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D-optimality of non-regular design spaces by using a Bayesian modification and a hybrid method
Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization.
Jönköping University, School of Engineering, JTH, Mechanical Engineering. Jönköping University, School of Engineering, JTH. Research area Engineering mechanics and optimization. (Teknisk mekanik)
2010 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 42, no 1, p. 73-88Article in journal (Refereed) Published
Abstract [en]

In this work a hybrid method of a genetic algorithm  and sequential linear programming is suggested to obtain a D-optimal design of experiments. Regular as well as non-regular design spaces are considered. A D-optimal design of experiments maximizes the determinant of the information matrix, which appears in the normal equation. It is known that D-optimal design of experiments sometimes include duplicate design points. This is, of course, not preferable since duplicates do not add any new information to the response surface approximation and the computational effort is therefore wasted. In this work a Bayesian modification, where higher order terms are added to the response surface approximation, is used in case of duplicates in the design of experiments. In such manner, the draw-back with duplicates might be eliminated. The D-optimal problem, which is obtained by using the Bayesian modification, is then solved by a hybrid method. A hybrid method of a genetic algorithm that generates a starting point for sequential linear programming is developed. The genetic algorithm performs genetic operators such as cross-over and mutation on a binary version of the design of experiments, while the real valued version is used to evaluate the fitness. Next, by taking the gradient of the objective, a LP-problem is formulated which is solved by an interior point method that is available in Matlab. This is repeated in a sequence until convergence is reached. The hybrid method is tested for four numerical examples. Results from the numerical examples show a very robust convergence to a global optimum. Furthermore, the results show that the problem with duplicates is eliminated by using the Bayesian modification.

Place, publisher, year, edition, pages
2010. Vol. 42, no 1, p. 73-88
Keyword [en]
D-optimality, Design of experiments (DoE), Sequential linear programming (SLP), Genetic algorithms (GA), Response surface methodology (RSM), Bayesian modification (BM)
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:hj:diva-9522DOI: 10.1007/s00158-009-0464-3OAI: oai:DiVA.org:hj-9522DiVA, id: diva2:223805
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MERA
Available from: 2009-06-15 Created: 2009-06-15 Last updated: 2017-12-13Bibliographically approved

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Hofwing, MagnusStrömberg, Niclas

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