Improving the identification of general Pareto fronts by global optimization

Bijan Mohammadi; Patrick Redont

doi:10.1016/j.crma.2009.01.020

Numerical Analysis

Improving the identification of general Pareto fronts by global optimization

Presented by: Olivier Pironneau

Bijan Mohammadi ¹; Patrick Redont ¹

¹ Institut de mathématiques et de modélisation de Montpellier, Université Montpellier II, CC51, 34095 Montpellier, France

Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 327-331.

Abstract
Résumé

We present a controllability result for a second order dynamic system and its application to global optimization in the context of multi-criteria problems. In particular, we address the issue of reaching points on nonconvex regions of Pareto fronts.

Nous présentons un résultat de controlabilité pour un système dynamique d'ordre deux et son utilisation en optimisation globale dans un context de minimisation multi-critère. En particulier, nous montrons comment atteindre les points sur des fronts de Pareto nonconvexes.

Received: 2008-04-15
Accepted: 2009-01-27
Published online: 2009-02-14

DOI: 10.1016/j.crma.2009.01.020

Author's affiliations:

Bijan Mohammadi ¹; Patrick Redont ¹

¹ Institut de mathématiques et de modélisation de Montpellier, Université Montpellier II, CC51, 34095 Montpellier, France

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     title = {Improving the identification of general {Pareto} fronts by global optimization},
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     doi = {10.1016/j.crma.2009.01.020},
     language = {en},
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Bijan Mohammadi; Patrick Redont. Improving the identification of general Pareto fronts by global optimization. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 327-331. doi : 10.1016/j.crma.2009.01.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.01.020/

References
Cited by

[1] I. Das; J.E. Dennis A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems, Struct. Optim., Volume 14 (1997), pp. 63-69

[2] I. Das; J.E. Dennis Normal-boundary intersection: A new method for generating Pareto optimal points in multicriteria optimization problems, SIAM J. Optim., Volume 8 (1998), pp. 631-657

[3] K. Deb Multi-objective genetic algorithms: Problem difficulties and construction of test problems, IEEE J. Evolutionary Comp., Volume 7 (1999), pp. 205-230

[4] L. Dumas; B. Ivorra; P. Redont; B. Mohammadi Semi-deterministic vs. genetic algorithms for global optimization of multichannel optical filters, Int. J. Comput. Sci. Eng., Volume 2 (2006) no. 3-4, pp. 170-188

[5] B. Ivorra; D. Hertzog; B. Mohammadi; J.F. Santiago Global optimization for the design of fast microfluidic protein folding devices, Int. J. Numer. Meth. Eng., Volume 26 (2006) no. 6, pp. 319-333

[6] B. Ivorra; B. Mohammadi; A. Ramos Semi-deterministic global optimization method and application to the control of Burgers equation, JOTA, Volume 135 (2007) no. 1, pp. 549-561

[7] A. Messac; G.J. Sundararaj; R. Tappeta; J.E. Renaud Ability of objective functions to generate points on non-convex Pareto frontiers, AIAA J., Volume 38 (2000) no. 6, pp. 155-163

[8] E. Miglierina; E. Molhob; M.C. Recchionici Box-constrained multi-objective optimization: A gradient-like method without a priori scalarization, Eur. J. Oper. Res., Volume 188 (2008), pp. 662-682

[9] B. Mohammadi Optimal transport, shape optimization and global minimization, C. R. Acad. Sci. Paris, Ser. I., Volume 344 (2007), pp. 591-596

[10] B. Mohammadi; O. Pironneau Applied Shape Optimization for Fluids, Oxford Univ. Press, 2009

[11] B. Mohammadi; J.H. Saiac Pratique de la simulation numérique, Dunod, Paris, 2003

[12] V. Pareto Manuale di Economia Politica, Manual of Political Economy, Societa Editrice Libraria, Milano, Italy, 1906 (Translated into English by Schwier, A.S, 1971, Macmillan, New York)

[13] W. Stadler A survey of multicriteria optimization, or the vector maximum problem, JOTA, Volume 29 (1979)

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