Formalization and classification of combinatorial optimization problems

Hulianytskyi L. F., Riasna I. I.

In: Optimization Methods and Applications (eds. Butenko S., Pardalos P. M., Shylo V.). – Cham: Springer International Publishing AG, 2017. – P. 239–250.


Original approach to determination of the concepts “combinatorial object” and “fuzzy combinatorial object” is offered, which allows to strictly formalize both the known and new classes of problems of combinatorial optimization. The offered approach to such formalization which is concept-based a local finiteness of the discrete spaces relies only on properties of the discrete spaces therefore has quite general character and allows to develop the constructive approach to creation of special objects in combinatorial spaces. The obtained results are important both in the theoretical plan and for development of methods of solving the combinatorial optimization problems.