Computational Combinatorial Optimization: Optimal or Provably Near-Optimal Solutions

Alexander Martin (auth.), Michael Jünger, Denis Naddef (eds.)9783540428770, 3-540-42877-1

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.

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Table of contents :
General Mixed Integer Programming: Computational Issues for Branch-and-Cut Algorithms….Pages 1-25
Projection and Lifting in Combinatorial Optimization….Pages 26-56
Mathematical Programming Models and Formulations for Deterministic Production Planning Problems….Pages 57-111
Lagrangian Relaxation….Pages 112-156
Branch-and-Cut Algorithms for Combinatorial Optimization and Their Implementation in ABACUS….Pages 157-222
Branch, Cut, and Price: Sequential and Parallel….Pages 223-260
TSP Cuts Which Do Not Conform to the Template Paradigm….Pages 261-303