Roskladka O. The tasks of optimization on polycombinatorial sets: properties and solutions

In dissertation the general task of polycombinatorial optimization is posed, are detected and the properties of a general polycombinatorial set, and also it of special cases - Euclidean combinatorial sets of polypermutations and polyarrangements are proved. Are proved necessary and sufficient conditions for fundamental properties of Euclidean combinatorial polyhedrons of permutations and polypermutations - nondegeneracy and equivalence. For convex envelopes of sets of the arrangements and polyarrangements the surplus restrictions in systems of linear inequalities are detected and the systems of nonreducible restrictions are obtained. The new mathematical model of the task of the arrangement of plants of a upkeep as the tasks of Euclidean polycombinatorial optimization is constructed and the exact solution is obtained it. The distribution of a method of a dynamic programming for a special class of the tasks of polycombinatorial optimization is justified.