Parallel Stochastic Global Optimization Using Radial Basis Functions

We develop a parallel implementation of a stochastic radial basis function (RBF) algorithm for global optimization by Regis and Shoemaker [Regis, R. G., C. A. Shoemaker. 2007a. A stochastic radial basis function method for the global optimization of expensive functions. INFORMS J. Comput. 19 (4) 497...

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Veröffentlicht in:INFORMS journal on computing Jg. 21; H. 3; S. 411 - 426
Hauptverfasser: Regis, Rommel G, Shoemaker, Christine A
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Linthicum INFORMS 22.06.2009
Institute for Operations Research and the Management Sciences
Schlagworte:
Algorithms
Bioremediation
expensive function
global optimization
Groundwater
groundwater bioremediation
Mathematical optimization
Methods
Multiprocessing
Optimization
Optimization algorithms
parallel optimization
Properties
radial basis function
stochastic algorithm
Stochastic models
Stochastic programming
Studies
surrogate model
Water, Underground
ISSN:1091-9856, 1526-5528, 1091-9856
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Zusammenfassung:We develop a parallel implementation of a stochastic radial basis function (RBF) algorithm for global optimization by Regis and Shoemaker [Regis, R. G., C. A. Shoemaker. 2007a. A stochastic radial basis function method for the global optimization of expensive functions. INFORMS J. Comput. 19 (4) 497–509]. The proposed parallel algorithm is suitable for the global optimization of computationally expensive objective functions and does not require derivatives. Each iteration of the algorithm consists of building an RBF model to approximate the expensive function and using this model to select multiple points for simultaneous function evaluation on multiple processors. The function evaluation points are selected from a set of random candidate points according to two criteria: estimated function value based on the RBF model, and minimum distance from previously evaluated points and previously selected points within each iteration. We compare the performance of our parallel stochastic RBF algorithm against alternative parallel global optimization methods, including two multistart parallel finite-difference quasi-Newton methods, a multistart implementation of Asynchronous Parallel Pattern Search [Hough, P., T. G. Kolda, V. J. Torczon. 2001. Asynchronous parallel pattern search for nonlinear optimization. SIAM J. Sci. Comput. 23 (1) 134–156], a parallel implementation of Probabilistic Global Search Lausanne [Raphael, B., I. F. C. Smith. 2003. A direct stochastic algorithm for global search. Appl. Math. Comput. 146 729–758], a parallel evolutionary algorithm, and a deterministic parallel RBF algorithm by Regis and Shoemaker [Regis, R. G., C. A. Shoemaker. 2007c. Parallel radial basis function methods for the global optimization of expensive functions. Eur. J. Oper. Res. 182 (2) 514–535]. We report good results for our parallel stochastic RBF method when using one, four, or eight processors in comparison with the alternatives on 20 test problems and on 3 optimization problems involving groundwater bioremediation.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.1090.0325