Combinatorial optimization is omnipresent when addressing numerous issues in planning and managing complex systems in important areas such as transportation, logistics, production, and telecommunications, to name but a few. Location, network design, routing, scheduling, and packing are among the major problem classes encountered in addressing these issues. These problems are difficult to address, particularly when the instance size increases, and require heuristic solution methods to obtain hopefully good solutions within acceptable computation times given the corresponding decision process. This series of lectures aims to provide the basic skills required in developing a heuristic solution method for a combinatorial optimization problem. The course in organized in classes giving both theory and examples from the literature, and laboratories introducing the main software frameworks for metaheuristic prototyping. The course is given in English and it is organized in order to guide student in the implementation of a metaheuristic for a given optimization problem. A few suggested textbooks: Tadei, Della Croce, Grosso, "Fondamenti di Ottimizzazione", Esculapio Editore. Tadei, Della Croce, "Elementi di Ricerca Operativa", Esculapio Editore. Handbook of Metaheuristics, M. Gendreau and J.-Y. Potvin (Eds), Springer, 2010. Period: January-February (exact calendar to be communicated a couple of months in advance)

Basic programming skills.

This series of lectures aims to provide a broad view of the field of heuristic solution methods applied to the optimization of the solutions of combinatorial optimization problems. Beginning from simple constructive heuristics methods, we then proceed to the presentation of local search algorithms, meta-heuristics and matheuristics. The lectures will present the basic concepts, the main classes of heuristic methods, and the evolution and trends of the field. Examples of applications to several combinatorial optimization problems will illustrate the concepts and support the discussions. The main topics covered: • Decisions, models, and problem solving; a brief overview of the concepts of “complexity” and “efficiency”; the concept of heuristic solution method; • Classical heuristics; Neighbourhoods and local search; Meta-heuristics; • Neighbourhood-based meta-heuristics (GRASP, Tabu Search, Variable Neighbourhood Search, Adaptive Large Neighbourhood Search, etc.) • Population-based meta-heuristics (Genetic and Evolutionary Algorithms, Swarms, etc.) • Linear programming models and matheuristics. • Currently available software tools (both free and licenced).

On site

Oral presentation - Laborartory test on experimental practice or informatics

P.D.1-1 - January

- Venerdì 14th 14.30PM-18.30PM - Mercoledì 19th 14.30PM-18.30PM - Venerdì 21st 14.30PM-18.30PM - Mercoledì 26th 14.30PM-18.30PM - Venerdì 28th 14.30PM-18.30PM The final exam is the presentation and discussion of the results obtained in developing a heuristic method for a given optimization problem.