A hybrid algorithm of evolution and simplex methods applied to global optimization

Abstract

In this paper, a hybrid method combining the evolution and simplex algorithms is proposed to deal with the global optimization problems of two-dimensional multi-minimum functions. Basically, the simplex method offers a search scheme without the gradient information and thus, it owns the merit of a better search speed for a local optimization problem and results in the deficiency of searching ability for the global one. In contrast, the evolution method has the better searching ability for the global problem but needs much more time. Therefore, the proposed hybrid method adopts the search technique of the simplex method and the concept of all population information. For an n-dimensional problem, the populations of equal to or greater than (n + 1) are taken with their all information of the respective generation to decide the next searching point. The proposed method has a better searching ability for the global optimization problem because this hybrid method has the characteristics of intensity and diversity during the evolution of populations moving stage. The searching ability for the global optimum is demonstrated by a benchmark testing example of multi-minimum function. Finally, several testing examples show that the success rate of global minimization approaches to 98%.