Solution and Investigation of Vector Problems of Combinatorial Optimization on a Set of Polypermutations

A polyhedral approach to solving multicriterion combinatorial optimization problems over sets of polyarrangements

“…The present paper continues and develops the studies [1, 5,6,[8][9][10][11][12][13][20][21][22]. We propose and substantiate an approach to solving the problem Z F X ( , ) based on reducing a vector combinatorial optimization problem to a problem defined on a convex hull of a set of polyarrangements.…”

“…The paper continues the studies of multicriterion problems over combinatorial and polycombinatorial sets presented in [8][9][10][11][12]. The interrelation established between multicriterion problems over combinatorial sets and optimization problems over a continuous feasible set is used to study some structural properties of the feasible domain and to formulate and prove a number of theorems on the optimality conditions for different types of efficient solutions of the problems considered.…”

“…, from Theorem 4.8 [17, p. 193], and from the definition of a polyhedron of polypermutations [10]. The theorems below are true [15].…”

“…In analyzing many classes of combinatorial models and developing new problem-solving methods, much attention has recently been paid to methods based on the structural properties of combinatorial sets [2,[8][9][10][11][12][13][14][15][16]. Using information on the structure of the convex hull of feasible solutions, which is the basis for many polyhedral methods, is one of the most efficient (in the authors' opinion) approaches to solving combinatorial optimization problems.…”

Vector optimization problems with linear criteria over a fuzzy combinatorial set of alternatives

“…B. Germeyer, et al made a significant contribution to the development of multicriteria optimization methods and their application in problems of control and design of complex systems. The studies [2][3][4][5][6][7][8][9] deal with various aspects of the vector optimization theory. I. V. Sergienko, V. S. Mikhalevich, N. Z. Shor, et al played an important role in the development of new methods to solve combinatorial discrete optimization problems.…”