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Improving the identification of general Pareto fronts by global optimization. (English. Abridged French version) Zbl 1157.93005
Summary: 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.

MSC:
93B05 Controllability
90C29 Multi-objective and goal programming
93C15 Control/observation systems governed by ordinary differential equations
93B30 System identification
Software:
NBI
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[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., 14, 63-69, (1997)
[2] Das, I.; Dennis, J.E., Normal-boundary intersection: A new method for generating Pareto optimal points in multicriteria optimization problems, SIAM J. optim., 8, 631-657, (1998) · Zbl 0911.90287
[3] Deb, K., Multi-objective genetic algorithms: problem difficulties and construction of test problems, IEEE J. evolutionary comp., 7, 205-230, (1999)
[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., 2, 3-4, 170-188, (2006)
[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., 26, 6, 319-333, (2006) · Zbl 1110.76311
[6] Ivorra, B.; Mohammadi, B.; Ramos, A., Semi-deterministic global optimization method and application to the control of Burgers equation, Jota, 135, 1, 549-561, (2007) · Zbl 1146.90053
[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., 38, 6, 155-163, (2000)
[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., 188, 662-682, (2008) · Zbl 1144.90482
[9] Mohammadi, B., Optimal transport, shape optimization and global minimization, C. R. acad. sci. Paris, ser. I., 344, 591-596, (2007) · Zbl 1115.65075
[10] Mohammadi, B.; Pironneau, O., Applied shape optimization for fluids, (2009), Oxford Univ. Press · Zbl 1179.65002
[11] Mohammadi, B.; Saiac, J.H., Pratique de la simulation numérique, (2003), Dunod Paris
[12] Pareto, V., Manuale di economia politica, Manual of political economy, (1971), Macmillan New York, Translated into English by Schwier, A.S
[13] Stadler, W., A survey of multicriteria optimization, or the vector maximum problem, Jota, 29, (1979) · Zbl 0388.90001
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