Trust-Tech Source-Point Method for Systematically Computing Multiple Local Optimal Solutions: Theory and Method
提出一种信任技术源点法，通过四个阶段系统计算连续无约束非线性优化问题的多个局部最优解，在50维测试函数上计算了5085个局部最优解，并能找到全局最优解。
In this article, a Trust-Tech source-point method is proposed to systematically compute multiple local optimal solutions (LOSs) for continuous unconstrained nonlinear optimization problems. This proposed method consists of four stages. Stage I finds one LOS (in which existing effective optimizers can be applied), stage II is the stage of escaping an LOS while stage III is the stage for entering the stability region (SR) of another stable equilibrium point (SEP) (i.e., another LOS). Stage IV computes other SEPs (i.e., LOSs) in corresponding SRs. A theoretical foundation for both stages II and III is developed, and these theoretical results are quite general on their own. The proposed method is numerically evaluated to compute multiple LOSs. For instance, a total of 5085 LOSs have been computed by the proposed Trust-Tech source point method on a 50-D test function. In addition, the proposed method can find the global optimal solutions of several test functions with 50 dimensions and 100 dimensions.