An Experimental Study of Univariate Global Optimization Algorithms for Finding the Shape Parameter in Radial Basis Functions

2020 ◽  
pp. 326-339 ◽  
Author(s):  
Marat S. Mukhametzhanov ◽  
Roberto Cavoretto ◽  
Alessandra De Rossi
Keyword(s):  
Experimental Study ◽  
Global Optimization ◽  
Radial Basis Functions ◽  
Shape Parameter ◽  
Optimization Algorithms ◽  
Basis Functions ◽  
Radial Basis

scholarly journals Global optimization via inverse distance weighting and radial basis functions

2020 ◽  
Vol 77 (2) ◽  
pp. 571-595 ◽  
Author(s):  
Alberto Bemporad
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Inverse Distance Weighting ◽  
Bayesian Optimization ◽  
Distance Weighting ◽  
Radial Basis ◽  
Feasible Space ◽  
Inverse Distance

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.

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