  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
large-scale optimization problem. In this article, we consider a new memetic
algorithm for this problem. That is to say, we use the continuation Newton
method with the deflation technique to find multiple stationary points of the
objective function and use those found stationary points as the initial seeds
of the evolutionary algorithm, other than the random initial seeds of the known
evolutionary algorithms. Meanwhile, in order to retain the usability of the
derivative-free method and the fast convergence of the gradient-based method,
we use the automatic differentiation technique to compute the gradient and
replace the Hessian matrix with its finite difference approximation. According
to our numerical experiments, this new algorithm works well for unconstrained
optimization problems and finds their global minima efficiently, in comparison
to the other representative global optimization methods such as the multi-start
methods (the built-in subroutine GlobalSearch.m of MATLAB R2021b, GLODS and
VRBBO), the branch-and-bound method (Couenne, a state-of-the-art open-source
solver for mixed integer nonlinear programming problems), and the
derivative-free algorithms (CMA-ES and MCS).
