Kolyechkina L. The properties of tasks of the combinatorial optimization with the fraction-linear aim function. Methods and algorithms for its decisions

Object of researches are the tasks combinatorial of optimization. The purpose of work - research of properties of tasks combinatorial of optimization with fraction-linear functions of the purpose, improvement of a method combinatorial of cutting off for the decision of such tasks. The transition from tasks with fraction -linear criterion functions to tasks with linear functions of the purpose is made. For linear are formulated and the properties of area of the allowable decisions of a task are proved, which convex environment represents polyhedron: the theorem of sides polyhedron, criterion of top, criterion of a contiguity of sides. The nonreducible system of linear restrictions of this polyhedron is obtained. The algorithms constructed on a method к combinatorial of cutting off, program are realized on PC. The analysis of algorithms is made on the basis of numerical experiments. The models of applied tasks with fraction-linear criterion function on permutation sets are constructed. The results dissertation are used in scientific researches of the Poltava national technical university of a name Yuriy Kondratyuka, and as are introduced into educational process of university. Sphere of use is the industrial and agricultural sphere of a national economy.