1,721,105 research outputs found
Optimization Under Uncertainty: Applications to Machine Learning and Waste Management
Full text linkIn 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.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
A novel robust optimization model for nonlinear Support Vector Machine
Full text linkIn this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel functions and consists in two consecutive phases: first, a classical SVM model is solved, followed by a linear search procedure, aimed at minimizing the total number of misclassified data points. To address the problem of data perturbations and protect the model against uncertainty, we construct bounded-by-norm uncertainty sets around each training data and apply robust optimization techniques. We rigorously derive the robust counterpart extension of the deterministic SVM approach, providing computationally tractable reformulations. Closed-form expressions for the bounds of the uncertainty sets in the feature space have been formulated for typically used kernel functions. Finally, extensive numerical results on real-world datasets show the benefits of the proposed robust approach in comparison with various SVM alternatives in the machine learning literature
A robust twin parametric margin support vector machine for multiclass classification
Full text linkIn this paper, we introduce novel Twin Parametric Margin Support Vector Machine (TPMSVM) models designed to address multiclass classification tasks under feature uncertainty. To handle data perturbations, we construct bounded-by-norm uncertainty sets around each training observation and derive the robust counterparts of the deterministic models using robust optimization techniques. To capture complex data structures, we explore both linear and kernel-induced classifiers, providing computationally tractable reformulations of the resulting robust models. Additionally, we propose two alternatives for the final decision function, enhancing models’ flexibility. Finally, we validate the effectiveness of the proposed robust multiclass TPMSVM methodology on real-world datasets, showing the good performance of the approach in the presence of uncertainty
A stochastic electric vehicle routing problem under uncertain energy consumption
Full text linkThe increasing adoption of Electric Vehicles (EVs) for service and goods distribution operations has led to the emergence of Electric Vehicle Routing Problems (EVRPs), a class of vehicle routing problems addressing the unique challenges posed by the limited driving range and recharging needs of EVs. While the majority of EVRP variants have considered deterministic energy consumption, this paper focuses on the Stochastic Electric Vehicle Routing Problem with a Threshold
recourse policy (SEVRP-T), where the uncertainty in energy consumption is considered, and a recourse policy is employed to ensure that EVs recharge at Charging Stations (CSs) whenever their State of Charge (SoC) falls below a specified threshold. We formulate the SEVRP-T as a two-stage stochastic mixed-integer second-order cone model, where the first stage determines the sequences of customers to be visited, and the second stage incorporates charging activities. The objective is
to minimize the expected total duration of the routes, composed by travel times and recharging operations. To cope with the computational complexity of the model, we propose a heuristic based on an Iterated Local Search (ILS) procedure coupled with a Set Partitioning problem. To further speed up the heuristic, we develop two lower bounds on the corresponding first-stage customer sequences. Furthermore, to handle a large number of energy consumption scenarios, we employ
a scenario reduction technique. Extensive computational experiments are conducted to validate
the effectiveness of the proposed solution strategy and to assess the importance of considering the stochastic nature of the energy consumption. The research presented in this paper contributes to the growing body of literature on EVRP and provides insights into managing the operational deployment of EVs in logistics activities under uncertainty
Start-up of a Test Rig for Organic Vapors
No full textThe Test Rig for Organic Vapors (TROVA) represents a novel facility built with
the purpose of providing experimental data on the typical expansion
ows taking
place within organic Rankine cycle (ORC) turbines. The facility has been built at
the Fluid-dynamics of Turbomachines Laboratory of Politecnico di Milano (Italy), in
collaboration with Turboden s.r.l. [1]. It consists in a blow down facility in which an
organic vapour is expanded from a high-pressure reservoir, kept at controlled supeheated
or supercritical conditions, into a low-pressure reservoir, where the vapour is condensed
and pumped back to the high pressure reservoir. Expansion from subsonic to supersonic
speeds occurs through a converging-diverging Laval nozzle, which has been chosen
as the test section for initial tests. The test rig can also accommodate liner blade
cascade, as it is required by later experiments, and can operate with dierent working
uids of interest for ORC applications. Within the test section the
ow eld can be
characterized by independent measurements of pressure, temperature, and velocity,
allowing also to verify the consistency of thermodynamic models currently employed to
predict the typical real-gas behaviour of ORC turbine
ows. The present paper describes
the commissioning of the TROVA, illustrates the test section setup and the adopted
measurement techniques, and nally presents the early tests
A Robust Nonlinear Support Vector Machine Approach for Vehicles Smog Rating Classification
No full textNowadays all new vehicles are labelled in terms of their emissions thanks to ad hoc legislation. However, from a practical perspective, it is difficult to rank all of them. This paper considers the problem of classifying vehicles in terms of smog rating emissions by adopting a Machine Learning technique. Specifically, a new Support Vector Machine approach is considered, designed for nonlinear separating decision boundaries. To protect the model against uncertainty arising in the measurement procedure, a robust optimization model with spherical uncertainty sets is formulated. Numerical results are performed on both synthetic and real-world datasets, showing the good performance of the proposed formulation
A rolling horizon heuristic approach for a multi-stage stochastic waste collection problem
Full text linkIn this paper we present a multi-stage stochastic optimization model to solve an inventory routing problem for the collection of recyclable municipal waste. The objective is the maximization of the total expected profit of the waste collection company. The decisions are related to the selection of the bins to be visited and
the corresponding routing plan in a predefined time horizon. Stochasticity in waste accumulation is modeled
through scenario trees generated via conditional density estimation and dynamic stochastic approximation techniques. The proposed formulation is solved through a rolling horizon approach, providing a rigorous worst-case analysis on its performance. Extensive computational experiments are carried out on small- and
large-sized instances based on real data provided by a large Portuguese waste collection company. The impact
of stochasticity on waste generation is examined through stochastic measures, showing the importance of adopting a stochastic model over a deterministic formulation when addressing a waste collection problem. The performance of the rolling horizon approach is evaluated, demonstrating that this heuristic provides cost-effective solutions in short computational time. Managerial insights related to different geographical configurations of the instances and varying levels of uncertainty are finally discussed
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