Solution of Optimization Problems with Fractional-Linear Objective Functions and Additional Linear Constraints on Permutations

Abstract

STATEMENT OF THE PROBLEMLet it be required to determine a pair <F(

A modification of the method of combinatorial truncation in optimization problems over vertex-located sets

“…This modification is distinguished by the procedure of deriving inequality (11). As is known from [5,[11][12][13][14][15][16][17][18], truncation (11) is proposed to be constructed as the inequality y j…”

“…Examples of such vertex-located sets are sets of permutations, polypermutations, some sets of arrangements, and many Euclidean combinatorial sets. The method of combinatorial truncation has been developed for such problems [11][12][13][14][15][16][17][18]. At the same time, its implementation involves some difficulties if solutions of auxiliary linear programming problems (LPP) are degenerate.…”

Analysis of mathematical models and methods of solving combinatorial optimization problems on game-type permutations

“…The purpose of the first player is to maximize the minimum payoff u due to his strategies, and since Since X E P m x Î ( )in this problem, it can be solved by a combinatorial truncation method (see, for example, [1, [6][7][8]11]). There are m n + variables here, m of which appear in the combinatorial constraint; therefore, we will apply the truncation method for partially combinatorial problems on permutations (see, for example, [7,8]).…”

Solving optimization problems with linear-fractional objective functions and additional constraints on arrangements

“…Methods and algorithms for the solution of conditional linear problems on permutations and arrangements and linear-fractional conditional problems on a set of permutations are described in [1, [6][7][8].…”