Mode-pursuing sampling method for global optimization on expensive black-box functions |
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Authors: | Liqun Wang Songqing Shan G. Gary Wang |
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Affiliation: | 1. Department of Statistics , The University of Manitoba , Winnipeg, MB, Canada , R3T 5V6gary_wang@umanitoba.ca;3. Department of Mechanical and Manufacturing Engineering , The University of Manitoba , Winnipeg, MB, Canada , R3T 5V6 |
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Abstract: | The presence of black-box functions in engineering design, which are usually computation-intensive, demands efficient global optimization methods. This article proposes a new global optimization method for black-box functions. The global optimization method is based on a novel mode-pursuing sampling method that systematically generates more sample points in the neighborhood of the function mode while statistically covering the entire search space. Quadratic regression is performed to detect the region containing the global optimum. The sampling and detection process iterates until the global optimum is obtained. Through intensive testing, this method is found to be effective, efficient, robust, and applicable to both continuous and discontinuous functions. It supports simultaneous computation and applies to both unconstrained and constrained optimization problems. Because it does not call any existing global optimization tool, it can be used as a standalone global optimization method for inexpensive problems as well. Limitations of the method are also identified and discussed. |
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Keywords: | Global optimization Simultaneous computation Constrained optimization Black-box function Discretization-based sampling Local quadratic fitting Design optimization |
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