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.

About the Authors

Timo Berthold is Lecturer at TU Berlin and a Director at FICO, leading the MIP research and development team of the FICO Xpress Solver. He is an expert on heuristic methods and computational mixed-integer linear and nonlinear programming. He has won multiple awards for his research.

Andrea Lodi is Andrew H. and Ann R. Tisch Professor at the Jacobs Technion-Cornell Institute at Cornell Tech and the Technion - ITT. His main research interests are in mixed-integer linear and nonlinear programming and data science. He has been recognized by IBM and Google faculty awards, and the INFORMS Optimization Society 2021 Farkas Prize. He is a 2023 INFORMS Fellow.

Domenico Salvagnin is Associate Professor in Operations Research at the University of Padua, Italy. He was lead development scientist in the IBM CPLEX team in 2015–2017 and is currently scientific consultant for FICO Xpress. His research interests include computational integer programming, constraint programming and hybrid methods for optimization.

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