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Parallel stochastic global optimization using radial basis functions. (English) Zbl 1243.90160
Summary: We develop a parallel implementation of a stochastic radial basis function (RBF) algorithm for global optimization by R. G. Regis and Ch. A. Shoemaker [INFORMS J. Comput. 19, No. 4, 497–509 (2007; Zbl 1241.90192)]. 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 [P. D. Hough et al. [SIAM J. Sci. Comput. 23, No. 1, 134–156 (2001; Zbl 0990.65067)], a parallel implementation of Probabilistic Global Search Lausanne [B. Raphael and I. F. C. Smith [Appl. Math. Comput. 146, No. 2–3, 729–758 (2003; Zbl 1032.65061)], a parallel evolutionary algorithm, and a deterministic parallel RBF algorithm by R. G. Regis and Ch. A. Shoemaker [Eur. J. Oper. Res. 182, No. 2, 514–535 (2007; Zbl 1178.90279)]. 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.

90C15 Stochastic programming
90C59 Approximation methods and heuristics in mathematical programming
minpack; DFO; COBYLA2; EGO; PGSL
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