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. We compare it with the multi-start method (the built-in subroutine GlobalSearch.m of the MATLAB R2020a environment), the branch-and-bound method (Couenne of the state-of-the-art open-source solver for mixed integer nonlinear programming problems), and two representative derivative-free algorithms (CMA-ES and MCS), 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.