Compact Extended Linear Programming Models

1. Front Matter

   Pages i-ix

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2. Introduction

   • Giuseppe Lancia, Paolo Serafini

   Pages 1-6

3. Polyhedra

   • Giuseppe Lancia, Paolo Serafini

   Pages 7-31

4. Linear Programming

   • Giuseppe Lancia, Paolo Serafini

   Pages 33-41

5. Integer Linear Programming

   • Giuseppe Lancia, Paolo Serafini

   Pages 43-66

6. Large-Scale Linear Programming

   • Giuseppe Lancia, Paolo Serafini

   Pages 67-74

7. General Techniques for Compact Formulations

   • Giuseppe Lancia, Paolo Serafini

   Pages 75-102

8. The Permutahedron

   • Giuseppe Lancia, Paolo Serafini

   Pages 103-112

9. The Parity Polytope

   • Giuseppe Lancia, Paolo Serafini

   Pages 113-121

10. Trees

    • Giuseppe Lancia, Paolo Serafini

    Pages 123-135

11. Cuts and Induced Bipartite Subgraphs

    • Giuseppe Lancia, Paolo Serafini

    Pages 137-147

12. Stable Sets

    • Giuseppe Lancia, Paolo Serafini

    Pages 149-154

13. Traveling Salesman Problems

    • Giuseppe Lancia, Paolo Serafini

    Pages 155-164

14. Packing

    • Giuseppe Lancia, Paolo Serafini

    Pages 165-171

15. Scheduling

    • Giuseppe Lancia, Paolo Serafini

    Pages 173-181

16. Computational Biology Problems

    • Giuseppe Lancia, Paolo Serafini

    Pages 183-195

17. Back Matter

    Pages 197-208

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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, but 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 practitionersand software engineers in industry exploring techniques for developing optimization models for their specific problems. 

• ILP
• combinatorial optimization
• branch-and-cut
• compact extended formulations
• max-cut
• bin packing
• cutting-stock
• knapsack
• Steiner-tree
• routing-cost

“This book is dedicated to presenting and applying the methods of compact extended formulations of linear optimization problems and polyhedra. … The main merit of this book is that it presents in a unified way the state of the art in the matter in discussion. … I consider the book to be a useful contribution to the literature on applications of (combinatorial) linear optimization problems … .” (Sorin-Mihai Grad, zbMATH 1390.90004, 2018)

• Department of Mathematics, Computer Science, and Physics, University of Udine, Udine, Italy

  Giuseppe Lancia, Paolo Serafini

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.

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