Modified Coordinate Method to Solve Multicriteria Optimization Problems on Combinatorial Configurations

Koliechkina, Liudmyla; Dvernaya, O. A.; Nagornaya, Alla N.

doi:10.1007/s10559-014-9650-4

Cited by 16 publications

(6 citation statements)

References 7 publications

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“…Це краще ніж для початкової функції, але гірше, ніж для початкової транспозиції 9,5 ; для другої -() FX = 2.28. Це також краще ніж для початкової функції, але гірше, ніж для транспозиції 9,6 . В свою чергу після транспозиції 9, 6 результат можна покращити за рахунок транспозиції 6,5 , яка дасть значення () FX = 2.52.…”

Section: випадок 2 нехай підмножиниunclassified

“…Це також краще ніж для початкової функції, але гірше, ніж для транспозиції 9,6 . В свою чергу після транспозиції 9, 6 результат можна покращити за рахунок транспозиції 6,5 , яка дасть значення () FX = 2.52. Цей результат кращий, ніж всі попередні.…”

Section: випадок 2 нехай підмножиниunclassified

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On Some Optimization Problems on Permutations

Donets

Biletskyi

2022

Cybernetics and Computer Technologies

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Numerous studies consider combinatorial optimization problems and their solution methods, since a large number of practical problems are described by means of combinatorial optimization models. Among these problems, the most prominent ones are function optimization problems on combinatorial configurations. Many of the studies mentioned above propose approaches and describe methods to solve combinatorial optimization problems for linear and fractionally linear functions on combinatorial sets such as permutations and arrangements. This work describes new approaches and methods to solve some maximization problems for linear, fractionally linear and quadratic functions on permutation set. Algorithms for solving these problems are given. For linear function, we provide a considerably easy method to find the permutation on which the function attains its maximum value. We describe the general algorithm to find fractionally linear function maximum. We consider the cases in which variables of numerator and denominator do not intersect, and when the numerator function and the denominator function have one common variable. We also describe the case in which the numerator function and the denominator function in total have incomplete variable list, i.e. when the total quantity of variables is less than the quantity of numbers in the permutation set. As for solving the problem of finding quadratic function maximum on permutation set, it turned out that there is no universal algorithm to solve this problem for any quadratic function. In this paper, we describe a method of finding maximum on permutation set for quadratic function consisting of two items. We provide examples of solving the considered optimization problems. Keywords: function, permutation, set, transposition, coefficients.

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Section: випадок 2 нехай підмножиниunclassified

On Some Optimization Problems on Permutations

Donets

Biletskyi

2022

Cybernetics and Computer Technologies

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“…It should be noted that quite often problems of this class are difficult to compute and cumbersome, because a full enumeration of options, as a solution method, is applicable only for problems of insignificant dimension . Therefore, there is an urgent need to improve existing methods and develop new approaches and algorithms [9][10][11][12][13] . When immersed in Euclidean space, combinatorial sets acquire a number of interesting properties that allow considering various original approaches to solving and increasing the efficiency of traditional combinatorial optimization methods [14][15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

Finding the Optimal Solution to the Problem of Conditional Optimization on the Graph of the set of Placements

Koliechkina¹,

Nahirna²

2020

Control syst. comput.

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The model of the problem of conditional optimization on the set of partial permutations is formulated. The linear form of the objective function is obtained by interpreting the elements of the set of partial permutations as points of the Euclidean space. A combinatorial polytope of allocations is considered for which there is a graph of the set of partial permutations An algorithm for solving this problem is proposed and its practical applicability is demonstrated. The proposed algorithm for solving the conditional optimization problem provides for the representation of the admissible of the Set of Partial Permutations in the form of a graph, which significantly reduces the search path for the optimal solution, as evidenced by the practical example considered.

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“…Since real-world systems are discrete-continuous by nature, they are modeled as partially integer programs. In particular, numerous problems of planning, management, design, and placement are modeled with the help of multiobjective problems whose solutions are of combinatorial nature, e.g., permutations, partial permutations, combinations, compositions, partitions, as well as their composition images [5,7,8,[22][23][24]. In this case, the search for an optimal solution is conducted on the correspondent combinatorial set or its proper subset.…”

Section: Introductionmentioning

confidence: 99%

“…MCP approaches take mainly are based on structural peculiarities of a particular combinatorial set. In [7,8], a multiobjective optimization on permutations without repetitions is considered. The formulation of MCP on poly-partial permutations is formulated in [22,23], and an approach to its solution using polyhedral relaxation is offered from the group of cutting methods.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Optimization on Permutations with Applications

Koliechkina¹,

Pichugina²

2019

dtcse

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A method of multiobjective optimization on permutations (MOP) is offered based on the Directed Structuring Method and using Graph Theory. Prospects of applying graph techniques are caused by representability of the feasible domain by graph vertices. It yields advantages in using traditional methods, as well as in developing new ones. Our method is a generalization of the Method for Sequential Analysis of Variants for multiobjective optimization on permutations and multi-permutations. Most problems on combinatorial configurations sets are NP-hard, and a search of an exact solution requires enumerating a factorial number of variants. To decrease it, the method includes: a choice of an unconstraint MOP method; a choice of a method for generating a sequence of feasible solutions for a constraint MOP adapted to objective function; constructing and examining a structural graph of the optimization problem; a polynomial algorithm choice for solving the problem on partially ordered vertices of the graph.

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Modified Coordinate Method to Solve Multicriteria Optimization Problems on Combinatorial Configurations

Cited by 16 publications

References 7 publications

On Some Optimization Problems on Permutations

On Some Optimization Problems on Permutations

Finding the Optimal Solution to the Problem of Conditional Optimization on the Graph of the set of Placements

Multiobjective Optimization on Permutations with Applications

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