Grebennik, I.Chorna, O.Urniaieva, I.2024-06-222024-06-222022Grebennik I. Distribution of Permutations with Different Cyclic Structure in Mathematical Models of Transportation Problems / I. Grebennik, O. Chorna, I. Urniaieva // Proc. 12th International Conference on Advanced Computer Information Technologies, ACIT 2022. - Proceedings, 2022. - pp. 18-21.https://openarchive.nure.ua/handle/document/27135The paper is devoted to the investigation of problems of the class Pick-up and Delivery routing problems (PDP). This class is characterized by the multidimensionality of the input data, the requirement for decision-making in conditions of uncertainty and the requirement for rapid generation of solutions. Therefore, heuristic algorithms have proven to be good for solving PDP problems. Among the heuristic algorithms used to solve such problems is a wide class of Large-scale neighborhood algorithms, in which algorithms based on the use of cyclic transfer theory deserve special attention. If the collection and delivery of goods from many senders to many recipients is served by several trucks - the question arises of the distribution of points to visit between vehicles. One approach to solving the problem of splitting multiple shipping points into non-intersecting clusters is an approach that uses heuristic start splitting and then improves it by moving some shipping points between clusters using cyclic transfers. The study of the properties of cyclic permutations and the study of the cyclic structure of arbitrary elements of the permutations set is a promising direction for increasing of efficiency of the cyclic transfer approach to solve PDP problems. This paper is devoted to the study of the distribution of permutations with different cyclic structure in the set of permutations for increasing the efficiency of solving PDP problems. Experiments were conducted to study the distribution of permutations with different cyclic structure among sample populations with different qualitative characteristics. On the basis of the analysis and results of experiments the conclusions concerning features of distribution of permutations with various cyclic structure are made. Taking into account these features allows you to increase the efficiency of the cyclic transfer method in solving transport routing problems.enpickup and delivery problempermutationscyclic transfersclusterizationConference proceedingshttps://doi.org/10.1109/ACIT54803.2022.9913183