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).

翻译：工程领域中，优化问题的全局极小点备受关注，但其求解颇具挑战性，尤其是对于非凸大规模优化问题。本文针对该问题提出一种新型模因算法：即采用基于收缩技术的连续牛顿法寻找目标函数的多个驻点，并将这些驻点作为进化算法的初始种子，替代现有进化算法中随机生成的初始种子。同时，为兼顾无导数方法的实用性与基于梯度方法的快速收敛特性，我们利用自动微分技术计算梯度，并用有限差分近似替代海森矩阵。数值实验表明，与多起点方法（MATLAB R2021b内置子程序GlobalSearch.m、GLODS和VRBBO）、分支定界方法（混合整数非线性规划领域最先进的开源求解器Couenne）以及无导数算法（CMA-ES和MCS）等代表性全局优化方法相比，本文所提新算法在无约束优化问题中表现出色，能高效找到全局极小点。