Direct cut-off method for combinatorial optimization problems with additional constraints

Abstract

A direct cut-off method to solve combinatorial optimization problems on polyarrangements with additional constraints is proposed and justified. The method allows obtaining a feasible solution at each stage without constructing the linear hull of the set of polyarrangements.

The Method of Cutting the Vertices of Permutation Polyhedron Graph to Solve Linear Conditional Optimization Problems on Permutations

“…To compare the results, the computing time is presented for these problems with the use of the first combinatorial cutting method [6,7,16], where auxiliary linear programming problems were solved by the simplex method. Column ² contains computing time for the method of cutting the vertices of the permutation polyhedron graph, and column ²² that for the first method of combinatorial cutting.…”

“…The studies [4,[6][7][8][9] consider cutting methods for the solution of combinatorial optimization problems on vertex-located sets with linear additional constraints and [10,11] for those with nonlinear objective function and nonlinear additional constraints. The algorithms of these methods are nonpolynomial.…”

Properties of the Linear Unconditional Problem of Combinatorial Optimization on Arrangements Under Probabilistic Uncertainty

“…An important trend in the modern theory of optimization is analysis of combinatorial problems: both general properties of combinatorial optimization problems and solution methods for separate classes of problems, in particular, Euclidean combinatorial optimization problems (for example, [1][2][3][4][5][6][7]). However, wide bibliography is devoted to solving optimization problems with regard for various types of uncertainty, including probabilistic one [8][9][10][11][12][13].…”