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Post-optimal analysis for multicriteria integer linear programming problem of ﬁnding extreme solutions

Emelichev V. A., Nikulin Y.

Control and Cybernetics

2018

Vol. 47, no. 3

225--238

We consider a multicriteria problem of integer linear programming and study the set of all individual criterion minimizers (extreme solutions) playing an important role in determining the range of Pareto optimal set. In this work, the lower and upper attainable bounds on the stability radius of the set of extreme solutions are obtained in the situation where solution and criterion spaces are endowed with various H¨older’s norms. In addition, the case of the Boolean problem is analyzed. Some computational challenges are also discussed.

On stability of some lexicographic multicriteria Boolean problem

Emelichev V. A., Gurevsky E. E.

Control and Cybernetics

2007

Vol. 36, no 2

333-346

We consider a multicriteria lexicographic Boolean problem of minimizing absolute deviations of linear functions from zero. We investigate the stability radius which can be understood as a limit level of independent perturbations of the parameters, for which new lexicographic optima do not appear. Lower and upper accessible bounds of the stability radius are obtained.

The stability radius of an efficient solution in minimax Boolean programming problem

Emelichev V. A., Krichko V. N., Nikulin Y. V.

Control and Cybernetics

2004

Vol. 33, no 1

127-132

We consider a vector minimax Boolean programming problem. The problem consists in finding the set of Pareto optimal solutions. When the problem's parameters vary then the optimal solution of the problem obtained for some initial parameters may appear non-optimal. We calculate the maximal perturbation of parameters which preseves the Optimality of a given solution of the problem. The formula for the stability radius of the given Pareto optimal solution was obtained.

Quality of solutions for perturbed combinatorial optimization problems

Libura M.

Control and Cybernetics

2000

Vol. 29, no 1

199-219

We consider a general combinatorial optimization problem in which the set of feasible solutions is defined as a given and fixed family of subsets for some finite ground set. To any element of the ground set the so-called weight is associated. The problem consists in finding a feasible subset for which the sum of weights of its elements is the minimum. When the weights of elements vary or are estimated with some accuracy, then the solution of the problem obtained for some initial weights may appear non-optimal. In this paper we consider the quality of a given solution in the case of weights perturbation or inaccuracy. Namely, we study the relative error of a given solution as a function of particular weights perturbation. We also calculate the maximum perturbation or estimation errors of weights which preserve the optimality of a given solution of the problem.