Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search

Authors:
Charles Audet;Vincent Béchard;Sébastien Le Digabel
Affiliations:
Département de Mathématiques et de Génie Industriel, Ecole Polytechnique de Montréal and GERAD, Montreal, Canada H3C 3A7;Département de Mathématiques et de Génie Industriel, Ecole Polytechnique de Montréal and GERAD, Montreal, Canada H3C 3A7;Département de Mathématiques et de Génie Industriel, Ecole Polytechnique de Montréal and GERAD, Montreal, Canada H3C 3A7
Venue:
Journal of Global Optimization
Year:
2008

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Abstract

This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm, which extends the Generalized Pattern Search (GPS) algorithm, with the Variable Neighborhood Search (VNS) metaheuristic, for nonsmooth constrained optimization. The resulting algorithm retains the convergence properties of MADS, and allows the far reaching exploration features of VNS to move away from local solutions. The paper also proposes a generic way to use surrogate functions in the VNS search. Numerical results illustrate advantages and limitations of this method.