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Decision trees are widely-used classification and regression models because of their interpretability and good accuracy. Classical methods such as CART are based on greedy approaches but a growing attention has recently been devoted to optimal decision trees. We investigate the nonlinear continuous optimization formulation proposed in Blanquero et al. (EJOR, vol. 284, 2020; COR, vol. 132, 2021) for (sparse) optimal randomized classification trees. Sparsity is important not only for feature selection but also to improve interpretability. We first consider alternative methods to sparsify such trees based on concave approximations of the $l_{0}$ ``norm". Promising results are obtained on 24 datasets in comparison with $l_1$ and $l_{\infty}$ regularizations. Then, we derive bounds on the VC dimension of multivariate randomized classification trees. Finally, since training is computationally challenging for large datasets, we propose a general decomposition scheme and an efficient version of it. Experiments on larger datasets show that the proposed decomposition method is able to significantly reduce the training times without compromising the accuracy.

In the last few years, the strong decentralization of energy production, fostered by the adoption of small renewable energy plants directly connected to the grid, has been placing the end user at the center of the electrical system management. Indeed, the end user has become at the same time producer and consumer of electricity. In addition, groups of end users are encouraged to form the so-called energy districts in which the energy is exchanged locally or negotiated, without intermediaries, directly with the energy provider. This paper proposes Power Cloud, an Internet of Things solution for energy districts. Power Cloud injects smartness into the management of an energy district by supplying a distributed computing layer that controls the physical devices of the end users, and interacts with a centralized cloud component that manages the whole district. In particular, each end user dwelling is equipped with a Smart Energy Aware Gateway (SEAG), which monitors and controls a nanogrid and a home automation system. The SEAG computes the optimal energy strategy for the local dwelling, starting from information achieved by means of complex prediction algorithms that are purposely executed on the cloud.

In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8 (EC8). However, a lack of accuracy of the N2 method in certain conditions has been pointed out by several studies. This paper addresses the assessment of effectiveness of the N2 method in seismic displacement demand determination in non-linear domain. The objective of this work is to investigate the accuracy of the N2 method through comparison with displacement demands computed using non-linear time-history analysis (NLTHA). Results show that the original N2 method may lead to overestimation or underestimation of displacement demand predictions. This may affect results of mechanical model-based assessment of seismic vulnerability at an urban scale. Hence, the second part of this paper addresses an improvement of the N2 method formula by empirical evaluation of NLTHA results based on EC8 ground-classes. This task is formulated as a mathematical programming problem in which coefficients are obtained by minimizing the overall discrepancy between NLTHA and modified formula results. Various settings of the mathematical programming problem have been solved using a global optimization metaheuristic. An extensive comparison between the original N2 method formulation and optimized formulae highlights benefits of the strategy.

Relying on multiobjective programming techniques, we have developed an optimization software to improve the services provided by the social co-operative OMNIA. OMNIA’s mission is to supply home-care assistance to children and people with disabilities. Our method is intended to optimize the social workers’ shift planning aiming at, on the one hand, maximizing the overall quality of the social care services, on the other hand, minimizing costs associated with OMNIA’s activity. In particular, our software provides Pareto optima of the resulting (difficult) bi-objective model by resorting to both a standard a priori weighted-sum approach and a new MINLP no-preference (hypervolume maximization-type) method. The product of this research is successfully employed by OMNIA.

This paper addresses seismic vulnerability assessment at urban scale. Particularly, it focuses on the differences in damage distribution obtained from the application of several simplified methods for displacement demand determination. The results obtained for two cities of Switzerland (Sion and Martigny) highlight the related impact. Displacement demands predicted using three simplified methods are compared with “reference” seismic demands obtained from non-linear time-history analysis (NLTHA). Comparing the urban seismic damage distributions from the three simplified methods with the one from NLTHA helps in understanding the reliability of displacement demand determination. The following three methods are compared: the usual N2 method, the Lin & Miranda proposal and an optimized version of the N2 method. These methods are evaluated based on the real seismic hazard (microzones), showing furthermore the importance of considering the real soil conditions in the general damage assessment.