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Using the Second-Order Information in Pareto-set Computations of a Multi-criteria Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7134))

Abstract

The paper presents an extension of a previously developed interval method for solving multi-criteria problems [13]. The idea is to use second order information (i.e., Hesse matrices of criteria and constraints) in a way analogous to global optimization (see e.g. [6], [9]). Preliminary numerical results are presented and parallelization of the algorithm is considered.

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References

  1. C-XSC interval library, http://www.xsc.de

  2. POSIX Threads Programming, https://computing.llnl.gov/tutorials/pthreads

  3. Barichard, V., Hao, J.K.: Population and Interval Constraint Propagation Algorithm. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 88–101. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Fernandez, J., Toth, B.: Obtaining an outer approximation of the efficient set of nonlinear biobjective problems. Journal of Global Optimization 38, 315–331 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Haimes, Y.Y.: Risk Modeling, Assessment, and Management. J. Wiley, New York (1998)

    MATH  Google Scholar 

  6. Hansen, E., Walster, W.: Global Optimization Using Interval Analysis. Marcel Dekker, New York (2004)

    MATH  Google Scholar 

  7. Herbort, S., Ratz, D.: Improving the efficiency of a nonlinear-system-solver using the componentwise Newton method, http://citeseer.ist.psu.edu/409594.html

  8. Jaulin, L., Walter, E.: Set Inversion Via Interval Analysis for nonlinear bounded-error estimation. Automatica 29, 1053–1064 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht (1996)

    Book  MATH  Google Scholar 

  10. Kearfott, R.B., Nakao, M.T., Neumaier, A., Rump, S.M., Shary, S.P., van Hentenryck, P.: Standardized notation in interval analysis (2002), http://www.mat.univie.ac.at/~neum/software/int/notation.ps.gz

  11. Kim, I.Y., de Weck, O.L.: Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Structural and Multidisciplinary Optimization 29, 149–158 (2005)

    Article  Google Scholar 

  12. Kubica, B.J.: Interval methods for solving underdetermined nonlinear equations systems. Presented at SCAN, Conference, El Paso, Texas, USA (2008)

    Google Scholar 

  13. Kubica, B.J., Woźniak, A.: Interval Methods for Computing the Pareto-Front of a Multicriterial Problem. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2007. LNCS, vol. 4967, pp. 1382–1391. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Kubica, B. J., Woźniak, A.: A multi-threaded interval algorithm for the Pareto-front computation in a multi-core environment. Presented at PARA 2008 Conference, accepted for publication in LNCS 6126 (2010)

    Google Scholar 

  15. Kubica, B.J., Woźniak, A.: Optimization of the multi-threaded interval algorithm for the Pareto-set computation. Journal of Telecommunications and Information Technology 1, 70–75 (2010)

    Google Scholar 

  16. Ruetsch, G.R.: An interval algorithm for multi-objective optimization. Structural and Multidisciplinary Optimization 30, 27–37 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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Kristján Jónasson

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Kubica, B.J., Woźniak, A. (2012). Using the Second-Order Information in Pareto-set Computations of a Multi-criteria Problem. In: Jónasson, K. (eds) Applied Parallel and Scientific Computing. PARA 2010. Lecture Notes in Computer Science, vol 7134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28145-7_14

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  • DOI: https://doi.org/10.1007/978-3-642-28145-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28144-0

  • Online ISBN: 978-3-642-28145-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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