Please cite this article in press as: A.H. Gandomi, X.-S. Yang, Chaotic bat algorithm, J. Comput. Sci. (2013), http://dx.doi.org/10.1016/j.jocs.2013.10.002 ARTICLE IN PRESS G Model JOCS-232; No. of Pages 9 Journal of Computational Science xxx (2013) xxx–xxx Contents lists available at ScienceDirect Journal of Computational Science journa l h om epage: www.elsevier.com/locate/jocs Chaotic bat algorithm Amir H. Gandomi a , Xin-She Yang b,∗ a Department of Civil Engineering, The University of Akron, Akron, OH 44325, USA b School of Science and Technology, Middlesex University, Hendon, London NW4 4BT, UK a r t i c l e i n f o Article history: Received 5 December 2012 Received in revised form 18 July 2013 Accepted 4 October 2013 Available online xxx Keywords: Bat algorithm Chaos Metaheuristic Global optimization a b s t r a c t Bat algorithm (BA) is a recent metaheuristic optimization algorithm proposed by Yang. In the present study, we have introduced chaos into BA so as to increase its global search mobility for robust global optimization. Detailed studies have been carried out on benchmark problems with different chaotic maps. Here, four different variants of chaotic BA are introduced and thirteen different chaotic maps are utilized for validating each of these four variants. The results show that some variants of chaotic BAs can clearly outperform the standard BA for these benchmarks. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Many design optimization problems are often highly nonlin- ear, which can typically have multiple modal optima, and it is thus very challenging to solve such multimodal problems. To cope with this issue, global optimization algorithms are widely attempted, however, traditional algorithms may not produce good results, and latest trends are to use new metaheuristic algorithms [1]. Meta- heuristic techniques are well-known global optimization methods that have been successfully applied in many real-world and com- plex optimization problems [2,3]. These techniques attempt to mimic natural phenomena or social behavior so as to generate better solutions for optimization problem by using iterations and stochasticity [4]. They also try to use both intensification and diversification to achieve better search performance. Intensifica- tion typically searches around the current best solutions and selects the best candidate designs, while the diversification process allows the optimizer to explore the search space more efficiently, mostly by randomization [1]. In recent years, several novel metaheuristic algorithms have been proposed for global search. Such algorithms can increase the computational efficiency, solve larger problems, and imple- ment robust optimization codes [5]. For example, Xin-She Yang [6] recently developed a promising metaheuristic algorithm, called bat algorithm (BA). Preliminary studies suggest that the BA can have ∗ Corresponding author. Tel.: +44 2084112351. E-mail addresses: a.h.gandomi@gmail.com, ag72@uakron.edu (A.H. Gandomi), x.yang@mdx.ac.uk (X.-S. Yang). superior performance over genetic algorithms and particle swarm optimization [6], and it can solve real world and engineering opti- mization problems [7–10]. On the other hand, recent advances in theories and applications of nonlinear dynamics, especially chaos, have drawn more attention in many fields [10]. One of these fields is the applications of chaos in optimization algorithms to replace certain algorithm-dependent parameters [11]. Previously, chaotic sequences have been used to tune param- eters in metaheuristic optimization algorithms such as genetic algorithms [12], particle swarm optimization [13], harmony search [14], ant and bee colony optimization [15,16], imperialist competi- tive algorithm [17], firefly algorithm [18], and simulated annealing [19]. Such a combination of chaos with metaheuristics has shown some promise once the right set of chaotic maps are used. It is still not clear why the use of chaos in an algorithm to replace cer- tain parameters may change the performance, however, empirical studies indeed indicate that chaos can have high-level of mixing capability, and thus it can be expected that when a fixed parame- ter is replaced by a chaotic map, the solutions generated may have higher mobility and diversity. For this reason, it may be useful to carry out more studies by introducing chaos to other, especially newer, metaheuristic algorithms. Therefore, one of the aims of this paper is to introduce chaos into the standard bat algorithm, and as a result, we propose a chaos- based bat algorithm (CBA). As different chaotic maps may lead to different behavior of the algorithm, we then have a set of chaos- based bat algorithms. In these algorithms, we use different chaotic systems to replace the parameters in BA. Thus different methods that use chaotic maps as potentially efficient alternatives to pseu- dorandom sequences have been proposed. In order to evaluate the 1877-7503/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jocs.2013.10.002