Journal
IEEE TRANSACTIONS ON CYBERNETICS
Volume 52, Issue 11, Pages 11686-11697Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2021.3071462
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)
Categories
Funding
- National Science Foundation (NSF) [1225682, 1508986]
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The article proposed a Trust-Tech source-point method to compute multiple local optimal solutions for continuous unconstrained nonlinear optimization problems, demonstrating its effectiveness through numerical evaluation.
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.
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