Lytvynenko O. Methods of generation of combinatorial configurations and their application in mathematical and computer modeling of freight transportation and processing problems.

The methods of generation of combinatorial configurations, as well as the application of these methods in mathematical and computer modeling of freight transportation and processing problems, are considered in the paper. Strategies and methods for generating combinatorial configurations are developed; a generalized method for generating combinatorial configurations is proposed. Methods of complete and partial generation of k-sets are developed. A new combinatorial set is introduced – permutations with a partially given signature; enumeration and generation problems for these permutations are solved on the basis of using the proposed generalized method. Mathematical models for the Pickup and Delivery Problem and the Transshipment Yards Scheduling Problem are constructed; these models use combinatorial configurations and take into account some additional restrictions. Solution methods for these problems are developed on the basis of using combinatorial generation; corresponding algorithms and software are created. Methods, algorithms and software developed by the author are used in software for solving freight transportation and processing problems. Keywords: combinatorial generation, combinatorial optimization, freight transportation and processing problems, heuristics, Pickup and Delivery Problem, beam search, k-sets, intermodal transportation.