A new optimization algorithm based on chaotic maps and golden section search method

• Published in: Engineering applications of artificial intelligence 2016-04, Vol.50, p.201-214
• Main Authors: Koupaei, J. Alikhani, Hosseini, S.M.M., Ghaini, F.M. Maalek
• Format: Article
• Language: English
• Subjects: Algorithms; Artificial intelligence; Chaos theory; Chaotic maps; Chaotic optimization algorithms; Expert systems; Golden section search method; Meta-heuristic algorithms; Nonlinear optimization problems; Optimization; Search methods; Searching
• ISSN: 0952-1976; 1873-6769
• DOI: 10.1016/j.engappai.2016.01.034

In this paper, we introduced a practical version of golden section search algorithm to optimize multi/uni-modal objective functions. Accordingly, this study presented a novel algorithm combining the capabilities of chaotic maps and the golden section search method in order to solve nonlinear optimization problems. To this end, a bipartite experimental procedure was utilized. (1) Chaotic convertor as a global search: the search space of a problem can be converted to a local search space using the chaotic concept. The chaotic maps can explore a sub-space to satisfy uni-modal condition for the golden section search (GSS) algorithm. (2) GSS as a local search: the n-D GSS applies over the achieved search space to exploit an optimal solution. In order to study the performance of the proposed algorithm, twenty benchmark functions and one real world problem were employed. The experimental results revealed that the proposed algorithm was an effective and efficient optimization algorithm in comparison with some state-of-the-art methods. The proposed algorithm performs effectively for the engineering applications such as the gear train deign problem.