no. 5-6
Numerical Analysis
Improving the identification of general Pareto fronts by global optimization
[Optimisation globale et génération de fronts de Pareto]

Présenté par : Olivier Pironneau

Mohammadi, Bijan1 ; Redont, Patrick1
1 Institut de mathématiques et de modélisation de Montpellier, Université Montpellier II, CC51, 34095 Montpellier, France
Comptes Rendus. Mathématique, Tome 347 (2009) no. 5-6, pp. 327-331.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.01.020
Mohammadi, Bijan 1 ; Redont, Patrick 1

1 Institut de mathématiques et de modélisation de Montpellier, Université Montpellier II, CC51, 34095 Montpellier, France 
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Mohammadi, Bijan; Redont, Patrick. Improving the identification of general Pareto fronts by global optimization. Comptes Rendus. Mathématique, Tome 347 (2009) no. 5-6, pp. 327-331. doi : 10.1016/j.crma.2009.01.020. http://www.numdam.org/articles/10.1016/j.crma.2009.01.020/

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

[4] Dumas, L.; Ivorra, B.; Redont, P.; Mohammadi, B. 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] Ivorra, B.; Hertzog, D.; Mohammadi, B.; Santiago, J.F. 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] Ivorra, B.; Mohammadi, B.; Ramos, A. Semi-deterministic global optimization method and application to the control of Burgers equation, JOTA, Volume 135 (2007) no. 1, pp. 549-561

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

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

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

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

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

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

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