The use of the number of permissible solutions of the algorithmic equations for the purely integer linear programming problem

A single algorithm is presented for the purely integer linear programming problem, in which the number and structure of the vectors to be selected are determined as a function of the distribution of the number of solutions of the equations forming the constraints of the problem. The possibility of using the number of solutions of the equations in algorithms of the branch and bound type as an additional cut-off mechanism is also described.