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Discrete Search in Design Optimization

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Complex Systems Design & Management

Abstract

It is a common feature of many real-life design optimization problems that some design components can only be selected from a finite set of choices. Each choice corresponds to a possibly multidimensional design point representing the specifications of the chosen design component. In this paper we present a method to explore the resulting discrete search space for design optimization. We use the knowledge about the discrete space represented by its minimum spanning tree and find a splitting based on convex relaxation.

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References

  1. Achterberg, T., Koch, T., Martin, A.: Branching rules revisited. Operations Research Letters 33(1), 42–54 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alexandrov, N., Hussaini, M.: Multidisciplinary design optimization: State of the art. In: Proceedings of the ICASE/NASA Langley Workshop on Multidisciplinary Design Optimization, Hampton, Virginia, USA (1997)

    Google Scholar 

  3. Floudas, C.: Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press, Oxford (1995)

    MATH  Google Scholar 

  4. Fuchs, M., Girimonte, D., Izzo, D., Neumaier, A.: Robust and automated space system design. In: Robust Intelligent Systems, pp. 251–272. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Fuchs, M., Neumaier, A.: Autonomous robust design optimization with potential clouds. International Journal of Reliability and Safety 3(1/2/3), 23–34 (2009)

    Article  Google Scholar 

  6. Fuchs, M., Neumaier, A.: A splitting technique for discrete search based on convex relaxation. Journal of Uncertain Systems, Special Issue on Global Optimization and Intelligent Algorithm (2009), accepted, preprint available on-line at: http://www.martin-fuchs.net/publications.php

  7. Huyer, W., Neumaier, A.: Global optimization by multilevel coordinate search. Journal of Global Optimization 14(4), 331–355 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Huyer, W., Neumaier, A.: SNOBFIT – Stable Noisy Optimization by Branch and Fit. ACM Transactions on Mathematical Software 35(2), Article 9, 25 (2008)

    Article  MathSciNet  Google Scholar 

  9. Jones, D., Perttunen, C., Stuckman, B.: Lipschitzian optimization without the Lipschitz constant. Journal of Optimization Theory and Applications 79(1), 157–181 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  10. Leyffer, S.: Deterministic methods for mixed integer nonlinear programming. Ph.D. thesis, University of Dundee, Department of Mathematics & Computer Science (1993)

    Google Scholar 

  11. Nemhauser, G., Wolsey, L.: Integer and combinatorial optimization. Wiley Interscience, Hoboken (1988)

    MATH  Google Scholar 

  12. Neumaier, A., Fuchs, M., Dolejsi, E., Csendes, T., Dombi, J., Banhelyi, B., Gera, Z.: Application of clouds for modeling uncertainties in robust space system design. ACT Ariadna Research ACT-RPT-05-5201, European Space Agency (2007)

    Google Scholar 

  13. Parker, R., Rardin, R.: Discrete optimization. Academic Press, London (1988)

    MATH  Google Scholar 

  14. Tawarmalani, M., Sahinidis, N.: Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Mathematical Programming 99(3), 563–591 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Weisstein, E.: Minimum spanning tree. MathWorld – A Wolfram Web Resource (2008), http://mathworld.wolfram.com/MinimumSpanningTree.html

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Fuchs, M., Neumaier, A. (2010). Discrete Search in Design Optimization. In: Aiguier, M., Bretaudeau, F., Krob, D. (eds) Complex Systems Design & Management. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15654-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-15654-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15653-3

  • Online ISBN: 978-3-642-15654-0

  • eBook Packages: EngineeringEngineering (R0)

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