Stochastic global optimization methods. part 11: multi level methods
Mathematical Programming: Series A and B
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
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
Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models
Journal of Global Optimization
Mesh Adaptive Direct Search Algorithms for Constrained Optimization
SIAM Journal on Optimization
Improved Strategies for Radial basis Function Methods for Global Optimization
Journal of Global Optimization
Convergence of Mesh Adaptive Direct Search to Second-Order Stationary Points
SIAM Journal on Optimization
An adaptive radial basis algorithm (ARBF) for expensive black-box global optimization
Journal of Global Optimization
Improved scatter search for the global optimization of computationally expensive dynamic models
Journal of Global Optimization
Introduction to Derivative-Free Optimization
Introduction to Derivative-Free Optimization
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
Design and Analysis of Simulation Experiments
Design and Analysis of Simulation Experiments
An informational approach to the global optimization of expensive-to-evaluate functions
Journal of Global Optimization
Adaptive memory programming for constrained global optimization
Computers and Operations Research
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We present the AQUARS (A QUAsi-multistart Response Surface) framework for finding the global minimum of a computationally expensive black-box function subject to bound constraints. In a traditional multistart approach, the local search method is blind to the trajectories of the previous local searches. Hence, the algorithm might find the same local minima even if the searches are initiated from points that are far apart. In contrast, AQUARS is a novel approach that locates the promising local minima of the objective function by performing local searches near the local minima of a response surface (RS) model of the objective function. It ignores neighborhoods of fully explored local minima of the RS model and it bounces between the best partially explored local minimum and the least explored local minimum of the RS model. We implement two AQUARS algorithms that use a radial basis function model and compare them with alternative global optimization methods on an 8-dimensional watershed model calibration problem and on 18 test problems. The alternatives include EGO, GLOBALm, MLMSRBF (Regis and Shoemaker in INFORMS J Comput 19(4):497---509, 2007), CGRBF-Restart (Regis and Shoemaker in J Global Optim 37(1):113---135 2007), and multi level single linkage (MLSL) coupled with two types of local solvers: SQP and Mesh Adaptive Direct Search (MADS) combined with kriging. The results show that the AQUARS methods generally use fewer function evaluations to identify the global minimum or to reach a target value compared to the alternatives. In particular, they are much better than EGO and MLSL coupled to MADS with kriging on the watershed calibration problem and on 15 of the test problems.