Modification of the random search method

The paper considers linear programming problems with Boolean variables. This is a part of mathematical programming focused on solving practical optimization problems, which could be solved and correctly described with a mathematical model of the problem of linear programming with Boolean variables. The discussed methods for exact and approximate solutions are constructed taking into account the features of these problems. The main focus of the article is the method of the random search. The main idea of this method is formulated and steps of the iterative process are described. Proposed modification of this method removes the conditions of non-negativity imposed on all coefficients of the problem. This modification makes it possible to apply the method for solving of a much larger number of linear programming problems with Boolean variables.