OPTIMIZATION, DISCRETE MATHEMATICS AND APPLICATIONS (OPTIMA)

 

The OPTIMA research group investigates all phases of the solution process of mathematical problems, including analysis, modelling, structural properties, algorithmic approaches, computer code implementation and testing.

Combinatorial and Polyhedral Optimization, Discrete Mathematics, Mixed-Integer Programming, Graph Theory, Approximation and Online Algorithms, Logic Programming, Machine Learning, Stochastic and Robust Optimization, Continuous Optimization, Global Optimization are the main methodological topics of research.

We deal with a broad range of applications of optimization and discrete mathematics: Data Analysis, Network Analysis, Statistical Physics, Scheduling, Factory of the Future (Industry 4.0), Transportation and Logistics, Telecommunications and Network Traffic, Energy and Smart-Grids, Finance, Medicine and Social care.

The activity is performed along three main research topics: Combinatorial Optimization and Discrete Mathematics, Mixed-Integer Programming, Continuous Optimization.

 


Research topics
COMBINATORIAL OPTIMIZATION AND DISCRETE MATHEMATICS

The OPTIMA research group studies discrete mathematical structures and combinatorial methodologies by means of Graph Theory, Enumeration, and Polyhedral Combinatorics, with the purpose to establish structural properties and define exact or approximation algorithms for problem solution.


CONTINUOUS OPTIMIZATION

The OPTIMA research group studies solution methods for Large-Scale Optimization problems with continuous variables, derivative-free methods, Global Optimization, Multi-criteria Optimization, Nondifferentiable Optimization.


MIXED-INTEGER PROGRAMMING

The OPTIMA research group studies exact solution methods for NP-hard problems based on Polyhedral Theory, Dynamic Programming, Mixed-Integer Nonlinear Programming, Semidefinite Programming relaxation, Lagrangian relaxation, Decomposition Methods. Data uncertainty is dealt with Stochastic and Robust Optimization methods.


OPTIMIZATION METHODS FOR DATA MINING

Desing and development of non linear optimization algorithms for the training of Neural Networks and Support Vector Machines; Methods for the extraction of knowledge in logic form from large datasets based on integer programming and the solution of Minimum Cost Satisfiability Problems; integer programming formulation of the Feature Selection problem in high dimensions and implementation of efficient heuristic algorithms for its solution.


METHODS AND TOOLS FOR TRANSPORT AND TRAFFIC SYSTEMS MANAGEMENT

OR and AI techniques for measuring, forecasting and controlling transport and traffic systems; Telematics systems for transport and mobility control; Neural networks for traffic modelling and forecasting; Intelligent transportation systems for road traffic management


APPLICATIONS OF OPERATIONS RESEARCH

Applications on tactical models for Power Production and Energy Market management; Hydrocarbon Products Distribution by ships; Fleet Management.


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