Polyhedral proof methods in combinatorial optimization

Polyhedral techniques in combinatorial optimization

Generally, combinatorial optimization problems are easy to formulate, but hard to solve. The most successfull approaches, cutting plane algorithms and column generation, rely on the (mixed) integer linear programming formulation of a problem. The theory of polyhedra, i.e., polyhedral combinatorics, is the foundation of these techniques. This manuscript intends to give an overview of polyhedral ...

Polyhedral Techniques in Combinatorial Optimization I: Theory

Combinatorial optimization problems appear in many disciplines ranging from management and logistics to mathematics, physics, and chemistry. These problems are usually relatively easy to formulate mathematically, but most of them are computationally hard due to the restriction that a subset of the variables have to take integral values. During the last two decades there has been a remarkable pr...

P : Polyhedral techniques in combinatorial optimization

Polyhedral Techniques in Combinatorial Optimization II: Computations

The polyhedral approach is one of the most powerful techniques available for solving hard combinatorial optimization problems. The main idea behind the technique is to consider the linear relaxation of the integer combinatorial optimization problem, and try to iteratively strengthen the linear formulation by adding violated strong valid inequalities, i.e., inequalities that are violated by the ...

Polyhedral Methods in Discrete Optimization

In the last decade our capability of solving integer programming problems has increased dramatically due to the effectiveness of cutting plane methods based on polyhedral investigations. Polyhedral cutting planes have become central features in optimization software packages for integer programming. Here we present some of the important polyhedral methods used in discrete optimization. We discu...