Research

My research interests can be summarized into the following topics:

• Infinite-dimensional optimization.
• Multi-stage dynamic optimization and optimal control.
• Rolling horizon optimization.
• Optimal estimation and least squares.
• Logistics and transportation problems.
• Optimal control of partial differential equations.
• Optimization of ICT infrastructures and robotic networks.
• Machine Learning and learning from data.
• Neural networks.

The common denominator of my theoretical research activity is the need of minimizing an index that quantifies the quality of a certain solution. For example, a given cost can be chosen to evaluate the effectiveness of a decision strategy for nonlinear systems or distributed parameter systems. A suitable index can be used to quantify the quality of the estimation of a stochastic variable in optimal estimation problems, or the estimation of the parameters of a mathematical model. In rolling horizon optimization, the minimization of a given cost function over a sliding window is performed at each time step in order to find optimal decisions.

In most of the cases listed above, it is not possible to compute exact solutions, unless in very specific situations. Therefore, a large part of my activity has focused on the study of methodologies to search for approximate solutions, with the following main features:

• reduced computational effort;
• accuracy;
• scalability;
• optimality;
• robustness;
• stability.

Beside this theoretical-methodological approach, my research activity has also focused on application-oriented topics. In this context, I have first devised a mathematical model of the problem under consideration, with the formalization of one or more optimization problems to pursue given objectives. Then, I have solved these problems with various exact or heuristic techniques, with the aim of finding also in this case a good compromise between accuracy and computational requirements. The main areas I have investigated are the following:

• Logistics and transportation systems.
• Supply chain management.
• Production planning and inventory control.
• Intermodal container terminals.
• Resource allocation.
• Management of water reservoirs.
• Computer networks.
• Robotic networks.
• Vehicular traffic.
• Wildland fire propagation.
• Imitation learning
• Cyber physical systems.
• Cybersecurity.
• Smart grids.
• Fluid turbomachinery.

The optimization problems I have considered can be divided into two classes. The first class is made up of problems with solutions given by functions belonging to infinite-dimensional spaces. Such a type of problems is known in the literature as "functional optimization problems" or "infinite-dimensional programming". The second class consists of problems whose solutions belong to finite-dimensional spaces: the solutions of such problems, also known as "mathematical programming problems", are the components of multidimensional vectors. In general, the first kind of problems can be reduced to the second one by means of suitable approximations. In my research activity, I have performed such operation by using neural networks and other linear or nonlinear approximators. In the case of mathematical programming problems, I have dealt with either real, integer, or mixed decision variables, and I have developed suitable approximate solution techniques for the problem at hand.

A detailed description of my research activity can be found in my Curriculum Vitae, with reference to the related scientific works (see here for the complete list of publications).