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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Vydáno v:Computational optimization and applications Ročník 77; číslo 2; s. 571 - 595
Hlavní autor: Bemporad, Alberto
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.11.2020
Springer Nature B.V
Témata:
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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Shrnutí: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 .
Bibliografie:ObjectType-Article-1
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-020-00215-w