A novel chaotic Jaya algorithm for unconstrained numerical optimization

Abstract

Jaya algorithm is one of the recent algorithms developed to solve optimization problems. The basic concept of this algorithm consists in moving the obtained solution, for a given problem, toward the best solution and avoiding the worst one. However, it severely suffers from premature convergence problem and therefore can be easily trapped in local optimums. This study aimed to alleviate these drawbacks and improve the performance of the original Jaya algorithm. Here, three new mutation strategies were implemented in the original Jaya to improve both its global and local search abilities. Chaotic maps were proved to be able to boost the search capabilities of meta-heuristic algorithms. Therefore, after demonstrating its chaotic behavior through the sensitivity to initial conditions, topological transitivity and the density of periodic points, we proposed a new 2D cross chaotic map. The chaotic sequences provided by the proposed chaotic map were embedded into the original Jaya algorithm to generate the initial population and control the search equations. It is worth mentioning that the modifications incorporated in the original algorithm did not affect its two essential characteristics, i.e., simplicity and nonrequirement of additional control parameters. As case studies, sixteen benchmark functions were used to evaluate the performance of the proposed chaotic Jaya algorithm (C-Jaya) regarding solution accuracy and convergence speed. Comparisons with some other meta-heuristic algorithms for low-, middle- and high-dimensional benchmark functions show that the proposed C-Jaya algorithm enhances the performance of original Jaya significantly. Moreover, it offers the fastest global convergence, the highest solution quality and it is the most robust on almost all the test functions among all the algorithms. Nonparametric statistical procedures, i.e., Friedman test, Friedman aligned ranks test and Quade test, conducted to analyze the obtained results, show the superiority of the proposed algorithm.