Abstract
Interval methods are known to be a precise and robust tool of global optimization. Several interval algorithms have been developed to deal with various kinds of this problem. Far less has been written about the use of interval methods in multicriterial optimization. The paper surveys two methods presented by other researchers and proposes a modified approach, combining PICPA algorithm with the use of derivative information. Preliminary numerical results are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Hansen, E.: Global Optimization Using Interval Analysis. Marcel Dekker, New York (1992)
Herbort, S., Ratz, D.: Improving the Efficiency of a Nonlinear–System–Solver Using the Componentwise Newton Method, available on the web at: http://www.ubka.uni-karlsruhe.de/vvv/1997/mathematik/5/5.pdf.gz
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, London (2001)
Jaulin, L., Walter, E.: Set Inversion Via Interval Analysis for nonlinear bounded-error estimation. Automatica 29, 1053–1064 (1993)
Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht (1996)
Kearfott, R. B., Nakao, M. T., Neumaier, A., Rump, S. M., Shary, S. P., van Hentenryck, P.: Standardized notation in interval analysis, available on the web at: http://www.mat.univie.ac.at/~neum/software/int/notation.ps.gz
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)
Kubica, B.J., Malinowski, K.: An Interval Global Optimization Algorithm Combining Symbolic Rewriting and Componentwise Newton Method Applied to Control a Class of Queueing Systems. Reliable Computing 11, 393–411 (2005)
Kubica, B.J., Niewiadomska-Szynkiewicz, E.: An Improved Interval Global Optimization Method and its Application to Price Management Problem. In: Kågström, B., Elmroth, E., Dongarra, J., Waśniewski, J. (eds.) PARA 2006. LNCS, vol. 4699, pp. 1055–1064. Springer, Heidelberg (2007)
Ruetsch, G.R.: An interval algorithm for multi-objective optimization. Structural and Multidisciplinary Optimization 30, 27–37 (2005)
Shary, S.P.: A Surprising Approach in Interval Global Optimization. Reliable Computing 7, 497–505 (2001)
Zitzler, E., Laumanns, M., Thiele, M.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In: Giannakoglou, K., Tsahalis, D., Periaux, J., Papailiou, K., Fogarty, T. (eds.) Evolutionary Methods for Design Optimization and Control, CIMNE, Barcelona, Spain (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kubica, B.J., Woźniak, A. (2008). Interval Methods for Computing the Pareto-front of a Multicriterial Problem. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_146
Download citation
DOI: https://doi.org/10.1007/978-3-540-68111-3_146
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68105-2
Online ISBN: 978-3-540-68111-3
eBook Packages: Computer ScienceComputer Science (R0)