Primal Heuristics in Integer Programming

The first comprehensive guide to the development and use of primal heuristics in mixed-integer programming technology and solvers.

Timo Berthold (Author), Andrea Lodi (Author), Domenico Salvagnin (Author)

9781009574785, Cambridge University Press

Hardback, published 3 April 2025

139 pages
22.9 x 15.2 x 1 cm, 0.347 kg

'Primal Heuristics in Integer Programming is a singular work in the area of computational integer optimization. It aggregates many of the most important techniques that state-of-the-art solvers use for actually producing high-quality solutions to large-scale and/or difficult mixed-integer linear optimization problems. This book fills a big gap left by the many textbooks on mixed-integer linear optimization problems. Certainly it should be on the shelf of any student, researcher or practitioner who wants a complete picture of how such solvers work.' Jon Lee, University of Michigan

Primal heuristics guarantee that feasible, high-quality solutions are provided at an early stage of the solving process, and thus are essential to the success of mixed-integer programming (MIP). By helping prove optimality faster, they allow MIP technology to extend to a wide variety of applications in discrete optimization. This first comprehensive guide to the development and use of primal heuristics within MIP technology and solvers is ideal for computational mathematics graduate students and industry practitioners. Through a unified viewpoint, it gives a unique perspective on how state-of-the-art results are integrated within the branch-and-bound approach at the core of the MIP technology. It accomplishes this by highlighting all the required knowledge needed to push the heuristic side of MIP solvers to their limit and pointing out what is left to do to improve them, thus presenting heuristic approaches for MIP as part of the MIP solving process.

1. Introduction and concepts
2. Large neighborhood search
3. Rounding, propagation and diving
4. The feasibility pump family
5. Pivoting and line search heuristics
6. Computational study
7. Primal heuristics for mixed integer nonlinear programming
8. Machine learning for primal heuristics
Appendix. Quiz solutions
References
Index.

Subject Areas: Optimization [PBU]