Global optimization via inverse distance weighting and radial basis functions

Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimizat...

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Veröffentlicht in:	Computational optimization and applications Jg. 77; H. 2; S. 571 - 595
1. Verfasser:	Bemporad, Alberto
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.11.2020 Springer Nature B.V
Schlagworte:	Algorithms Convex and Discrete Geometry Global optimization Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization Radial basis function Statistics Weighting Global optimization Radial basis functions Black-box optimization Surrogate models Bayesian optimization Inverse distance weighting Derivative-free algorithms
ISSN:	0926-6003, 1573-2894
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Abstract	Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum ( exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function ( exploration of the feasible space). This paper proposes a new global optimization algorithm that uses inverse distance weighting (IDW) and radial basis functions (RBF) to construct the acquisition function. Rather arbitrary constraints that are simple to evaluate can be easily taken into account. Compared to Bayesian optimization, the proposed algorithm, that we call GLIS (GLobal minimum using Inverse distance weighting and Surrogate radial basis functions), is competitive and computationally lighter, as we show in a set of benchmark global optimization and hyperparameter tuning problems. MATLAB and Python implementations of GLIS are available at http://cse.lab.imtlucca.it/~bemporad/glis .
AbstractList	Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum (exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function (exploration of the feasible space). This paper proposes a new global optimization algorithm that uses inverse distance weighting (IDW) and radial basis functions (RBF) to construct the acquisition function. Rather arbitrary constraints that are simple to evaluate can be easily taken into account. Compared to Bayesian optimization, the proposed algorithm, that we call GLIS (GLobal minimum using Inverse distance weighting and Surrogate radial basis functions), is competitive and computationally lighter, as we show in a set of benchmark global optimization and hyperparameter tuning problems. MATLAB and Python implementations of GLIS are available at http://cse.lab.imtlucca.it/~bemporad/glis. Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum ( exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function ( exploration of the feasible space). This paper proposes a new global optimization algorithm that uses inverse distance weighting (IDW) and radial basis functions (RBF) to construct the acquisition function. Rather arbitrary constraints that are simple to evaluate can be easily taken into account. Compared to Bayesian optimization, the proposed algorithm, that we call GLIS (GLobal minimum using Inverse distance weighting and Surrogate radial basis functions), is competitive and computationally lighter, as we show in a set of benchmark global optimization and hyperparameter tuning problems. MATLAB and Python implementations of GLIS are available at http://cse.lab.imtlucca.it/~bemporad/glis .
Author	Bemporad, Alberto
Author_xml	– sequence: 1 givenname: Alberto orcidid: 0000-0001-6761-0856 surname: Bemporad fullname: Bemporad, Alberto email: alberto.bemporad@imtlucca.it organization: IMT School for Advanced Studies Lucca
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SubjectTerms	Algorithms Convex and Discrete Geometry Global optimization Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization Radial basis function Statistics Weighting
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