Modern combinatorial algorithms for solving discrete optimization problems with the use of computer tools are presented. The following are considered: features of discrete optimization problems and their general properties; algorithms of guaranteed functioning; algorithms of type ; combined algorithms of various types for approximate and exact solution of problems; large-dimensional problems (parametrization and implementation). Focus on computational implementation of algorithms. The results of computational research of algorithms for classical problems of discrete optimization are given - problems about the backpack and problems about the salesman. Many examples are given for independent work. For students studying in the specialty and close to it, as well as for researchers, graduate students and specialists associated with solving discrete optimization problems .