On stability of some lexicographic integer optimization problem

• Autorzy: Emelichev V. A. , Gurevsky E. E. , Kuzmin K. G.
• Języki publikacji: EN

Abstrakty

EN

A lexicographic integer optimization problem with criteria represented by absolute values of linear functions is considered. Five types of stability for the set of lexicographic optima under small changes of the parameters of the vector criterion are investigated.

Słowa kluczowe

EN

multicriteria optimization; lexicographic integer optimization problem; absolute values of linear functions; lexicographic optima; stability; strong stability; quasi-stability; strong quasi-stability; unalterability

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2010
• Tom: Vol. 39, no 3
• Strony: 811--826
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Emelichev V. A.

autor

Gurevsky E. E.

autor

Kuzmin K. G.

• Mechanics and Mathematics Faculty, Belarusian State University, av. Nezavisimosti 4, 220030 Minsk, Belarus,

Bibliografia

• BUKHTOYAROV, S.E. and EMELICHEV, V.A. (2006) Measure of stability for a finite cooperative game with a parametric optimality principle (from Pareto to Nash). Computational Mathematics and Mathematical Physics 46 (7), 1193-1199.
• CHAKRAVARTI, N. and WAGELMANS, A. (1998) Calculation of stability radius for combinatorial optimization. Operations Research Letters 23 (1), 1-7.
• EHRGOTT, M. AND GANDIBLEUX, X. (2000) A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spectrum 22 (4), 425-460.
• EHRGOTT, M. (2005) Multicriteria Optimization. Second Edition. Springer, Berlin-Heidelberg.
• EMELICHEV, V.A., GIRLICH, E., NIKULIN, Yu.V. and PODKOPAEV, D.P. (2002) Stability and regularization of vector problem of integer linear programming. Optimization 51 (4), 645-676.
• EMELICHEV, V.A., KRICHKO, V.N. and NIKULIN, Y.V. (2004) The stability radius of an efficient solution in minimax Boolean programming problem. Control and Cybernetics 33 (1), 127-132.
• EMELICHEV, V.A., KUZMIN, K.G. and NIKULIN, Yu.V. (2005) Stability analysis of the Pareto optimal solution for some vector Boolean optimization problem. Optimization 54 (6), 545-561.
• EMELICHEV, V.A. and KUZMIN, K.G. (2006) Stability radius of an efficient solution of a vector problem of integer linear programming in the Gölder metric. Cybernetics and Systems Analysis 42 (4), 609-614.
• EMELICHEV, V.A. and GUREVSKY, E.E. (2007a) On stability of some lexicographic multicriteria Boolean problem. Control and Cybernetics 36 (2), 333-346.
• EMELICHEV, V.A. and GUREVSKY, E.E. (2007b) Boolean problem of sequential minimization of moduli of linear functions and stability theorems. Cybernetics and Systems Analysis 43 (5), 759-766.
• EMELICHEV, V.A. and KUZ’MIN, K.G. (2007) On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm. Journal of Computer and Systems Sciences International 46 (5), 714-720.
• FIACCO, A.V. (1998) Mathematical Programming with Data Perturbations. Marcel Dekker, New York.
• GREENBERG, H.J. (1998) An annotated bibliography for post-solution analysis in mixed integer programming and combinatorial optimization. In: D.L. Woodruff, ed., Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search. Kluwer Academic Publishers, Boston, 97-148.
• GUREVSKII, E.E. and EMELICHEV, V.A. (2006) Stability of the vector Boolean minimization problem on absolute deviations of linear functions from zero. Russian Mathematics (Iz. VUZ) 50 (12), 24-29.
• GUREVSKII, E.E. and EMELICHEV, V.A. (2007) On stability of an efficient solution of a vector Boolean problem of maximisation of absolute values of linear functions. Discrete Mathematics and Applications 17 (3), 231-236.
• VAN HOESEL, S. and WAGELMANS, A. (1999) On the complexity of postoptimality analysis of 0-1 programs. Discrete Applied Mathematics 91 (1-3), 251-263.
• KOZERATSKA, L., FORBES, J.F., GOEBEL, R.G. and KRESTA, J.V. (2004) Perturbed cones for analysis of uncertain multi-criteria optimization problems. Linear Algebra and its Applications 378, 203-229.
• LIBURA, M., VAN DER POORT, E.S., SIERKSMA, G. and VAN DER VEEN, J.A.A. (1998) Stability aspects of the traveling salesman problem based on k-best solutions. Discrete Applied Mathematics 87 (1-3), 159-185.
• LIBURA, M. and NIKULIN, Y. (2004) Stability and accuracy functions in multicriteria combinatorial optimization problem with ∑-MINMAX and ∑-MINMIN partial criteria. Control and Cybernetics 33 (3), 511-524.
• LIBURA, M. (2007) On the adjustment problem for linear programs. European Journal of Operational Research 183 (1), 125-134.
• SAWARAGI, Y., NAKAYAMA, H. and TANINO, T. (1985) Theory of Multi-Objective Optimization. Academic Press, Orlando.
• SERGIENKO, I.V. and SHILO, V.P. (2003) Discrete Optimization Problems: Issues, Solution Methods and Investigations (in Russian). Naukova dumka, Kiev.
• SOTSKOV, Yu.N., LEONTEV, V.K. and GORDEEV, E.N. (1995) Some concepts of stability analysis in combinatorial optimization. Discrete Applied Mathematics 58 (2), 169-190.
• SUHUBI, E. (2003) Functional Analysis. Springer.
• TANINO, T. and SAWARAGI, Y. (1980) Stability of nondominated solutions in multicriteria decision-making. Journal of Optimization Theory and Applications 30 (2), 229-253.
• TANINO, T. (1988) Sensitivity analysis in multiobjective optimization. Journal of Optimization Theory and Applications 56 (3), 479-499.