The rank pricing problem: Models and branch-and-cut algorithms

Branch-and-Cut Algorithms

Branch and Cut Algorithms

is the objective function to be optimized over P . Whenever all variables in (1.1) are restricted to be integral, the problem is known as a linear integer programming (IP) problem. Conversely, a pure linear programming (LP) problem results when all variables in (1.1) are restricted to be real valued. As is frequently the case for MIP, instead of attempting to optimize (1.3) directly over P , it...

Stable Set Problem: Branch & Cut Algorithms

In this article, we provide an overview on how the maximum weighted stable set problem can be solved exactly with Branch & Cut techniques. In addition, we provide selected references to other exact methods. We start with a brief introduction of the stable set problem and a few basic definitions but assuming that the reader is already familiar with the basic concepts. The main stress of this art...

Branch-and-cut Algorithms for Integer Programming, Branch-and-cut

Branch-and-cut methods are exact algorithms for integer programming problems. They consist of a combination of a cutting plane method with a branch-and-bound algorithm. These methods work by solving a sequence of linear programming relaxations of the integer programming problem. Cutting plane methods improve the relaxation of the problem to more closely approximate the integer programming probl...

Branch-Price-and-Cut Algorithms

In many mixed integer programs there is some embedded problem structure which can be exploited, often by a decomposition. When the relaxation in each node of a branch-andbound tree is solved by column generation, one speaks of branch-and-price. Optionally, cutting planes can be added in order to strengthen the relaxation, and this is called branchprice-and-cut. We introduce the common concepts ...