Integrating surrogate modeling to improve DIRECT, DE and BA global optimization algorithms for computationally intensive problems
Date
2018-05-02
Authors
Saad, Abdulbaset Elha
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Abstract
Rapid advances of computer modeling and simulation tools and computing hardware have turned Model Based Design (MBD) a more viable technology. However, using a computationally intensive, “black-box” form MBD software tool to carry out design optimization leads to a number of key challenges. The non-unimodal objective function and/or non-convex feasible search region of the implicit numerical simulations in the optimization problems are beyond the capability of conventional optimization algorithms. In addition, the computationally intensive simulations used to evaluate the objective and/or constraint functions during the MBD process also make conventional stochastic global optimization algorithms unusable due to their requirement of a huge number of objective and constraint function evaluations. Surrogate model, or metamodeling-based global optimization techniques have been introduced to address these issues. Various surrogate models, including kriging, radial basis functions (RBF), multivariate adaptive regression splines (MARS), and polynomial regression (PR), are built using limited samplings on the original objective/constraint functions to reduce needed computation in the search of global optimum.
In many real-world design optimization applications, computationally expensive numerical simulation models are used as objective and/or constraint functions. To solve these problems, enormous fitness function evaluations are required during the evolution based search process when advanced Global Optimization algorithms, such as DIRECT search, Differential Evolution (DE), and Bat Algorithm (BA) are used. In this work, improvements have been made to three widely used global optimization algorithms, Divided Rectangles (DIRECT), Differential Evolution (DE), and Bat Algorithm (BA) by integrating appropriate surrogate modeling methods to increase the computation efficiency of these algorithms to support MBD. The superior performance of these new algorithms in comparison with their original counterparts are shown using commonly used optimization algorithm testing benchmark problems. Integration of the surrogate modeling methods have considerably improved the search efficiency of the DIRECT, DE, and BA algorithms with significant reduction on the Number of Function Evaluations (NFEs). The newly introduced algorithms are then applied to a complex engineering design optimization problem, the design optimization of floating wind turbine platform, to test its effectiveness in real-world applications. These newly improved algorithms were able to identify better design solutions using considerably lower NFEs on the computationally expensive performance simulation model of the design. The methods of integrating surrogate modeling to improve DIRECT, DE and BA global optimization searches and the resulting algorithms proved to be effective for solving complex and computationally intensive global optimization problems, and formed a foundation for future research in this area.
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Keywords
computer modeling, Model Based Design, optimization algorithms, design optimization applications, global optimization algorithms