Interval-based global optimization in engineering using model reformulation and constraint propagation |
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| Authors: | Issam Mazhoud Khaled Hadj-Hamou Jean Bigeon Ghislain Remy |
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| Affiliation: | 1. Grenoble-INP/UJF-Grenoble 1/CNRS, G-SCOP UMR5272, Grenoble F-38031, France;2. LGEP CNRS/SUPELEC, 11 rue Joliot Curie, Plateau de Moulon, 91192 Gif sur Yvette, France;1. Department of Physical and Computer Sciences, McPherson University, Seriki Sotayo, Ogun State, Nigeria;2. Department of Computer Science, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria;3. Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria;1. Department of Mathematics, University of Ilorin, Ilorin, Nigeria;2. School of Computational and Applied Mathematics, Faculty of Science, University of the Witwatersrand, South Africa;3. TCSE, Faculty of Engineering and the Built Environment, University of the Witwatersrand, South Africa;4. Department of Mathematical Sciences, Ekiti State University, Ado-Ekiti, Nigeria;1. MRC Epidemiology Unit, Institute of Metabolic Science, School of Clinical Medicine, Cambridge University, Cambridge, United Kingdom;2. Genetics of Complex Traits, University of Exeter Medical School, University of Exeter, Royal Devon & Exeter Hospital, Exeter, United Kingdom;3. Computational Medicine, Berlin Institute of Health (BIH) at Charité, Universitätsmedizin Berlin, Berlin, Germany;4. Institute for Molecular Medicine Finland (FIMM), Helsinki Institute of Life Science (HiLIFE), University of Helsinki, Helsinki, Finland |
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| Abstract: | This paper deals with the preliminary design problem when the product is modeled as an analytic model. The analytic models based method aims to use mathematical equations to address both multi-physic and economic characteristics of a product. The proposed approach is to convert the preliminary design problem into a global constrained optimization problem. The objective is to develop powerful optimization methods enough to handle complex analytical models. We propose to adapt an approach to solve this problem based on interval analysis, constraint propagation and model reformulation. In order to understand the optimization algorithm used for engineering design problems, some basic definitions and properties of interval analysis are introduced. Then, the basic optimization algorithms for both unconstrained and constrained problems are introduced and illustrated. The next section introduces the reformulation technique as main accelerating device. An application of the reformulation device and its global optimization algorithm on the optimal design of electrical actuators is presented. |
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