Control Systems and Computers, N6, 2020, Article 3

https://doi.org/10.15407/csc.2020.06.029

Control Systems and Computers, 2020, Issue 6 (290), pp. 29-34.

UDC 519.718

UDC 364.2:331; 681.513

L.M. KoliechkinaDoctor of Physical and mathematical sciences, Professor, University of Lodz, 22 Banahast., Lodz, 90-238, Poland, ludapl@ukr.net

A.M. Nahirna, PhD, Physical and mathematical, Associate Professor, National University of “Kyiv-Mohyla Academy”, 2 Skovorodast., Kyiv, 04070, Ukraine, naghirnaalla@ukr.net

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

Introduction. An optimization problem on a combinatorial set of partial permutations with additional constraints is formulated in the paper. An algorithm for solving this type of problem is considered, which consists of four steps. The algorithm lies in constructing a graph of a set of partial permutations to find the optimal solution. An example of a practical implementation of the presented algorithm is given.

Purpose of this article is to present a method for solving the problem of conditional optimization on a graph of the set of partial permutations and to demonstrate a practical example of implementation.

Methods. The method for solving the conditional optimization problem on the combinatorial set of partial permutations.

Results. 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.

Conclusion. 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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Keywords: conditional optimization problem, optimal solution, graph, subgraph, of the Set of Partial Permutations, objective function, constraints.

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Received 24.11.2020