A Hybrid Method for Solving Global Optimization Problems

In this paper, a hybrid descent method, consisting of a genetic algorithm and the filled function method, is proposed. The genetic algorithm is used to locate descent points for previously converged local minima. The combined method has the decent property and the convergence is monotonic. To demonstrate the effectiveness of the proposed hybrid method, several multi-dimensional or non-convex optimization problems are solved. Numerical experiments on benchmark functions with different dimansions denmonstrate that the new algorithm has a more rapid convergence and a higher success rate, and can fine the solutions with higher quality, compared with some other existing similar algorithms, which is consistent with the analysis in theory.