A Heuristic for Nonlinear Global Optimization

We propose a new heuristic for nonlinear global optimization combining a variable neighborhood search framework with a modified trust-region algorithm as local search. The proposed method presents the capability to prematurely interrupt the local search if the iterates are converging to a local mini...

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Bibliographic Details
Published inINFORMS journal on computing Vol. 22; no. 1; pp. 59 - 70
Main Authors Bierlaire, M, Themans, M, Zufferey, N
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.01.2010
Institute for Operations Research and the Management Sciences
Subjects
Algorithms
Convergence (Mathematics)
Functional equations
Functions
global minimum
Heuristic
Mathematical optimization
nonlinear optimization
Nonlinear programming
Optimization algorithms
Studies
trust-region algorithm
United States
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Summary:We propose a new heuristic for nonlinear global optimization combining a variable neighborhood search framework with a modified trust-region algorithm as local search. The proposed method presents the capability to prematurely interrupt the local search if the iterates are converging to a local minimum that has already been visited or if they are reaching an area where no significant improvement can be expected. The neighborhoods, as well as the neighbors selection procedure, are exploiting the curvature of the objective function. Numerical tests are performed on a set of unconstrained nonlinear problems from the literature. Results illustrate that the new method significantly outperforms existing heuristics from the literature in terms of success rate, CPU time, and number of function evaluations.
ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.1090.0343