Yemets` Oleg O.

On Estimating the Acceptable Sets of Solutions of Combinatorial Transport Problem on Permutations Solved by the Method of Branches and Bounds

We estimate the acceptable set in the method of branches and bounds at solving a transport problem on permutations. We prove the property of this estimation. It allows reducing a number of the operations in the method of branches and bounds

The Optimization of Linear Function on Permutations: Transformation of Permutable Polyhedron to Kind, Necessary for the Use in Karmarkar’s Algorithm

The Optimization of Linear Function on Permutations: Transformation of Permutable Polyhedron to Kind, Necessary for the Use in Karmarkar’s Algorithm

The construction of the mathematical model of the one combinatorial problem of rectangles packing with fuzzy sizes

In this paper, we define the arrangement of rectangles with fuzzy sizes in a breadth – tangency, intersection, non-intersection. We also define the arrangement of rectangles with fuzzy sizes in the fuzzy size breadth – tangency, intersection, non-intersection. Finally, we construct a new mathematical model of the one problem of the rectangle packing as a problem of the Euclidian combinatorial optimization on a set of fuzzy permutations.

Operations and relations on fuzzy numbers

In this paper, we introduce the concept of the characteristic function of a fuzzy number. Through the samples provided, we demonstrate the operation of addition and the order relation of fuzzy numbers. Moreover, we study the properties of proposed operations and relations. We determine that these concepts can be used in simulation of optimization problems with indefinite data.

Iteration method for solving game problems on the arrangements

This paper proposes a novel method, used to find a player’s optimal strategy considering the combinatorial restrictions determined by arrangements in the optimization combinatorial problems of the game type.