Optimization problem on permutations with linear-fractional objective function: properties of the set of admissible solutions.

We consider an optimization problem on permutations with a linear-fractional objective function. We investigate the properties of the domain of admissible solutions of the problem

Solution of optimization problems with fractional-linear objective functions and additional linear constraints on permutations.

The statement of a problem of Euclidean combinatorial optimization with a fractional-linear objective function on a common set of permutations and with additional linear constraints is formulated. A problem with a fractional-linear objective function is transformed into that with a linear objective function. An approach is proposed to the solution of such problems, and a method of combinatorial truncation of solutions of problems of combinatorial type with fractional-linear objective functions on permutations is developed

Multicriteria combinatorial optimization problems on a set of polypermutations.

The studies on multicriteria combinatorial optimization are continued. A possible approach to solving multicriterion problems is developed and substantiated. An algorithm is developed and implemented. Some peculiarities of efficient solutions to multicriterion problems are described

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

The paper deals with a new method of solving a combinatorial problem with account for the properties of the set of permutations and its structure. Using this method, the values of the linear objective function are sequenced and the set of permutations is decomposed over hyperplanes, with account of element recurrences. This makes it possible to develop an algorithm of finding the point (an element of the set of permutations) at which the objective function attains a given value

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

The paper deals with a new method of solving a combinatorial problem with account for the properties of the set of permutations and its structure. Using this method, the values of the linear objective function are sequenced and the set of permutations is decomposed over hyperplanes, with account of element recurrences. This makes it possible to develop an algorithm of finding the point (an element of the set of permutations) at which the objective function attains a given value

Optimization problem on permutations with linear-fractional objective function: properties of the set of admissible solutions.

We consider an optimization problem on permutations with a linear-fractional objective function. We investigate the properties of the domain of admissible solutions of the problem

Construction of hamiltonian paths in graphs of permutation polyhedra.

The problem of finding an extremum of a linear function over a permutation set is considered. The polyhedron of admissible values of this function over permutations is constructed. The constructed graph is shown to be partially ordered with respect to the transposition of two elements of a permutation. Based on this property, a method is proposed for the construction of a Hamiltonian path in the graph corresponding to the permutation set for n 4

Solution of optimization problems with fractional-linear objective functions and additional linear constraints on permutations.

The statement of a problem of Euclidean combinatorial optimization with a fractional-linear objective function on a common set of permutations and with additional linear constraints is formulated. A problem with a fractional-linear objective function is transformed into that with a linear objective function. An approach is proposed to the solution of such problems, and a method of combinatorial truncation of solutions of problems of combinatorial type with fractional-linear objective functions on permutations is developed

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

Vector optimization problems over a fuzzy combinatorial set of permutations are investigated. Based on the properties of the convex hull of a fuzzy combinatorial set of permutations, modifications of multicriteria choice methods are developed and substantiated for a fuzzy feasible combinatorial set. Mathematical models of some application problems are presented

Modified coordinate method to solve multicriteria optimization problems on combinatorial configurations.

We propose an approach to solve a multicriteria optimization problem on combinatorial configuration of permutations by using graph theory, taking into account the properties and structure of the set of permutations. The subprogram of the method of searching for configuration points that uses the coordinate method in the proposed modified approach is described