Browsing by Author "Gaudioso, Manlio"

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Classification of medical images: instance space optimization models for Multiple Instance Learning
(Università della Calabria, 2020-05-07) Vocaturo, Eugenio; Fuduli, Antonio; Gaudioso, Manlio
Feature Selection in Classification by means of Optimization and Multi-Objective Optimization
(Università della Calabria, 2023-05-10) Pirouz, Behzad; Fortino, Giancarlo; Gaudioso, Manlio
The thesis is in the area of mathematical optimization with application to Machine Learning. The focus is on Feature Selection (FS) in the framework of binary classification via Support Vector Machine paradigm. We concentrate on the use of sparse optimization techniques, which are widely considered as the election tool for tackling FS. We study the problem both in terms of single and multi-objective optimization. We propose first a novel Mixed-Integer Nonlinear Programming (MINLP) model for sparse optimization based on the polyhedral k-norm. We introduce a new way to take into account the k-norm for sparse optimization by setting a model based on fractional programming (FP). Then we address the continuous relaxation of the problem, which is reformulated via a DC (Difference of Convex) decomposition. On the other hand, designing supervised learning systems, in general, is a multi-objective problem. It requires finding appropriate trade-offs between several objectives, for example, between the number of misclassified training data (minimizing the squared error) and the number of nonzero elements separating the hyperplane (minimizing the number of nonzero elements). When we deal with multi-objective optimization problems, the optimization problem has yet to have a single solution that represents the best solution for all objectives simultaneously. Consequently, there is not a single solution but a set of solutions, known as the Pareto-optimal solutions. We overview the SVM models and the related Feature Selection in terms of multi-objective optimization. Our multi-objective approach considers two simultaneous objectives: minimizing the squared error and minimizing the number of nonzero elements of the normal vector of the separator hyperplane. In this thesis, we propose a multi-objective model for sparse optimization. Our primary purpose is to demonstrate the advantages of considering SVM models as multi-objective optimization problems. In multi-objective cases, we can obtain a set of Pareto optimal solutions instead of one in single-objective cases. Therefore, our main contribution in this thesis is of two levels: first, we propose a new model for sparse optimization based on the polyhedral k-norm for SVM classification, and second, use multi-objective optimization to consider this new model. The results of several numerical experiments on some classification datasets are reported. We used all the datasets for single-objective and multi-objective models.
Nonsmooth convex optimizationRisorsa elettronica
(2014-05-27) Gorgone, Enrico; Grandinetti, Lucio; Gaudioso, Manlio; Monaco, Maria Flavia
Omega our multi ethnic genetic algorithm
(2014-03-13) Cerrone, Carmine; Grandinetti, Lucio; Gaudioso, Manlio
Combinatorial optimization is a branch of optimization. Its domain is optimization problems where the set of feasible solutions is discrete or can be reduced to a discrete one, the goal being that of nding the best possible solution. Two fundamental aims in optimization are nding algorithms characterized by both provably good run times and provably good or even optimal solution quality. When no method to nd an optimal solution, under the given constraints (of time, space etc.) is available, heuristic approaches are typically used. A metaheuristic is a heuristic method for solving a very general class of computational problems by combining user- given black-box procedures, usually heuristics themselves, in the hope of obtaining a more e cient or more robust procedure. The genetic algorithms are one of the best metaheuristic approaches to deal with optimization problems. They are a population- based search technique that uses an ever changing neighborhood structure, based on population evolution and genetic operators, to take into account di erent points in the search space. The core of the thesis is to introduce a variant of the classic GA approach, which is referred to as OMEGA (Multi Ethnic Genetic Algorithm). The main feature of this new metaheuristic is the presence of di erent populations that evolve simultaneously, and exchange genetic material with each other. We focus our attention on four di erent optimization problems de ned on graphs. Each one is iii iv proved to be NP-HARD. We analyze each problem from di erent points of view, and for each one we de ne and implement both a genetic algorithm and our OMEGA.