A chaotic optimization method based on logistic-sine map for numerical function optimization

Abstract

Meta-heuristic optimization algorithms have been used to solve mathematically unidentifiable problems. The main purpose of the optimization methods on problem-solving is to choose the best solution in predefined conditions. To increase performance of the optimization methods, chaotic maps for instance Logistic, Singer, Sine, Tent, Chebyshev, Circle have been widely used in the literature. However, hybrid 1D chaotic maps have higher performance than the 1D chaotic maps. The hybrid chaotic maps have not been used in the optimization process. In this article, 1D hybrid chaotic map (logistic-sine map)-based novel swarm optimization method is proposed to achieve higher numerical results than other optimization methods. Logistic-sine map has good statistical result, and this advantage is used directly to calculate global optimum value in this study. The proposed algorithm is a swarm-based optimization algorithm, and the seed value of the logistic-sine map is generated from local best solutions to reach global optimum. In order to test the proposed hybrid chaotic map-based optimization method, widely used numerical benchmark functions are chosen. The proposed chaotic optimization method is also tested on compression spring design problem. Results and comparisons clearly show that the proposed chaotic optimization method is successful.