An approach to solving discrete vector optimization problems over a combinatorial set of permutations

Abstract

AN APPROACH TO SOLVING DISCRETE VECTOR

Modified Coordinate Method to Solve Multicriteria Optimization Problems on Combinatorial Configurations

“…The present paper continues the studies in combinatorial optimization under multicriteriality condition [3,[8][9][10][11][12]. Our purpose is to develop a modified approach to the solution of the multicriteria problem on the set of permutations, to construct an algorithm for the modified approach, and to carry out a numerical experiment.…”

“…[1][2][3][4]. Depending on the complexity of problems and objectives, it can be interpreted as a solution of certain extremum problem of searching the maximum or minimum value of a given parameter to be optimized.…”

Method of ordering the values of a linear function on a set of permutations

“…Let us consider a one-criterion problem without additional constraints. Statement 1 [3]. If conditions (2) and the condition…”

“…Note that the graph B can be obtained from the graph A, where elements 4 and 3 are transposed in all the permutations. Similarly, the graph C can be obtained from the graph B after the transposition (3,2), and the graph D can be obtained from the graph C after the transposition (2, 1). Hence, the higher the graph, the greater the value of the function.…”

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.…”