Fast chaotic optimization algorithm based on locally averaged strategy and multifold chaotic attractor

Abstract

Recently, chaos theory has been used in the development of novel techniques for global optimization , and particularly, in the specification of chaos optimization algorithms (COA) based on the use of numerical sequences generated by means of chaotic map.In this paper, we present an improved chaotic optimization algorithm using a new two-dimensional discrete multifold mapping for optimizing nonlinear functions(ICOMM). The proposed method is a powerful optimization technique, which is demonstrated when three nonlinear functions of reference are minimized using the proposed technique.

Emerging Physics-based CI Algorithms

“…Several ChOA applications and variants can also be found in the literature (Lu et al 2006;Tavazoei and Haeri 2007a, b;Yang et al , 2012Han and Lu 2008;Cheshomi et al 2010;Henao 2011;Jiang et al 2012;Hamaizia et al 2012;Yuan et al 2012;Bouras and Syam 2013;Shayeghi et al 2009). To implement the ChOA algorithm, the following steps need to be performed (Li and Jiang 1998;Cheshomi et al 2010):…”

Fast chaotic optimization algorithm based on spatiotemporal maps for global optimization

“…In general, chaos characterized by their high sensitivity to initial conditions assessed by Lyapunov exponents and some properties like stochasticity and ergodicity, strange attractor with self-similar fractal pattern and pseudo-random behavior of chaotic sequences are the most attractive features that caused significant interest. Due to the benefit of a few properties as stochasticity and ergodicity of chaos, the idea of using chaotic sequences instead of random sequences has been noticed in several fields, one of these fields is the optimization theory [4][5][6][7][8][9][10][11][12][13][14][15]. The aim of global optimization is the task of seeking the absolutely best set of parameters to maximize or minimize an objective function, and it is important to find a global or nearglobal optimal solution.…”

“…Such as chaotic Monte Carlo optimization [22], chaotic BFGS [4][5][6], chaotic particle swarm optimization [7,[13][14][15], chaotic genetic algorithms [23,25], chaotic harmony search algorithm [26], chaotic simulated annealing [27], gradient-based methods [17] and so on. Optimization algorithms based on the chaos theory are search methodologies that differ from any of the existing classical stochastic optimization techniques.…”

“…Hybrid COA can more easily escape from local minimal and exhibit better numerical performance than stochastic algorithms. The hybrid COA algorithm is a two stages search technique, the first stage is the chaos search for global searching, and the second stage is the heuristic algorithm for accurate local searching [4][5][6].…”

“…The COA algorithm is proposed and developed to solve various kinds of global optimization problem [4][5][6][7][8][9][10][11][12][13][14][15].…”