MATSuMoTo: The MATLAB Surrogate Model Toolbox For Computationally Expensive Black-Box Global Optimization Problems

MATSuMoTo is the MATLAB Surrogate Model Toolbox for computationally expensive, black-box, global optimization problems that may have continuous, mixed-integer, or pure integer variables. Due to the black-box nature of the objective function, derivatives are not available. Hence, surrogate models are used as computationally cheap approximations of the expensive objective function in order to guide the search for improved solutions. Due to the computational expense of doing a single function evaluation, the goal is to find optimal solutions within very few expensive evaluations. The multimodality of the expensive black-box function requires an algorithm that is able to search locally as well as globally. MATSuMoTo is able to address these challenges. MATSuMoTo offers various choices for surrogate models and surrogate model mixtures, initial experimental design strategies, and sampling strategies. MATSuMoTo is able to do several function evaluations in parallel by exploiting MATLAB's Parallel Computing Toolbox.Comment: 13 pages, 7 figure

An Efficient Algorithm for Automatic Structure Optimization in X-ray Standing-Wave Experiments

X-ray standing-wave photoemission experiments involving multilayered samples are emerging as unique probes of the buried interfaces that are ubiquitous in current device and materials research. Such data require for their analysis a structure optimization process comparing experiment to theory that is not straightforward. In this work, we present a new computer program for optimizing the analysis of standing-wave data, called SWOPT, that automates this trial-and-error optimization process. The program includes an algorithm that has been developed for computationally expensive problems: so-called black-box simulation optimizations. It also includes a more efficient version of the Yang X-ray Optics Program (YXRO) [Yang, S.-H., Gray, A.X., Kaiser, A.M., Mun, B.S., Sell, B.C., Kortright, J.B., Fadley, C.S., J. Appl. Phys. 113, 1 (2013)] which is about an order of magnitude faster than the original version. Human interaction is not required during optimization. We tested our optimization algorithm on real and hypothetical problems and show that it finds better solutions significantly faster than a random search approach. The total optimization time ranges, depending on the sample structure, from minutes to a few hours on a modern laptop computer, and can be up to 100x faster than a corresponding manual optimization. These speeds make the SWOPT program a valuable tool for realtime analyses of data during synchrotron experiments

Optimization Of Groundwater Remediation With New Efficient Parallel Algorithm For Global Optimization

Application of optimization algorithm to PDE modeling groundwater remediation can greatly reduce remediation cost. However, groundwater remediation analysis requires a computational expensive simulation, therefore, effective parallel optimization could potentially greatly reduce computational expense. The optimization algorithm used in this research is Parallel Stochastic radial basis function. This is designed for global optimization of computationally expensive functions with multiple local optima and it does not require derivatives. In each iteration of the algorithm, an RBF is updated based on all the evaluated points in order to approximate expensive function. Then the new RBF surface is used to generate the next set of points, which will be distributed to multiple processors for evaluation. The criteria of selection of next function evaluation points are estimated function value and distance from all the points known. Algorithms created for serial computing are not necessarily efficient in parallel so Parallel Stochastic RBF is different algorithm from its serial ancestor. The application for two Groundwater Superfund Remediation sites, Umatilla Chemical Depot, and Former Blaine Naval Ammunition Depot. In the study, the formulation adopted treats pumping rates as decision variables in order to remove plume of contaminated groundwater. Groundwater flow and contamination transport is simulated with MODFLOW-MT3DMS. For both problems, computation takes a large amount of CPU time, especially for Blaine problem, which requires nearly fifty minutes for a simulation for a single set of decision variables. Thus, efficient algorithm and powerful computing resource are essential in both cases. The results are discussed in terms of parallel computing metrics i.e. speedup and efficiency. We find that with use of up to 24 parallel processors, the results of the parallel Stochastic RBF algorithm are excellent with speed up efficiencies close to or exceeding 100%

Kriging Models That Are Robust With Respect to Simulation Errors

In the field of the Design and Analysis of Computer Experiments (DACE) meta-models are used to approximate time-consuming simulations. These simulations often contain simulation-model errors in the output variables. In the construction of meta-models, these errors are often ignored. Simulation-model errors may be magnified by the meta-model. Therefore, in this paper, we study the construction of Kriging models that are robust with respect to simulation-model errors. We introduce a robustness criterion, to quantify the robustness of a Kriging model. Based on this robustness criterion, two new methods to find robust Kriging models are introduced. We illustrate these methods with the approximation of the Six-hump camel back function and a real life example. Furthermore, we validate the two methods by simulating artificial perturbations. Finally, we consider the influence of the Design of Computer Experiments (DoCE) on the robustness of Kriging models.Kriging;robustness;simulation-model error

Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization

In this paper we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) functions programming to solve the resulting subproblems which consist of the minimization of the RBF models subject to simple bounds on the variables. Extensive numerical results are reported with a test set of bound and linearly constrained problems