Empirical model-building and response surface
Empirical model-building and response surface
Recent progress in unconstrained nonlinear optimization without derivatives
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
Asynchronous Parallel Pattern Search for Nonlinear Optimization
SIAM Journal on Scientific Computing
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
A Radial Basis Function Method for Global Optimization
Journal of Global Optimization
A Template for Scatter Search and Path Relinking
AE '97 Selected Papers from the Third European Conference on Artificial Evolution
Scatter Search: Methodology and Implementations in C
Scatter Search: Methodology and Implementations in C
Radial Basis Functions
On the Convergence of Asynchronous Parallel Pattern Search
SIAM Journal on Optimization
Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions
Journal of Global Optimization
Improved Strategies for Radial basis Function Methods for Global Optimization
Journal of Global Optimization
ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions
SIAM Journal on Scientific Computing
A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions
INFORMS Journal on Computing
Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization
INFORMS Journal on Computing
Numerical assessment of metamodelling strategies in computationally intensive optimization
Environmental Modelling & Software
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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.