Matheuristics for Combinatorial Optimization Problems (Module 1)

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 introduces the basic concepts of mathematical programming and 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.
The two modules are rather independent, but the second one requires the basic concepts recalled in the first one.