Parallel surrogate-assisted global optimization with expensive functions – a survey

Surrogate assisted global optimization is gaining popularity. Similarly, modern advances in computing power increasingly rely on parallelization rather than faster processors. This paper examines some of the methods used to take advantage of parallelization in surrogate based global optimization. A key issue focused on in this review is how different algorithms balance exploration and exploitation. Most of the papers surveyed are adaptive samplers that employ Gaussian Process or Kriging surrogates. These allow sophisticated approaches for balancing exploration and exploitation and even allow to develop algorithms with calculable rate of convergence as function of the number of parallel processors. In addition to optimization based on adaptive sampling, surrogate assisted parallel evolutionary algorithms are also surveyed. Beyond a review of the present state of the art, the paper also argues that methods that provide easy parallelization, like multiple parallel runs, or methods that rely on population of designs for diversity deserve more attention.United States. Dept. of Energy (National Nuclear Security Administration. Advanced Simulation and Computing Program. Cooperative Agreement under the Predictive Academic Alliance Program. DE-NA0002378

Full-field strain determination for additively manufactured parts using radial basis functions

Additively manufactured components, especially those produced in deposition welding processes, have a rough curvilinear surface. Strain and surface deformation analysis of such components is increasingly performed using digital image correlation (DIC) methods, which raises questions regarding interpretability of the results. Furthermore, in triangulation or local tangential plane based DIC strain analysis, the principal strain directions are difficult to be calculated at any point, which is due to the non-continuity of the approach. Thus, both questions will be addressed in this article. Apart from classical local strain analysis based on triangulation or local linearization concepts, the application of globally formulated radial basis functions (RBF) is investigated for the first time, with the advantage that it is possible to evaluate all interesting quantities at arbitrary points. This is performed for both interpolation and regression. Both approaches are studied at three-dimensional, curvilinear verification examples and real additively manufactured cylindrical specimens. It is found out that, if real applications are investigated, the RBF-approach based on interpolation and regression has to be considered carefully due to so-called boundary effects. This can be circumvented by only considering the region that has a certain distance to the edges of the evaluation domain. Independent of the evaluation scheme, the error of the maximum principal strains increases with increasing surface roughness, which has to be kept in mind for such applications when interpreting or evaluating the results of manufactured parts. However, the entire scheme offers interesting properties for the treatment of DIC-data

An adaptive radial basis algorithm (ARBF) for expensive black-box global optimization’.

Abstract Response surface methods based on kriging and radial basis function (RBF) interpolation have been successfully applied to solve expensive, i.e. computationally costly, global black-box nonconvex optimization problems. In this paper we describe extensions of these methods to handle linear, nonlinear, and integer constraints. In particular, algorithms for standard RBF and the new adaptive RBF (ARBF) are described. Note, however, while the objective function may be expensive, we assume that any nonlinear constraints are either inexpensive or are incorporated into the objective function via penalty terms. Test results are presented on standard test problems, both nonconvex problems with linear and nonlinear constraints, and mixed-integer nonlinear problems (MINLP). Solvers in the TOMLAB Optimization Environment (http://tomopt.com/tomlab/) have been compared, specifically the three deterministic derivative-free solvers rbfSolve, ARBFMIP and EGO with three derivative-based mixed-integer nonlinear solvers, OQNLP, MINLPBB and MISQP, as well as the GENO solver implementing a stochastic genetic algorithm. Results show that the deterministic derivative-free methods compare well with the derivative-based ones, but the stochastic genetic algorithm solver is several orders of magnitude too slow for practical use. When the objective function for the test problems is costly to evaluate, the performance of the ARBF algorithm proves to be superior

Surrogate Optimization of Deep Neural Networks for Groundwater Predictions

Sustainable management of groundwater resources under changing climatic conditions require an application of reliable and accurate predictions of groundwater levels. Mechanistic multi-scale, multi-physics simulation models are often too hard to use for this purpose, especially for groundwater managers who do not have access to the complex compute resources and data. Therefore, we analyzed the applicability and performance of four modern deep learning computational models for predictions of groundwater levels. We compare three methods for optimizing the models' hyperparameters, including two surrogate model-based algorithms and a random sampling method. The models were tested using predictions of the groundwater level in Butte County, California, USA, taking into account the temporal variability of streamflow, precipitation, and ambient temperature. Our numerical study shows that the optimization of the hyperparameters can lead to reasonably accurate performance of all models (root mean squared errors of groundwater predictions of 2 meters or less), but the ''simplest'' network, namely a multilayer perceptron (MLP) performs overall better for learning and predicting groundwater data than the more advanced long short-term memory or convolutional neural networks in terms of prediction accuracy and time-to-solution, making the MLP a suitable candidate for groundwater prediction.Comment: submitted to Journal of Global Optimization; main paper: 25 pages, 19 figures, 1 table; online supplement: 11 pages, 18 figures, 3 table

Numerical Modeling of Flexible Structures in Open Ocean Environment

The dissertation presents advancements in numerical modeling of offshore aquaculture and harbor protection structures in the open ocean environment. The advancements were implemented in the finite element software Hydro-FE that expands the Morison equation approach previously incorporated in Aqua-FE software developed at the University of New Hampshire. The concept of equivalent dropper was introduced and validated on the example of a typical mussel longline design. Parametric studies for mussel dropper drag coefficients and bending stiffness contributions were performed for different environmental conditions. To model kelp aggregates in macroalgae aquaculture, a corresponding numerical technique was developed. The technique proposes a modified Morison-type approach calibrated in full-scale physical tow tank experiments conducted at Hydromechanics Laboratory of the United States Naval Academy. In addition to the numerical modeling techniques, an advanced methodology for multidimensional approximation of the current velocity fields around offshore installations was proposed. The methodology was applied to model a response of a kelp farm by utilizing tidal-driven acoustic Doppler current profiler measurements. Finally, a numerical model of a floating protective barrier was built in the Hydro-FE software to evaluate its seaworthiness. The model was validated by comparison to measurements obtained in scaled physical wave tank tests and field deployments

Study of post-necking hardening identification and deformation-induced surface roughening of metals

This thesis covers topics at two fundamental scales at which plastic deformation is occurring – macroscopic and microscopic. The first topic is related to the localization of deformation and subsequent necking that happens in metals during deformation, e.g., sheet metal during forming. The open fundamental question is – what happens to the material properties inside of the localized region. The localization process is very challenging to analyze, even using a conventional tension test since several effects such as material hardening as well as effects of strain-rate and temperature are strongly coupled. In this thesis we propose a novel approach that allows to decouple these effects and furthermore to identify the true hardening behavior of material. The solution is based on solving an inverse problem that involves optimization of an expensive black-box function. The methodology developed is presented in detail. In the second topic we consider the microscopic aspects of deformation, namely grain-scale plasticity. More specifically, we apply a crystal plasticity finite element framework to analyze the deformation-induced surface roughening effect. This task also involves a number of challenges. One such challenge is the accurate calibration of the model, which was tackled here using the black-box optimization procedure developed earlier. The second challenge is the accurate non-destructive reconstruction of a 3D texture based on images of several planar sections. The texture reconstruction problem was solved and presented as a general methodology. Subsequently it was possible to construct a comprehensive model that accounts for all major effects. It is shown that this model is able to capture the physics of deformation-induced surface roughening, however primarily in the average sense

Experimentally validated heat exchanger refrigerant charge model and optimization of refrigerant charge for a heat pump

Refrigerant charge affects the efficiency, capacity, and reliability of a heat pump, and incorrect charge can lead to increased energy consumption and decreased performance as well as potential damage to the system. Furthermore, refrigerant charge has an environmental impact, with high Global Warming Potential (GWP) refrigerants contributing to climate change. The HVAC&R society is adopting low-GWP refrigerants to alleviate the concern. For these reasons, accurate prediction of refrigerant charge is vital in designing heat pumps, particularly for low-GWP refrigerants; this charge prediction is done by charge models.Meanwhile, existing charge models are limited in their charge prediction accuracy due to uncertainty in void-fraction models the charge models rely on for charge prediction. Experimental charge validation data can improve the accuracy of the charge model, but such data for low-GWP refrigerant charge is rare in the open literature.The goal of this study is to address the issue by improving the accuracy of charge prediction; that is done by creating a high-accuracy charge model that is verified by experimental charge validation data. To gather this experimental charge data, a novel charge measurement method and charge measurement facility for measuring charge is created, resulting in high-fidelity experimental charge data for heat exchangers across various operating conditions of heat pumps. This database includes multiple refrigerants, including low-GWP refrigerants, R1234yf and R468C, and additional R410A as a reference. Employing this experimental data, a high-accuracy charge model is developed and validated, which is used to optimize the charge and cooling capacity of a heat pump simultaneously on a developed multi-objective optimization framework