OPTIMIZATION, DISCRETE MATHEMATICS AND APPLICATIONS (OPTIMA)

Coordinator: Paolo Ventura

Description

The OPTIMA research group investigates all phases of the solution process of mathematical problems. Combinatorial Optimization, Discrete Mathematics, Mixed -Integer Programming, Graph Theory, Algorithmics, Machine Learning,Continuous Optimization are the main methodological topics of interest and research.

Research Activities

COMBINATORIAL OPTIMIZATION AND DISCRETE MATHEMATICS

The OPTIMA research group studies discrete mathematical structures and uses methodologies of Graph Theory, Polyhedral Combinatorics, and Algorithmics to characterize structural properties and to develop exact or approximation algorithms for combinatorial optimization problems. MIXED-INTEGER PROGRAMMING Exact solution methods are developed for NP-hard problems, based on Polyhedral Theory, Dynamic Programming, Mixed-Integer Nonlinear Programming, Semidefinite Programming and Lagrangian relaxations, Decomposition Methods. Data uncertainty is dealt with Stochastic and Robust Optimization methods. OPTIMIZATION METHODS FOR DATA MINING AND AI Continuous and global optimization methods for designing non linear optimization algorithms for the training of Neural Networks and Support Vector Machines. Methods for the extraction of knowledge in form or rules from large datasets. Mixed Integer formulations for feature and outliers selection in large scale regression. OR APPLICATIONS OR and AI techniques and simulation modelling are applied for dealing with: Digital Twin e Green Transition applications; measuring, forecasting and controlling Transport and Road Traffic Systems; Power Production problems, Distribution problems in AC/DC settings (both in primary and in secondary levels), and in Energy Market management; Fleet Management; Railways Transportation; Logistics; Containers Management; Waste Management; Telecommunications; Health Care.