Technical reports

Separating two finite sets of points in a Euclidean space is a fundamental problem in classification. Customarily linear separation is used, but nonlinear separators such as spheres have been shown to have better performances in some tasks, such as edge detection in images. We exploit the relationships between the more general version of the spherical separation, where we use general ellipsoids, and the SVM model with quadratic kernel to propose a new classification approach. The implementation basically boils down to adding a SDP constraint to the standard SVM model in order to ensure that the chosen hyperplane in the feature space represents a non-degenerate ellipsoid in the input space; albeit being somewhat more costly than the original formulation, this still allows to exploit many of the techniques developed for SVR in combination with SDP approaches. We test our approach on several classification tasks, among which the edge detection problem for gray-scale images, proving that the approach is competitive with both the spherical classification one and the quadratic-kernel SVM one without the ellipsoidal restriction.

The paper deals with a sequencing and routing problem originated by a real-world application context. The problem consists in defining the best sequence of locations to visit within a warehouse for the storage and/or retrieval of a given set of items during a specified time horizon, where the storage/retrieval location of an item is given. Picking and put away of items are simultaneously addressed, by also considering some specific requirements given by the layout design and operating policies which are typical in the kind of warehouses under study. Specifically, the considered sequencing policy prescribes that storage locations must be replenished or emptied one at a time by following a specified order of precedence. Moreover, two fleet of vehicles are used to perform retrieving and storing operations, whose routing is restricted to disjoint areas of the warehouse. We model the problem as a constrained multicommodity flow problem on a space-time network, and we propose a Mixed-Integer Linear Programming formulation, whose primary goal is to minimize the time traveled by the vehicles during the time horizon. Since large-size realistic instances are hardly solvable within the time limit commonly imposed in the considered application context, a matheuristic approach based on a time horizon decomposition is proposed. Finally, we provide an extensive experimental analysis aiming at identifying suitable parameter settings for the proposed approach, and testing the matheuristic on particularly hard realistic scenarios. The computational experiments show the efficacy and the efficiency of the proposed approach.

Energy communities (ECs) are essential policy tools to meet the Energy Transition goals, as they can promote renewable energy sources, demand side management, demand response and citizen participation in energy matters. However, to fully unleash their potential, their design and scheduling requires a coordinated technical operation that the community itself may be ill-equipped to manage, in particular in view of the mutual technical and legal constraints ensuing from a coordinated design. Aggregators and Energy Service COmpanies (ESCOs) can perform this support role, but only provided that their goals are aligned to those of the community, not to incur in the agency problem. In this study, we propose a business model for aggregators of ECs, and its corresponding technical optimization problem, taking into account all crucial aspects: i) alleviating the risk of the agency problem, ii) fairly distributing the reward awarded to the EC, iii) estimating the fair payment for the aggregator services, and iv) defining appropriate exit clauses that rule what happens when a user leaves the EC. A detailed mathematical model is derived and discussed, employing several fair and theoretically-consistent reward distribution schemes, some of which are, to the best of our knowledge, proposed here for the first time. A case study is developed to quantify the value of the aggregator and compare the coordinated solution provided by the aggregator with non-coordinated configurations, numerically illustrating the impact of the reward distribution schemes. The results show that, in the case study, the aggregator enables reducing costs by 16% with respect to a baseline solution, and enables reaching 52.5% renewable share and about 46% self/shared consumption, whereas these same numbers are only 28-35% for the non-coordinated case. Our results suggest that the aggregator fair retribution is around 16-24% the added benefit produced with respect to the non-coordinated solution, and that stable reward distribution schemes such as Shapley/Core or Nucleolus are recommended. Moreover, the results highlight the unwanted effect that some non-cooperative ECs may have an added benefit without providing any positive effect to the power system. Our work lays the foundations for future studies on business models of aggregators for ECs and provides a methodology and preliminary results that can help policy makers and developers in tailoring national-level policies and market-offerings.