Mathematical Programming bounds for Large-Scale Unit Commitment Problems in Medium-Term Energy System Simulations

We consider a large-scale unit commitment problem arising in medium-term simulation of energy networks, stemming from a joint project between the University of Milan and a major energy research centre in Italy. Optimal plans must be computed for a set of thermal and hydroelectric power plants, located in one or more countries, over a time horizon spanning from a few months to one year, with a hour-by-hour resolution. We propose a mixed-integer linear programming model for the problem. Since the complexity of this unit commitment problem and the size of real-world instances make it impractical to directly optimise this model using general purpose solvers, we devise ad-hoc heuristics and relaxations to obtain approximated solutions and quality estimations. We exploit an incremental approach: at first, a linear relaxation of an aggregated model is solved. Then, the model is disaggregated and the full linear relaxation is computed. Finally, a tighter linear relaxation of an extended formulation is obtained using column generation. At each stage, metaheuristics are run to obtain good integer solutions. Experimental tests on real-world data reveal that accurate results can be obtained by our framework in affordable time, making it suitable for efficient scenario simulations

Densita con la proprieta di media per i sub-Laplaciani

Nella tesi studiamo le densità con la proprietà di media per i sub-Laplaciani. In particolare determiniamo un’espressione generale per una densità positiva con la proprietà di media, su un insieme Ω generico che soddisfi certe prorpietà di regolarità. Troviamo inoltre delle stime della funzione di Green e del nucleo di Poisson per un qualsiasi sub-Laplaciano su un generico gruppo di Carnot e tramite queste stime troviamo delle condizioni sufficienti affinchè, con la densità precedentemente trovata, si possa avere una struttura di Γ-tripla sull’insieme Ω. Studiamo infine un problema inverso per il quale sarà fondamentale avere una struttura di Γ-tripla

The isoperimetric problem for regular and crystalline norms in H1\mathbb H^1

We study the isoperimetric problem for anisotropic left-invariant perimeter measures on $\mathbb R^3$, endowed with the Heisenberg group structure. The perimeter is associated with a left-invariant norm $\phi$ on the horizontal distribution. We first prove a representation formula for the $\phi$-perimeter of regular sets and, assuming some regularity on $\phi$ and on its dual norm $\phi^*$, we deduce a foliation property by sub-Finsler geodesics of $\mathrm C^2$-smooth surfaces with constant $\phi$-curvature. We then prove that the characteristic set of $\mathrm C^2$-smooth surfaces that are locally extremal for the isoperimetric problem is made of isolated points and horizontal curves satisfying a suitable differential equation. Based on such a characterization, we characterize $\mathrm C^2$-smooth $\phi$-isoperimetric sets as the sub-Finsler analogue of Pansu's bubbles. We also show, under suitable regularity properties on $\phi$, that such sub-Finsler candidate isoperimetric sets are indeed $\mathrm C^2$-smooth. By an approximation procedure, we finally prove a conditional minimality property for the candidate solutions in the general case (including the case where $\phi$ is crystalline)

Ag-sensitized Tb3+/Yb3+ codoped silica-zirconia glasses and glass-ceramics: Systematic and detailed investigation of the broadband energy-transfer and downconversion processes

Abstract Various studies report that Tb3+/Yb3+ co-doped materials can split one UV or 488 nm (visible) photon in two near infrared (NIR) photons at 980 nm by an energy-transfer process involving one Tb3+ and two Yb3+ ions. Additionally, it was demonstrated that Ag multimers can provide an efficient optical sensitizing effect for rare earth ions (RE3+ ions), resulting in a broadband enhanced excitation, which could have a significant technological impact, overcoming their limited spectral absorptions and small excitation cross sections. However, a systematic and detailed investigation of the down-conversion process enhanced by Ag nanoaggregates is still lacking, which is the focus of this paper. Specifically, a step by step analysis of the energy-transfer quantum-cutting chain in Ag-exchanged Tb3+/Yb3+ co-doped glasses and glass-ceramics is presented. Moreover, the direct Ag-Yb3+ energy-transfer is also considered. Results of structural, compositional, and optical characterizations are given, providing quantitative data for the efficient broadband Ag-sensitization of Tb3+/Yb3+ quantum cutting. A deeper understanding of the physical processes beneath the optical properties of the developed materials will allow a wiser realization of more efficient energy-related devices, such as spectral converters for silicon solar cells and light-emitting devices (LEDs) in the visible and NIR spectral regions

Column generation for a real world vehicle routing problem

We present an optimization algorithm we developed for a software provider of planning tools for distribution logistics companies. The algorithm computes a daily plan for a heterogeneous fleet of vehicles, that can depart from different depots and must visit a set of customers for delivery operations. Besides multiple capacities and time windows associated with depots and customers, the problem also considers incompatibility constraints between goods, depots, vehicles and customers, maximum route length and durations, upper limits on the number of consecutive driving hours and compulsory drivers' rest periods, the possibility to skip some customers and to use express courier services instead of the given fleet to fulfill some orders, the option of splitting up the orders, the possible existence of pick-up operations to be performed by empty vehicles traveling back to their depots and the possibility of ``open" routes that do not terminate at depots. Moreover, the cost of each vehicle route is computed through a system of fares, depending on the locations visited by the vehicle, the distance traveled, the vehicle load and the number of stops along the route. We developed a column generation algorithm, where the pricing problem is a particular resource constrained elementary shortest path problem, solved through a bounded bi-directional dynamic programming algorithm. We describe how to encode the cost function and the complicating constraints by an appropriate use of resources and we present computational results on real instances obtained from the software company

La villa di Galileo in Arcetri / Galileo's villa at Arcetri

Villa Il Gioiello, built in the measured, harmonious style of the mid-16th century on the hill of Arcetri just outside Florence, is where Galileo spent his last years, under house arrest. Recently restored, it was not simply Galileo’s prison, it was also an observatory, a place of study and maybe even a place of leisure when he was tending the small vineyard that grew just over the courtyard wall