Generalized Algorithms of Discrete Optimization and Their Applications

Abstract:- Generalized algorithms for solving problems of discrete, integer, and Boolean programming are discussed. These algorithms are associated with the method of normalized functions, are based on a combination of formal and heuristic procedures, and allow one to obtain quasioptimal solutions after a small number of steps, that promotes overcoming the NP-completeness of discrete optimization problems. Questions of building so-called "duplicate " algorithms are considered to improve the quality of discrete optimization problem solutions. The subsequent development of the algorithms is related to using their modifications to solve optimization problems under conditions of uncertainty within the framework of a general approach to analyzing models with fuzzy coefficients in objective functions and constraints. In practical aspect, the algorithms are already being used to solve diverse problems of power engineering