A Radial Basis Function Method for Global Optimization

By Hans-Martin Gutmann. Journal of Global Optimization, 2001

899 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b8ea85f7b1a10c2ed6c4c90dc6443a997e972e95

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Citations in the corpus

Review of surrogate modeling in water resources (2012, methodology): “…based on response surface surrogates such as EGO [Jones et al., 1998], GMSRBF and MLMSRBF [Regis and Shoemaker, 2007a], and Gutmann’s method [Gutmann, 2001] and also uncertainty analysis algorithms such as ACUARS [Mugunthan and Shoemaker, 2006] and RBF-enabled MCMC [Bliznyuk et al., 2008]…”
An experimental methodology for response surface optimization methods (2011, background): “…surface methods has been steady over the past 40 years (Kushner 1964; Perttunen et al. 1989; Stuckman 1989; Mockus 1989; Sacks et al. 1989; Elder 1992; Cox and John 1995; Schonlau 1997; Jones and Schonlau 1998; Gutmann 2001; Sasena 2002; Santner et al. 2003; Boyle 2006; Regis 2007; Lizotte 2008).”
Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. (2002, methodology): “Gutmann successfully applied Radial Basis Function models to a statistical-based algorithm [35].”
On the Design of Optimization Strategies Based on Global Response Surface Approximation Models (2005, methodology): “For such situations Gutmann (2001) suggests cycling through the available range of global-local balances as the search progresses.”
A review of recent advances in global optimization (2009, methodology): “Regis and Shoemaker (2005) proposed strategies that improve the performance of the radial basis function method of Gutmann (2001).”
Crashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate models (2013, background): “1989), support vector regression (SVR) (Smola and Scholkopf 2004), and radial basis function (RBF) (Gutmann 2001; Sun et al. 2010c, 2011; Regis and Shoemaker 2005; Mullur and Messac 2006; Zhao and Xue 2010) are considered herein to approximate functional responses.”
A Taxonomy of Global Optimization Methods Based on Response Surfaces (2001, methodology): “Gutmann (2001) proves this result for Kushner's original one-dimensional algorithm (it is a special case of a more general convergence theorem).”
Recent advances in surrogate-based optimization (2009, methodology): “Thus, of the methods reviewed in this paper, we are limited to the Gaussian process based methods, although Gutmann [30] has employed a one-stage goal seeking approach for a variety of radial basis functions.”
Using response surfaces and expected improvement to optimize snake robot gait parameters (2011, methodology): “In this paper, we focus on Gaussian process techniques (see [11] for a more complete treatment) in fitting response surfaces for the performance of snake robot gaits.”
Surrogate-based methods for black-box optimization (2017, methodology): “In [24], all RBFs listed above are discussed (using the concept of conditionally positive/negative deﬁniteness), but later the author concluded that the situation in the multiquadric and Gaussian cases is disappointing (according to [10]).”
Managing computational complexity using surrogate models: a critical review (2020, methodology): “Global optimization algorithms based on RSMs, such as EGO (Jones et al. 1998), GMSRBF, MLMSRBF (Regis and Shoemaker 2007), and Gutmann’s method (Gutmann 2001), and uncertainty analysis algorithms, such as ACUARS (Mugunthan and Shoemaker 2006) and RBF-enabled MCMC (Bliznyuk et al. 2008), can help…”
Provably Convergent Multifidelity Optimization Algorithm Not Requiring High-Fidelity Derivatives (2012, background): “This technique works well in practice, can be proven to find a globally optimal solution (withmodifications to the common definition of themethod) [14,15],”
Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions (2005, methodology): “The interpolation model that will be described below was extensively studied by Powell (1992, 1999) and was used as the basis of the RBF method by Gutmann (2001b) .”
Recent advances and applications of surrogate models for finite element method computations: a review (2022, methodology): “In the case of Kriging surrogates, one of the popular approaches is based on the Expected Improvement (EI) criterion (Jones et al. 1998), while for Radial Basis Function (RBF) surrogates, an analogous quantitative measure is achieved using a so called bumpiness criterion (Gutmann 2001).”