Evolutionary model type selection for global surrogate modeling

Due to the scale and computational complexity of currently used simulation codes, global surrogate (metamodels) models have become indispensable tools for exploring and understanding the design space. Due to their compact formulation they are cheap to evaluate and thus readily facilitate visualization, design space exploration, rapid prototyping, and sensitivity analysis. They can also be used as accurate building blocks in design packages or larger simulation environments. Consequently, there is great interest in techniques that facilitate the construction of such approximation models while minimizing the computational cost and maximizing model accuracy. Many surrogate model types exist ( Support Vector Machines, Kriging, Neural Networks, etc.) but no type is optimal in all circumstances. Nor is there any hard theory available that can help make this choice. In this paper we present an automatic approach to the model type selection problem. We describe an adaptive global surrogate modeling environment with adaptive sampling, driven by speciated evolution. Different model types are evolved cooperatively using a Genetic Algorithm ( heterogeneous evolution) and compete to approximate the iteratively selected data. In this way the optimal model type and complexity for a given data set or simulation code can be dynamically determined. Its utility and performance is demonstrated on a number of problems where it outperforms traditional sequential execution of each model type

Automatic surrogate model type selection during the optimization of expensive black-box problems

The use of Surrogate Based Optimization (SBO) has become commonplace for optimizing expensive black-box simulation codes. A popular SBO method is the Efficient Global Optimization (EGO) approach. However, the performance of SBO methods critically depends on the quality of the guiding surrogate. In EGO the surrogate type is usually fixed to Kriging even though this may not be optimal for all problems. In this paper the authors propose to extend the well-known EGO method with an automatic surrogate model type selection framework that is able to dynamically select the best model type (including hybrid ensembles) depending on the data available so far. Hence, the expected improvement criterion will always be based on the best approximation available at each step of the optimization process. The approach is demonstrated on a structural optimization problem, i.e., reducing the stress on a truss-like structure. Results show that the proposed algorithm consequently finds better optimums than traditional kriging-based infill optimization

Variable-fidelity electromagnetic simulations and co-kriging for accurate modeling of antennas

Accurate and fast models are indispensable in contemporary antenna design. In this paper, we describe the low-cost antenna modeling methodology involving variable-fidelity electromagnetic (EM) simulations and co-Kriging. Our approach exploits sparsely sampled accurate (high-fidelity) EM data as well as densely sampled coarse-discretization (low-fidelity) EM simulations that are accommodated into one model using the co-Kriging technique. By using coarse-discretization simulations, the computational cost of creating the antenna model is greatly reduced compared to conventional approaches, where high-fidelity simulations are directly used to set up the model. At the same time, the modeling accuracy is not compromised. The proposed technique is demonstrated using three examples of antenna structures. Comparisons with conventional modeling based on high-fidelity data approximation, as well as applications for antenna design, are also discussed

ONLINE APPROXIMATION ASSISTED MULTIOBJECTIVE OPTIMIZATION WITH HEAT EXCHANGER DESIGN APPLICATIONS

Computer simulations can be intensive as is the case in Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA). The computational cost can become prohibitive when using these simulations with multiobjective design optimization. One way to address this issue is to replace a computationally intensive simulation by an approximation which allows for a quick evaluation of a large number of design alternatives as needed by an optimizer. This dissertation proposes an approach for multiobjective design optimization when combined with computationally expensive simulations for heat exchanger design problems. The research is performed along four research directions. These are: (1) a new Online Approximation Assisted Multiobjective Optimization (OAAMO) approach with a focus on the expected optimum region, (2) a new approximation assisted multiobjective optimization with global and local metamodeling that always produces feasible solutions, (3) a framework that integrates OAAMO with multiscale simulations (OAAMOMS) for design of heat exchangers at the segment and heat exchanger levels, and (4) applications of OAAMO combined with CFD for shape design of a header for a new generation of heat exchangers using Non-Uniform Rational B-Splines (NURBS). The approaches developed in this thesis are also applied to optimize a coldplate used in electronic cooling devices and different types of plate heat exchangers. In addition many numerical test problems are solved by the proposed methods. The results of these studies show that the proposed online approximation assisted multiobjective optimization is an efficient approach that can be used to predict optimum solutions for a wide class of problems including heat exchanger design problems while reducing significantly the computational cost when compared with existing methods

Driving efficiency in design for rare events using metamodeling and optimization

Rare events have very low probability of occurrence but can have significant impact. Earthquakes, volcanoes, and stock market crashes can have devastating impact on those affected. In industry, engineers evaluate rare events to design better high-reliability systems. The objective of this work is to increase efficiency in design optimization for rare events using metamodeling and variance reduction techniques. Opportunity exists to increase deterministic optimization efficiency by leveraging Design of Experiments to build an accurate metamodel of the system which is less resource intensive to evaluate than the real system. For computationally expensive models, running many trials will impede fast design iteration. Accurate metamodels can be used in place of these expensive models to probabilistically optimize the system for efficient quantification of rare event risk. Monte Carlo is traditionally used for this risk quantification but variance reduction techniques such as importance sampling allow accurate quantification with fewer model evaluations. Metamodel techniques are the thread that tie together deterministic optimization using Design of Experiments and probabilistic optimization using Monte Carlo and variance reduction. This work will explore metamodeling theory and implementation, and outline a framework for efficient deterministic and probabilistic system optimization. The overall conclusion is that deterministic and probabilistic simulation can be combined through metamodeling and used to drive efficiency in design optimization. Applications are demonstrated on a gas turbine combustion autoignition application where user controllable independent variables are optimized in mean and variance to maximize system performance while observing a constraint on allowable probability of a rare autoignition event

MULTI-DIMENSIONAL SURROGATE BASED AFT FORM OPTIMIZATION OF SHIPS USING HIGH FIDELITY SOLVERS

Surrogate (metamodel) based optimization has numerous potential applications in the field of naval architecture. It is aimed here to establish a methodology for the aft form optimization for minimum viscous resistance, thus the present study is focused on the aft form where the viscous effects become dominant. It is necessary to solve this problem within acceptable time span from practical naval architectural point of view which requires metamodeling techniques currently under investigation. Accordingly, the present paper investigates the metamodeling ability of the Kriging interpolation and attempts to explore its capabilities and limitations in the aft form optimization from viscous resistance point of view. As metamodeling techniques become more widely used, their constraints are more apparent. Especially in highly nonlinear design spaces, the effect of dimensionality should be taken into consideration. Taking all those factors into account, the present paper is to examine the capabilities of Kriging and to establish the learning performance in terms of RMS error, correlation coefficient and required number of training points according to selected optimization algorithm for multidimensional ship design problem. The results show that, at least 5% reduction in viscous pressure drag can be attained by the present optimization methodology