Space exploration and region elimination global optimization algorithms for multidisciplinary design optimization

Date

2011-05-30

Authors

Younis, Adel Ayad Hassouna

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Abstract

In modern day engineering, the designer has become more and more dependent on computer simulation. Oftentimes, computational cost and convergence accuracy accompany these simulations to reach global solutions for engineering design problems causes traditional optimization techniques to perform poorly. To overcome these issues nontraditional optimization algorithms based region elimination and space exploration are introduced. Approximation models, which are also known as metamodels or surrogate models, are used to explore and give more information about the design space that needs to be explored. Usually the approximation models are constructed in the promising regions where global solutions are expected to exist. The approximation models imitate the original expensive function, black-box function, and contribute towards getting comparably acceptable solutions with fewer resources and at low computation cost. The primary contributions of this dissertation are associated with the development of new methods for exploring the design space for large scale computer simulations. Primarily, the proposed design space exploration procedure uses a hierarchical partitioning method to help mitigate the curse of dimensionality often associated with the analysis of large scale systems. The research presented in this dissertation focuses on introducing new optimization algorithms based on metamodeling techniques that alleviate the burden of the computation cost associated with complex engineering design problems. Three new global optimization algorithms were introduced in this dissertation, Approximated Unimodal Region Elimination (AUMRE), Space Exploration and Unimodal Region Elimination (SEUMRE), and Mixed Surrogate Space Exploration (MSSE) for computation intensive and black-box engineering design optimization problems. In these algorithms, the design space was divided into many subspaces and the search was focused on the most promising regions to reach global solutions with the resources available and with less computation cost. Metamodeling techniques such as Response Surface Method (RSM), Radial Basis Function (RBF), and Kriging (KRG) are introduced and used in this work. RSM has been used because of its advantages such as being easy to construct, understand and implement. Also due to its smoothing capability, it allows quick convergence of noisy functions in the optimization. RBF has the advantage of smoothing data and interpolating them. KRG metamodels can provide accurate predictions of highly nonlinear or irregular behaviours. These features in metamodeling techniques have contributed largely towards obtaining comparably accurate global solutions besides reducing the computation cost and resources. Many multi-objective optimization algorithms, specifically those used for engineering problems and applications involve expensive fitness evaluations. In this dissertation, a new multi-objective global optimization algorithm for black-box functions is also introduced and tested on benchmark test problems and real life engineering applications. Finally, the new proposed global optimization algorithms were tested using benchmark global optimization test problems to reveal their pros and cons. A comparison with other well known and recently introduced global optimization algorithms were carried out to highlight the proposed methods’ advantages and strength points. In addition, a number of practical examples of global optimization in industrial designs were used and optimized to further test these new algorithms. These practical examples include the design optimization of automotive Magnetorheological Brake Design and the design optimization of two-mode hybrid powertrains for new hybrid vehicles. It is shown that the proposed optimization algorithms based on metamodeling techniques comparably provide global solutions with the added benefits of fewer function calls and the ability to efficiently visualize the design space.

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Keywords

approximation models, computer simulation, algorithms

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