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Trust-Tech Source-Point Method for Systematically Computing Multiple Local Optimal Solutions: Theory and Method
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DOI：10.1109/TCYB.2021.3071462.png)
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Abstract
En 中文
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.
Keywords:
Optimization
Numerical stability
Manifolds
Nonlinear dynamical systems
Transforms
Systematics
Stability criteria
Global optimal solution (GOS)
multiple local optimal solutions (LOSs)
nonlinear dynamic system
optimization problem
source point
stability region (SR)
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