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

TL;DR

This paper develops stochastic models for Jaya algorithms, revealing key update behaviors and deriving complexity bounds, supported by empirical validation, to aid in designing improved optimization heuristics.

Contribution

The paper introduces stochastic models for Jaya and semi-steady-state Jaya algorithms, providing analytical bounds and insights into their update dynamics and complexities.

Findings

Maximum expected worst-index updates per generation is 1.7.

Expected best-index updates decrease monotonically with generations.

Upper bounds and asymptotics for update counts depend on distribution type.

Abstract

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.