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A Heuristic for Nonlinear Global Optimization

École Polytechnique Fédérale de Lausanne (EPFL), TRANSP-OR Transport and Mobility Laboratory, CH-1015 Lausanne, Switzerland
Nestlé Research Center, Lausanne, Switzerland
Université de Genève, Section des HEC, Facultés des Sciences Économiques et Sociales, 1211 Genève 4, Switzerland
michel.bierlaire{at}epfl.ch
michael.themans{at}epfl.ch
nicolas.zufferey-hec{at}unige.ch

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.

Key words: nonlinear optimization; global minimum; heuristic; trust-region algorithm
History: received June 2007; revised May 2008; accepted April 2009.