Generalized algorithms for solving problems of discrete, integer, and Boolean programming are discussed. These algorithms are associated with the method of normalized functions and are based on a combination of formal...Generalized algorithms for solving problems of discrete, integer, and Boolean programming are discussed. These algorithms are associated with the method of normalized functions and are based on a combination of formal and heuristic procedures. This allows one to obtain quasi-optimal solutions after a small number of steps, overcoming the NP-completeness of discrete optimization problems. Questions of constructing so-called “duplicate” algorithms are considered to improve the quality of discrete problem solutions. An approach to solving discrete problems with fuzzy coefficients in objective functions and constraints on the basis of modifying the generalized algorithms is considered. Questions of applying the generalized algorithms to solve multicriteria discrete problems are also discussed. The results of the paper are of a universal character and can be applied to the design, planning, operation, and control of systems and processes of different purposes. The results of the paper are already being used to solve power engineering problems.展开更多
The results of research into the use of fuzzy set based models and methods of multicriteria decision making for solving power engineering problems are presented. Two general classes of models related to multiobjective...The results of research into the use of fuzzy set based models and methods of multicriteria decision making for solving power engineering problems are presented. Two general classes of models related to multiobjective (X,M> models) and multiattribute (X,R> models) problems are considered. The analysisX,M> of models is based on the use of the Bellman-Zadeh approach to decision making in a fuzzy environment. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. Several techniques based on fuzzy preference modeling are considered for the analysis of?X,R> models. A review of the authors’ results associated with the application of these models and methods for solving diverse types of problems of power system and subsystems planning and operation is presented. The recent results on the use ofX,M> andX,R> models and methods of their analysis for the allocation of reactive power sources in distribution systems and for the prioritization in maintenance planning in distribution systems, respectively, are considered.展开更多
文摘Generalized algorithms for solving problems of discrete, integer, and Boolean programming are discussed. These algorithms are associated with the method of normalized functions and are based on a combination of formal and heuristic procedures. This allows one to obtain quasi-optimal solutions after a small number of steps, overcoming the NP-completeness of discrete optimization problems. Questions of constructing so-called “duplicate” algorithms are considered to improve the quality of discrete problem solutions. An approach to solving discrete problems with fuzzy coefficients in objective functions and constraints on the basis of modifying the generalized algorithms is considered. Questions of applying the generalized algorithms to solve multicriteria discrete problems are also discussed. The results of the paper are of a universal character and can be applied to the design, planning, operation, and control of systems and processes of different purposes. The results of the paper are already being used to solve power engineering problems.
文摘The results of research into the use of fuzzy set based models and methods of multicriteria decision making for solving power engineering problems are presented. Two general classes of models related to multiobjective (X,M> models) and multiattribute (X,R> models) problems are considered. The analysisX,M> of models is based on the use of the Bellman-Zadeh approach to decision making in a fuzzy environment. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. Several techniques based on fuzzy preference modeling are considered for the analysis of?X,R> models. A review of the authors’ results associated with the application of these models and methods for solving diverse types of problems of power system and subsystems planning and operation is presented. The recent results on the use ofX,M> andX,R> models and methods of their analysis for the allocation of reactive power sources in distribution systems and for the prioritization in maintenance planning in distribution systems, respectively, are considered.
