Chaotic bat algorithm

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 vailable online xxx eywords: at algorithm haos etaheuristic lobal optimization 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.   Many design optimization problems are often highly nonlinar, which can typically have multiple modal optima, and it is thus ery challenging to solve such multimodal problems. To cope with his issue, global optimization algorithms are widely attempted, owever, traditional algorithms may not produce good results, and atest trends are to use new metaheuristic algorithms . Metaeuristic techniques are well-known global optimization methods hat have been successfully applied in many real-world and comlex optimization problems [2,3]. These techniques attempt to imic natural phenomena or social behavior so as to generate etter solutions for optimization problem by using iterations and tochasticity . They also try to use both intensification and iversification to achieve better search performance. Intensificaion typically searches around the current best solutions and selects he best candidate designs, while the diversification process allows he optimizer to explore the search space more efficiently, mostly y randomization . In recent years, several novel metaheuristic algorithms have een proposed for global search. Such algorithms can increase he computational efficiency, solve larger problems, and implePlease cite this article in press as: A.H. Gandomi, X.-S. http://dx.doi.org/10.1016/j.jocs.2013.10.002 ent robust optimization codes . For example, Xin-She Yang  ecently developed a promising metaheuristic algorithm, called bat lgorithm (BA). Preliminary studies suggest that the BA can have ∗ Corresponding author.  E-mail addresses: a.h.gandomi@gmail.com, ag72@uakron.edu (A.H. Gandomi), .yang@mdx.ac.uk (X.-S. Yang). 877-7503/$ – see front matter , and it can solve real world and engineering optimization 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 parameters in metaheuristic optimization algorithms such as genetic algorithms , particle swarm optimization [13], harmony search [14], ant and bee colony optimization [15,16], imperialist competitive algorithm , 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 certain 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 parameter 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 chaosbased bat algorithm (CBA). As different chaotic maps may lead to different behavior of the algorithm, we then have a set of chaosYang, Chaotic bat algorithm,  (2013), 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 pseudorandom sequences have been proposed. In order to evaluate the