Computational Combinatorial Optimization

1. Front Matter

   Pages I-I

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2. General Mixed Integer Programming: Computational Issues for Branch-and-Cut Algorithms

   • Alexander Martin

   Pages 1-25

3. Projection and Lifting in Combinatorial Optimization

   • Egon Balas

   Pages 26-56

4. Mathematical Programming Models and Formulations for Deterministic Production Planning Problems

   • Yves Pochet

   Pages 57-111

5. Lagrangian Relaxation

   • Claude Lemaréchal

   Pages 112-156

6. Branch-and-Cut Algorithms for Combinatorial Optimization and Their Implementation in ABACUS

   • Matthias Elf, Carsten Gutwenger, Michael Jünger, Giovanni Rinaldi

   Pages 157-222

7. Branch, Cut, and Price: Sequential and Parallel

   • Laszlo Ladányi, Ted K. Ralphs, Leslie E. Trotter Jr

   Pages 223-260

8. TSP Cuts Which Do Not Conform to the Template Paradigm

   • David Applegate, Robert Bixby, Vašek Chvátal, William Cook

   Pages 261-303

9. Back Matter

   Pages 305-305

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This tutorial contains written versions of seven lectures on Computational Combinatorial Optimization given by leading members of the optimization community. The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches. Polyhedral combinatorics as the mathematical backbone of successful algorithms are covered from many perspectives, in particular, polyhedral projection and lifting techniques and the importance of modeling are extensively discussed. Applications to prominent combinatorial optimization problems, e.g., in production and transport planning, are treated in many places; in particular, the book contains a state-of-the-art account of the most successful techniques for solving the traveling salesman problem to optimality.

• Branch and Cut Algorithms
• Combinatorial Optimization
• Computational Combinatorial Optimization
• Discrete Computations
• Discrete Structures
• Optimization Algorithms
• Polyhedral Combinatorics
• Traveling Salesman Problem (TSP)
• algorithms
• modeling
• optimization
• programming
• algorithm analysis and problem complexity
• data structures
• combinatorics

• Universität zu Köln,Institut für Informatik, Köln, Germany

  Michael Jünger

• ENSIMAG - antenne de Montbonnot Laboratoire Informatique et Distribution, ZIRST, Montbonnot Saint Martin, France

  Denis Naddef

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