Compact Extended Linear Programming Models

This book provides a handy, unified introduction to the theory of compact extended formulations of exponential-size integer linear programming (ILP) models. Compact extended formulations are equally powerful polynomial-sized models whose solutions do not require the implementation of separation and pricing procedures. The book is written in a general, didactic form, first developing the background theoretical concepts (polyhedra, projections, linear and integer programming) and then delving into the various techniques for compact extended reformulations. The techniques are illustrated through a wealth of examples touching on many application areas, such as classical combinatorial optimization, network design, timetabling, scheduling, routing, computational biology and bioinformatics. The book is intended for graduate or PhD students - either as an advanced course on selected topics or within a more general course on ILP and mathematical programming - as well as for practitioners andsoftware engineers in industry exploring techniques for developing optimization models for their specific problems.

Auteur

Giuseppe Lancia is Professor of Operations Research in the Department of Mathematics and Computer Science at the University of Udine, Italy.Paolo Serafini is Professor of Operations Research in the Department of Mathematics and Computer Science at the University of Udine, Italy.

Contenu

Introduction.- Polyhedra.- Linear Programming.- Integer Linear Programming.- Large-scale Linear Programming.- General Techniques for Compact Formulations.- The Permutahedron.- The Parity Polytope.- Trees.- Cuts and Induced Bipartite Subgraphs.- Stable Sets.- Traveling Salesman Problems.- Packing.- Scheduling.- Computational Biology Problems.