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Finding optimal algorithmic parameters using a mesh adaptive direct search

Charles Audet (Charles.Audet***at***gerad.ca)
Dominique Orban (Dominique.Orban***at***polymtl.ca)

Abstract: The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algorithmic parameters. This is done by devising a general framework for parameter tuning. The framework makes provision for surrogate objectives. Parameters are sought so as to minimize some measure of performance of the algorithm being fine-tuned. This measure is treated as a black-box and may be chosen by the user. Examples are given in the text. The second objective illustrates this framework by specializing it to the identification of locally optimal trust-region parameters in unconstrained optimization. Parameters are identified that minimize, in a certain sense, the computational time or the number of function evaluations required to solve a set of problems from the CUTEr collection. Each function call may take several hours and may not always return a predictable result. A surrogate function, taylored to the experiment at hand, is used to guide the MADS towards a local solution. The parameters thus identified differ from traditionally used values, and are used to solve problems from the CUTEr collection that remained otherwised unsolved in a reasonable time using traditional values.

Keywords: Trust-region methods, unconstrained optimization, mesh adaptive direct search algorithms, black-box optimization, surrrogate functions, parameter estimation

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Category 3: Nonlinear Optimization

Citation: Cahiers du GERAD G-2004-xx, GERAD, Montreal QC, Canada. December 2004.

Download: [Compressed Postscript][PDF]

Entry Submitted: 12/01/2004
Entry Accepted: 12/02/2004
Entry Last Modified: 12/01/2004

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