A chaotic optimization method based on logistic-sine map for numerical function optimization
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ORIGINAL ARTICLE
A chaotic optimization method based on logistic-sine map for numerical function optimization Fahrettin Burak Demir1 • Tu¨rker Tuncer2 • Adnan Fatih Kocamaz3 Received: 13 May 2019 / Accepted: 24 February 2020 Springer-Verlag London Ltd., part of Springer Nature 2020
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 (logisticsine 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. Keywords Chaotic optimization Logistic-sine map Swarm-based optimization Chaos
1 Introduction Meta-heuristic optimization algorithms have been often used to solve the problems which are usually impossible to solve with conventional mathematical methods [1]. The main purpose of the optimization algorithms is to find a global optimum in a solution space. Local optima are also & Fahrettin Burak Demir [email protected] Tu¨rker Tuncer [email protected] Adnan Fatih Kocamaz [email protected] 1
Department of Computer Technologies, Dog˘ans¸ ehir Vahap Ku¨c¸u¨k Vocational School, Malatya Turgut Ozal University, Malatya, Turkey
2
Department of Digital Forensics Engineering, Technology Faculty, Firat University, Elazig, Turkey
3
Department of Computer Engineering, Engineering Faculty, Inonu University, Malatya, Turkey
used to find the global optimum. Optimization methods send continuous random values to the target function to solve problems and thus keep the best values in memory [2, 3]. Researchers consider various branches of science, for instance, natural sciences, biology, mathematics, physics, chemistry, space science, and etc. to propose a new efficient meta-heuristic optimization technique [1, 4]. One of the commonly used algorithms by researchers is the genetic algorithm. Genetic algorithms were inspired by the theory of
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