Optimization Under Uncertainty: Applications to Machine Learning and Waste Management

In this thesis, we deal with optimization problems affected by uncertainty. The first class of problems we analyze aims at separating sets of data points by means of linear and nonlinear classifiers. The classification task is performed according to variants of the Support Vector Machine (SVM) and the uncertainty in real-world data is handled by means of Robust Optimization (RO) techniques. In the case of binary classification, we start by formulating a novel SVM-type model with nonlinear classifiers and perfectly known data points. Secondly, to prevent low accuracies in the classification process due to data perturbations, we construct bounded-by-norm uncertainty sets around the samples. Then, we derive the robust counterpart of the deterministic model thanks to RO strategies. To tackle the problem of multiclass classification, we design a new multiclass Twin Parametric Margin SVM (TPMSVM). We consider the cases of both linear and kernel-induced boundaries and propose two alternatives for the final decision function. Data perturbations are then included in the model and RO techniques are applied to prevent the TPMSVM against the worst possible realization of the uncertainty. All the aforementioned approaches are tested on real-world datasets, showing the advantages of explicitly considering the uncertainty versus deterministic approaches. The second problem we analyze is related to waste collection. Within this application, uncertainty lies in the waste accumulation rate of the network bins. Since information on the empirical distribution of the uncertainty is available, Stochastic Optimization (SO) techniques are applied. We model the waste collection problem as a multi-stage stochastic inventory routing problem, where the decisions are related to the selection of bins to be visited and the corresponding visiting sequence in a predefined time horizon. Given the computational complexity of the model, we solve it through a rolling horizon heuristic approach, and carry out computational experiments on real-data instances. The impact of stochasticity on waste generation is examined through stochastic measures, and the performance of the rolling horizon approach is evaluated. Finally, we discuss some managerial insights.