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 solved, especially for a nonconvex large-scale optimization problem. In this article, we consider a new memetic algorithm for this problem. That is to say, we use the determined points (the stationary points of the function) as the initial seeds of the evolutionary algorithm, other than the random initial seeds of the known evolutionary algorithms. Firstly, we revise 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.Finally, we compare it with the multi-start method (the built-in subroutine GlobalSearch.m of the MATLAB R2020a environment), the differential evolution algorithm (the DE method, the subroutine de.m of the MATLAB Central File Exchange 2021) and the branch-and-bound method (Couenne of a state-of-the-art open source solver for mixed integer nonlinear programming problems), respectively. Numerical results show that the proposed method performs well for the large-scale global optimization problems, especially the problems of which are difficult to be solved by the known global optimization methods.