Matheuristics for Combinatorial Optimization problems (Module 1) - November 2025

Length:  10 hours - 2 cfu

Abstract:

Combinatorial Optimization is a huge domain of study, focused on optimization problems with a finite set of solutions.

It has important practical applications to manifold fields, including artificial intelligence, machine learning,

routing, scheduling, location, network analysis and design.

As many Combinatorial Optimization problems are NP-hard, heuristics are a natural solution approach.

Matheuristics, also known as model-based heuristics,

exploit the information provided by mathematical programming models, that is the representation

of the feasible solution space by means of equalities and inequalities on suitable decision variables.

The advantage of these methods with respect to the classical solution-based heuristics and metaheuristics

consists in the additional information they give, for example in terms of a priori or a posteriori

guarantees on the quality of the solution returned.

The first module of the course surveys the matheuristics based on relaxation methods and decomposition methods. The second module of the course reviews the matheuristics which exploit the availability

of mathematical programming solvers and those that interact with solution-based metaheuristics.

Dates & Venue

Suggested Readings:

Lecturer:

Prof. Maurizio Bruglieri - Politecnico di Milano

Assessor:

Prof. Maurizio Bruglieri - Politecnico di Milano