Nonlinear Dyn
https://doi.org/10.1007/s11071-018-4271-5
ORIGINAL PAPER
A novel chaotic Jaya algorithm for unconstrained numerical
optimization
Anouar Farah · Akram Belazi
Received: 20 June 2017 / Accepted: 4 April 2018
© Springer Science+Business Media B.V., part of Springer Nature 2018
Abstract Jaya algorithm is one of the recent algo-
rithms 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. How-
ever, it severely suffers from premature convergence
problem and therefore can be easily trapped in local
optimums. This study aimed to alleviate these draw-
backs 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 demonstrat-
ing its chaotic behavior through the sensitivity to ini-
tial conditions, topological transitivity and the den-
sity of periodic points, we proposed a new 2D cross
chaotic map. The chaotic sequences provided by the
proposed chaotic map were embedded into the orig-
inal Jaya algorithm to generate the initial population
and control the search equations. It is worth mentioning
that the modifications incorporated in the original algo-
rithm did not affect its two essential characteristics, i.e.,
A. Farah
CEM Laboratory, National Engineering School of Sfax,
Sfax, Tunisia
e-mail: farah.anouar@gmail.com
A. Belazi (B )
RISC Laboratory, National Engineering School of Tunis,
University of Tunis El Manar, 1002 Tunis, Tunisia
e-mail: akram.belazi@enit.utm.tn
simplicity and nonrequirement of additional control
parameters. As case studies, sixteen benchmark func-
tions were used to evaluate the performance of the pro-
posed chaotic Jaya algorithm (C-Jaya) regarding solu-
tion 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 solu-
tion quality and it is the most robust on almost all the
test functions among all the algorithms. Nonparamet-
ric statistical procedures, i.e., Friedman test, Friedman
aligned ranks test and Quade test, conducted to ana-
lyze the obtained results, show the superiority of the
proposed algorithm.
Keywords Chaos theory · 2D cross chaotic map ·
Optimization · Jaya algorithm · C-Jaya algorithm
1 Introduction
1.1 Research background
Several problems in various engineering domains can
be formulated as optimization problems. Thus, the
achievement of optimal solutions requires better opti-
mization algorithms. Traditional optimization algo-
rithms like dynamic programming, linear program-
ming, steepest descent usually fail to reach optimal
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