Abstract:
We consider a multicriteria combinatorial problem with majority optimality principle whose particular criteria are of the form MINSUM, MINMAX, and MINMIN. We obtain a lower attainable bound for the radius of quasistability of such a problem in the case of the Chebyshev norm on the space of perturbing parameters of the vector criterion. We give sufficient conditions for the quasistability of the problem; these are also necessary in the case of linear special criteria.
Citation:
V. A. Emelichev, Yu. v. Stepanishina, “Quasistability of a Vector Trajectory Majority Optimization Problem”, Mat. Zametki, 72:1 (2002), 38–47; Math. Notes, 72:1 (2002), 34–42
This publication is cited in the following 4 articles:
V. A. Emelichev, K. G. Kuzmin, “Analiz chuvstvitelnosti effektivnogo resheniya vektornoi bulevoi zadachi minimizatsii
proektsii lineinykh funktsii na R+ i R−”, Diskretn. analiz i issled. oper., ser. 2, ser. 2, 12:2 (2005), 24–43
Ernelichev, VA, “The stability radius of an efficient solution to a vector problem of Boolean programming in the l(1) metric”, Doklady Mathematics, 71:2 (2005), 266
S. E. Bukhtoyarov, V. A. Emelichev, “On the quasistability of a vector trajectory problem with a parametric optimality principle”, Russian Math. (Iz. VUZ), 48:1 (2004), 23–27
V. A. Emelichev, K. G. Kuz'min, A. M. Leonovich, “On a type of stability for a vector combinatorial problem with partial criteria of the form Σ-MINMAX and Σ-MINMIN”, Russian Math. (Iz. VUZ), 48:12 (2004), 15–25