Barbolina T. Methods and algorithms for solving optimization problems on arrangements with additional conditions

The models of practical problems are built as Euclidean problems of lexicographic combinatorial optimization on arrangements which are a new class of Euclidian combi-natorial optimization problems. Cutting methods for solving linear and convex optimization problems on arrange-ments are developed. The splitting of polyhedral sets with an equivalence relation is proposed. On the basis of such splitting a lexicographic equivalence method for solving all-combinatorial lexicographic optimization on arrangements are developed. Algorithms of cutting method and lexicographic equivalence method for solving optimization problems on arrangements are proposed and validated. The algorithms based on such ideas are proved to be finite.