Continuation Newton methods with deflation techniques and quasi-genetic evolution for global optimization problems

The global minimum point of an optimization problem is of interest in engineering fields and it is difficult to be found, especially for a nonconvex optimization problem. In this article, we consider the continuation Newton method with the deflation technique and the quasi-genetic evolution for this problem. Firstly, we use the continuation Newton method with the deflation technique to find the stationary points from several determined initial points as many as possible. Then, we use those found stationary points as the initial evolutionary seeds of the quasi-genetic algorithm. After it evolves into several generations, we obtain a suboptimal point of the optimization problem. Finally, we use the continuation Newton method with this suboptimal point as the initial point to obtain the stationary point, and output the minimizer between this final stationary point and the found suboptimal point of the quasi-genetic algorithm. Numerical results show that the proposed method performs well for the global optimization problems,compared to the multi-start method and the differential evolution algorithm, respectively.