INTEGRAL LATTICES ON A PLANE IN DISCRETE OPTIMIZATION PROBLEMS

A novel approach to solving the problems of discrete (integer) optimization based on the numbering of points in the plane with integer coordinates, i. e. lattice points, is considered. An analytical description (in the closed form) of the whole point coordinates dependence on its number and the whole point number on its coordinates was found using the function antje. On this basis, it is proposed to avoid a preliminary solution of the problem of mathematical programming with weak constraints, i. e. excluding the requirements of integer variables, as in the methods of pruning and combinatorial methods. Finding the optimum of the objective function is carried out directly on the set of lattice points i. e. a subset of the domain of admissible values of variables.