Geodesic
Interval entropy method for equality constrained multiobjective optimization problems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 1, pp. 29-39 
Hai-jun Wang; De-xin Cao; Su-bei Li. Interval entropy method for equality constrained multiobjective optimization problems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 1, pp. 29-39. http://geodesic.mathdoc.fr/item/SJVM_2008_11_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Based on the maximum entropy principle and the idea of penalty function, an evaluation function to solve multiobjective optimization problems with equality constraints is given. Combining with interval analysis method, we define generalized Krawczyk operator, design interval iteration with constrained functions and new region deletion test rules, present an interval algorithm for equality constrained multiobjective optimization problems, and also prove relevant properties. The theoretic analysis and numerical results indicate that the algorithm is effective and reliable.

[1] Moore R. E., Methods and Application of Interval Analysis, SIAM, Philadelphia, 1979 | MR | Zbl

[2] Ratschek H. and Rokne J., New Computer Methods for Global Optimization, Ellis Horwood, Chichester, 1988 | MR | Zbl

[3] Li X. S., “The Coherent Function Method Solving Nonlinear Program”, Sci. China (A), 12 (1991), 1283–1288

[4] Das I. and Dennis J., “A Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problems”, Struct. Optim., 14 (1997), 63–69 | DOI

[5] Ruhul S., “A New Multiobjective Evolutionary Algorithm”, Eur. J. Operat. Res., 140 (2002), 12–23 | DOI | MR | Zbl

[6] Wolfe M. A., “An Interval Algorithm for Constrained Global Optimization”, Appl. Math. Comput., 50 (1994), 605–612 | DOI | MR | Zbl

[7] Shen Z. H., Huang Z. Y., and Wolfe M. A., “An Interval Maximum Entropy Method for a Discrete Minimax Problem”, Appl. Math. Comput., 87:1 (1997), 49–68 | DOI | MR | Zbl

[8] Cao D. X., Ye S. M., and Wang H. J., “An Interval Maximum-Entropy Method for a Class of Constrained Nondifferentiable Optimization Problems”, OR Trans., 3:4 (1999), 55–64

[9] Jaynes E. T., “Information Theory and Statistical Mechanics”, Phys. Rev., 106 (1957), 620–630 | DOI | MR | Zbl

[10] Boltzmann L., “Weitere Studien über das Warmegleichgewicht Unter Gasmolekulen”, Wien. Akad. Sitz., 66 (1972), 275–370