Computational Combinatorial Optimization

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.

Inhalt

General Mixed Integer Programming: Computational Issues for Branch-and-Cut Algorithms.- Projection and Lifting in Combinatorial Optimization.- Mathematical Programming Models and Formulations for Deterministic Production Planning Problems.- Lagrangian Relaxation.- Branch-and-Cut Algorithms for Combinatorial Optimization and Their Implementation in ABACUS.- Branch, Cut, and Price: Sequential and Parallel.- TSP Cuts Which Do Not Conform to the Template Paradigm.