"Branch-and-Cut Algorithms for Combinatorial Optimization and Their Implementation in ABACUS"
Article by Matthias Elf, Carsten Gutwenger, Michael Jünger, Giovanni Rinaldi, available as BibTeX Source.
Zentrum für Angewandte Informatik Köln, Lehrstuhl Jünger
Preprint Key:	zaik2003-454
Keywords:	Branch and Cut Algorithms, combinatorial optimization, Computational Combinatorial Optimization, Discrete Computations, Discrete Structures, Optimization Algorithms, polyhedral combinatorics, Traveling Salesman Problem (TSP)
MSC codes:	90C27, 90C57
This article was published in 2001 by Springer in the book "Computational Combinatorial Optimization" (edited by Michael Jünger, Denis Naddef), series "Lecture Notes in Computer Science", volume 2241, pages 157-222.
Abstract:	Branch-and-Cut-and-Price algorithms belong to the most successful techniques forsolving mixed integer linear programs and combinatorial optimization problems to optimality (or, at least, with certified quality). In this unit, we concentrate on sequential Branch-and-Cut for hard combinatorial optimization problems, while Branch-and-Cut for general mixed integer linear programming is treated in [longrightarrow Martin] and parallel Branch-and-Cut is treated in [longrightarrow~Lad'{a}nyi/Ralphs/Trotter]. After telling our most recent story of a successful application of Branch-and-Cut, we give in a brief review of the history, including the contributions of pioneers with an emphasis on the computational aspects of their work. The components of a generic Branch-and-Cut algorithm are described and illustrated on the traveling salesman problem. We first elaborate a bit on the important separation problem where we use the traveling salesman problem and the maximum cut problem as examples, then we show how Branch-and-Cut can be applied to problems with a very large number of variables Branch-and-Cut-and-Price. The last sectionis devoted to the design and applications of the ABACUS software framework for the implementation of Branch-and-Cut algorithms. Finally we make a few remarks on the solution of the exercise consisting of the design of a simple TSP-solver in ABACUS.