A New Hybrid Global Optimization Algorithm Based on Chaos Search and Complex Method

Abstract

The paper presents a new hybrid global optimization algorithm based on chaos search and complex method for nonlinear constrained optimization problems. To fit for chaos optimization algorithm, a constrained optimization problem is transformed into an unconstrained problem by penalty function method. The mapping mode of standard complex method is improved to solve the problem of low computational efficiency caused by the infeasible central point which leads to the algorithm restarting. The parallel chaos optimization algorithm is applied to generate the initial complex shape, which has higher efficiency than stochastic method. And then complex method is employed to accelerate the search velocity. Chaos fine search is used to jump out of the local optimum obtained from complex method. Taking advantages of the global search of parallel chaos optimum algorithm and the fast convergence of complex method, this algorithm overcomes the low convergence rate of chaos optimization algorithm and the local optimum of complex method. Finally, the high efficiency and stability of this hybrid algorithm is demonstrated by five benchmark functions.