Romanova N. The Euclidean Combinatorial Optimization Problems on the Polyarrangements and Methods of their Solving

Mathematical models were researched and developed: for the problems of color packing of rectangles and the problem to denote the order of order services for maximization of profitability of service system. The mathematical model of color packing was realized. Number experiments were conducted. New complex method for solving linear combinatorial optimization problems on top-situated Euclidean combinatorial sets was developed and grounded. The method of Stoyan-Yakovlev of convex function extensions with arrangements was extended on the set of polyarrangements. The properties of combinatorial set and combinatorial polyhedron for the optimization problem with linear conditional function and one linear restriction to which unconditional optimization problem on polyarrangement set is led were considered. The theorem about polyhedron sides was proved. The criterion of its tops, the criterion of combination of polyhedron tops were received and grounded, and their number was counted. The theorem about the equivalence of solving for the linear fractional problem with conditional function on polyarrengements and conditional optimization problem with linear conditional function on Euclidean combinatorial set of special kind was proved.