Unimodular transformations for problems of integer programming and analysis of the efficiency of their application

The paper is devoted to issues of applying unimodular transformations in integer linear programming with the aim of decreasing the cardinality of $L$-covers of problems and increasing the efficiency of algorithms of their solution. Families of problems are constructed that are difficult for some cutting, branch and bound, and $L$-class enumeration algorithms. Unimodular transformations are suggested that allow one to accelerate the process of solving such problems and to increase the stability of some algorithms under small variations of initial data.