Abstract. In this paper, we propose a strategy for solving the problem of optimization of a linear function on the set of cyclic permutations. The strategy is based on the properties of the transpositions of a special kind. The properties of this class of transpositions are investigated. Assertions about the impact of compositions of such transpositions on an arbitrary permutation are proved. For the approximate solutions obtained using the above strategy, estimation is substantiated.
Keywords: combinatorial optimization, linear function, permutations, transpositions, cyclic permutations.
1Kharkiv National University of Radioelectronics, Kharkiv, Ukraine,
e-mail: igorgrebennik@gmail.com.
2Kharkiv National University of Radioelectronics, Kharkiv, Ukraine,
e-mail: titovaolga90@gmail.com.