An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron

TL;DR

This paper introduces an exact separation algorithm for the unsplittable capacitated network design problem, utilizing polyhedral techniques and acceleration methods to generate effective cutting planes.

Contribution

It presents a novel exact separation algorithm with acceleration techniques for generating cutting planes in the unsplittable capacitated network design problem.

Findings

The algorithm guarantees facet-defining inequalities.

Acceleration significantly reduces iteration count.

Computational results show improved solution quality.

Abstract

In this paper, we concentrate on generating cutting planes for the unsplittable capacitated network design problem. We use the unsplittable flow arc-set polyhedron of the considered problem as a substructure and generate cutting planes by solving the separation problem over it. To relieve the computational burden, we show that, in some special cases, a closed form of the separation problem can be derived. For the general case, a brute-force algorithm, called exact separation algorithm, is employed in solving the separation problem of the considered polyhedron such that the constructed inequality guarantees to be facet-defining. Furthermore, a new technique is presented to accelerate the exact separation algorithm, which significantly decreases the number of iterations in the algorithm. Finally, a comprehensive computational study on the unsplittable capacitated network design problem is presented to demonstrate the effectiveness of the proposed algorithm.