Empirical model-building and response surface
Empirical model-building and response surface
Response surfaces: designs and analyses
Response surfaces: designs and analyses
Global optimization
Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
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
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
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 Taxonomy of Global Optimization Methods Based on Response Surfaces
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Multi-funnel optimization using Gaussian underestimation
Journal of Global Optimization
An adaptive radial basis algorithm (ARBF) for expensive black-box global optimization
Journal of Global Optimization
Parallel Stochastic Global Optimization Using Radial Basis Functions
INFORMS Journal on Computing
A review of recent advances in global optimization
Journal of Global Optimization
Mixture surrogate models based on Dempster-Shafer theory for global optimization problems
Journal of Global Optimization
A metamodel-assisted evolutionary algorithm for expensive optimization
Journal of Computational and Applied Mathematics
MICAI'11 Proceedings of the 10th international conference on Artificial Intelligence: advances in Soft Computing - Volume Part II
Hoeffding bound based evolutionary algorithm for symbolic regression
Engineering Applications of Artificial Intelligence
Registrar: a complete-memory operator to enhance performance of genetic algorithms
Journal of Global Optimization
Structural and Multidisciplinary Optimization
Computers and Operations Research
Enhancing intill sampling criteria for surrogate-based constrained optimization
Journal of Computational Methods in Sciences and Engineering - Special issue on Advances in Simulation-Driven Optimization and Modeling
Global optimization of expensive black box problems with a known lower bound
Journal of Global Optimization
Sequential approximate multi-objective optimization using radial basis function network
Structural and Multidisciplinary Optimization
Parallel Parameter Identification in Industrial Biotechnology
International Journal of Parallel Programming
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We present a new strategy for the constrained global optimization of expensive black box functions using response surface models. A response surface model is simply a multivariate approximation of a continuous black box function which is used as a surrogate model for optimization in situations where function evaluations are computationally expensive. Prior global optimization methods that utilize response surface models were limited to box-constrained problems, but the new method can easily incorporate general nonlinear constraints. In the proposed method, which we refer to as the Constrained Optimization using Response Surfaces (CORS) Method, the next point for costly function evaluation is chosen to be the one that minimizes the current response surface model subject to the given constraints and to additional constraints that the point be of some distance from previously evaluated points. The distance requirement is allowed to cycle, starting from a high value (global search) and ending with a low value (local search). The purpose of the constraint is to drive the method towards unexplored regions of the domain and to prevent the premature convergence of the method to some point which may not even be a local minimizer of the black box function. The new method can be shown to converge to the global minimizer of any continuous function on a compact set regardless of the response surface model that is used. Finally, we considered two particular implementations of the CORS method which utilize a radial basis function model (CORS-RBF) and applied it on the box-constrained Dixon--Szegö test functions and on a simple nonlinearly constrained test function. The results indicate that the CORS-RBF algorithms are competitive with existing global optimization algorithms for costly functions on the box-constrained test problems. The results also show that the CORS-RBF algorithms are better than other algorithms for constrained global optimization on the nonlinearly constrained test problem.