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Top1. Introduction
Optimization problems deal with the situations in which it is mandatory to search for the most appropriate solution among all the available solutions of a particular problem in a reasonable amount of time. These large scale optimization problems often suffer from the problems of multi-modality, non-continuous, dimensionality, non-convex and so-on. So, to tackle these real world complicated problems, efficient optimization algorithms are urgently required. Therefore, various evolutionary techniques have been developed and applied in recent years which include Genetic Algorithms (GAs), Particle Swarm Optimization algorithm (PSO), Differential Evolution algorithm (DE), Ant Colony Optimization (ACO), Artificial Bee Colony Strategy (ABC), and BBO (Simon, 2008).
From the last decade or so, the recent advances in theories and applications of nonlinear dynamics especially chaotic maps have drawn much attention in many fields of optimization in replacing certain algorithm dependent parameters (Jalili, Hosseinzadeh & Kaveh, 2014; Li-Jiang & Tian-Lun, 2002; Talatahari, Azar, Sheikholeslami & Gandomi, 2012). Chaotic maps have shown increase in population diversity and high level of mixing capability. Therefore, replacing a fixed parameter with the chaotic map may provide solutions with higher mobility and greater diversity. Many chaotic maps have been used by these meta-heuristic algorithms to improve upon the results of these algorithms through proper balance between exploration and exploitation activities (Li-Jiang & Tian-Lun, 2002; Talatahari, Azar, Sheikholeslami & Gandomi, 2012; Yang, Li & Cheng, 2007).
Mingjun & Huanwen (2004) presented a novel algorithm by replacing the Gaussian distribution of simulated annealing with chaotic initialization and chaotic sequences. The proposed algorithm has been validated on typical complex function optimization problems. Alatas, Akin & Ozer, (2009) have presented twelve chaos-embedded PSO methods with the use of eight chaotic maps and analysed them on the benchmark functions. The simulation results demonstrated the robustness of the proposed methods with increased solution quality, i.e., in some cases they improved the global searching capability by escaping the local solutions. Alatas (2010a) presented two new ABC algorithms in combination with seven chaotic maps for parameter adaptation for improved convergence characteristics and to prevent the ABC from plunging into local solutions.
Alatas (2010b) presented seven new harmony search algorithms which employ chaotic maps for better convergence characteristics. In this research work, chaotic number generators are employed whenever there is a need for it by the classical harmony search algorithm. It has been demonstrated that results obtained from these coupling of various areas, like those of harmony search and complex dynamics, can significantly improve the quality of results in some optimization problems. Gharooni-fard et al. (2010) introduced a novel chaos based genetic based algorithm. The proposed approach, when applied to both balanced and unbalanced workflow structures, have validated its usage. Basically, the proposed approach scatters the solutions among the whole search space by employing the positive characteristics of the chaotic variables which together with avoiding premature convergence of the solutions also generates superior results within a shorter time.