Improved parallel chaos optimization algorithm

Chaos optimization algorithm (COA), which has the features of easy implementation, short execution time and robust mechanisms of escaping from the local optimum, is a promising tool for the engineering applications. The design of approaches to improve the convergence of the COA is a challenging issue. Improved mutative-scale parallel chaotic optimization algorithm (MPCOA) are proposed in this paper, and three ways of improvements for MPCOA are investigated in detail: MPCOA combined with simplex search method, MPCOA based on competitive/cooperative inter-communication, MPCOA combined with harmony search algorithm. Several simulation results are used to show the effective performance of these chaos optimization algorithms. Chaos often exists in the nonlinear systems. It is a kind of highly unstable motion of the deterministic systems in finite phase space [1,2]. Chaos is a kind of characteristic which has a bounded unstable dynamic behavior and exhibits sensitive dependence on its initial conditions. An essential feature of the chaotic systems is that small changes in the parameters or the starting values for the data lead to the vastly different future behaviors, such as stable fixed points, periodic oscillations, bifurcations, and ergodicity [2]. This sensitive dependence on the initial conditions is generally exhibited by systems containing multiple elements with non-linear interactions, particularly when the system is forced and dissipative. Sensitive dependence on the initial conditions is not only observed in the complex systems, but even in the simplest logistic equation. The application of the chaotic sequences can be an interesting alternative to provide the search diversity in an optimization procedure, called chaos optimization algorithm (COA) [2–5] (some literatures also called chaotic optimization algorithm [5]). Due to the non-repetition of the chaos, the COA can carry out overall searches at higher speeds than stochastic ergodic searches that depend on the probabilities. The COA, which has the features of easy implementation, short execution time and robust mechanisms of escaping from the local optimum, is a promising tool for the engineering applications and has attracted much attention [3]. Due to the pseudo-randomness of chaotic motion, the motion step of chaotic variables between two successive iterations is always big, which resulted in the big jump of the design variables in design space [3]. Thus, even if the above COAs in [2–5] have reached the neighborhood of the optimum, it needs to spend much computational effort to approach the global optimum eventually by searching numerous points. Hence, the hybrid methods attract the attention …