On one Problem of Optimization of a Linear Fractional Function on Permutations

Donets, G. A.; Kolechkina, Lyudmila N.

doi:10.1615/jautomatinfscien.v42.i4.10

Cited by 6 publications

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“…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.…”

Section: Introductionmentioning

confidence: 91%

“…As the number of optimization criteria increases, the problem complexity grows [6][7][8][9][10][11] and the need arises to develop a new approach to the solution of vector combinatorial problems since the general algorithm can not always be adapted and applied efficiently. Therefore, the form of its mathematical formulation and search for solution methods are important.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modified Coordinate Method to Solve Multicriteria Optimization Problems on Combinatorial Configurations

Koliechkina

Dvernaya

Nagornaya³

2014

Cybern Syst Anal

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Modified Coordinate Method to Solve Multicriteria Optimization Problems on Combinatorial Configurations

Koliechkina

Dvernaya

Nagornaya³

2014

Cybern Syst Anal

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“…Перейдем к описанию метода локализации на примере для при 5  n . Будем образовывать перестановки, у которых первые два числа изменяются за счет транспозиций чисел с правой части перестановки 9  , что приводит к неразрешимому балансу (2,3,9). 13.…”

Section: обозначим перемену мест чиселunclassified

“…3,4,8, 13). Необходимо найти перестановку, для которой функция примет значение, равное 96.Начнем с рассмотрения перестановок с числом на…”

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On the Problem of a Linear Function Localization on Permutations

Donets

Biletskyi

2020

Cybernetics and Computer Technologies

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Combinatorial optimization problems and methods of their solution have been a subject of numerous studies, since a large number of practical problems are described by combinatorial optimization models. Many studies consider approaches to and describe methods of solution for combinatorial optimization problems with linear or fractionally linear target functions on combinatorial sets such as permutations and arrangements. Studies consider solving combinatorial problems by means of well-known methods, as well as developing new methods and algorithms of searching a solution. We describe a method of solving a problem of a linear target function localization on a permutation set. The task is to find those locally admissible permutations on the permutation set, for which the linear function possesses a given value. In a general case, this problem may have no solutions at all. In the article, we propose a newly developed method that allows us to obtain a solution of such a problem (in the case that such solution exists) by the goal-oriented seeking for locally admissible permutations with a minimal enumeration that is much less than the number of all possible variants. Searching for the solution comes down to generating various permutations and evaluating them. Evaluation of each permutation includes two steps. The first step consists of function decreasing by transposing the numbers in the first n – 3 positions, and the second step is evaluation of the permutations for the remaining three numbers. Then we analyze the correlation (which is called balance) to define whether the considered permutation is the solution or not. In our article, we illustrate the localization method by solving the problem for n = 5. Keywords: localization, linear function, permutation, transposition, balance, position.

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Solving Extremum Problems with Linear Fractional Objective Functions on the Combinatorial Configuration of Permutations Under Multicriteriality

Koliechkina

Dvirna

2017

Cybern Syst Anal

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On one Problem of Optimization of a Linear Fractional Function on Permutations

Cited by 6 publications

References 0 publications

Modified Coordinate Method to Solve Multicriteria Optimization Problems on Combinatorial Configurations

Modified Coordinate Method to Solve Multicriteria Optimization Problems on Combinatorial Configurations

On the Problem of a Linear Function Localization on Permutations

Solving Extremum Problems with Linear Fractional Objective Functions on the Combinatorial Configuration of Permutations Under Multicriteriality

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