problem of practical importance show that the proposed strategy produces results that are better and faster in the majority of cases. Statistical tests of significance are used to validate the performance improvement.