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In this paper, we deal with semi-supervised Minimum Sum-of-Squares Clustering (MSSC) problems where background knowledge is given in the form of instance-level constraints. In particular, we take into account "must-link" and "cannot-link" constraints, each of which indicates if two dataset points should be associated to the same or to a different cluster. The presence of such constraints makes the problem at least as hard as its unsupervised version: it is no more true that each point is associated to its nearest cluster center, thus requiring some modifications in crucial operations, such as the assignment step. In this scenario, we propose a novel memetic strategy based on the Differential Evolution paradigm, directly extending a state-of-the-art framework recently proposed in the unsupervised clustering literature. As far as we know, our contribution represents the first attempt to define a memetic methodology designed to generate a (hopefully) optimal feasible solution for the semi-supervised MSSC problem. The proposal is compared with some state-of-the-art algorithms from the literature on a set of well-known datasets, highlighting its effectiveness and efficiency in finding good quality clustering solutions.

In this paper, we deal with batch Bayesian Optimization (Bayes-Opt) problems over a box and we propose a novel bi-objective optimization (BOO) acquisition strategy to sample points where to evaluate the objective function. The BOO problem involves the Gaussian Process posterior mean and variance functions, which, in most of the acquisition strategies from the literature, are generally used in combination, frequently through scalarization. However, such scalarization could compromise the Bayes-Opt process performance, as getting the desired trade-off between exploration and exploitation is not trivial in most cases. We instead aim to reconstruct the Pareto front of the BOO problem based on optimizing both the posterior mean as well as the variance, thus generating multiple trade-offs without any a priori knowledge. The reconstruction is performed through the Non-dominated Sorting Memetic Algorithm (NSMA), recently proposed in the literature and proved to be effective in solving hard MOO problems. Finally, we present two clustering approaches, each of them operating on a different space, to select potentially optimal points from the Pareto front. We compare our methodology with well-known acquisition strategies from the literature, showing its effectiveness on a wide set of experiments.

In this paper we consider multi-objective optimization problems over a box. The problem is very relevant and several computational approaches have been proposed in the literature. They broadly fall into two main classes: evolutionary methods, which are usually very good at exploring the feasible region and retrieving good solutions even in the nonconvex case, and descent methods, which excel in efficiently approximating good quality solutions. In this paper, first we confirm, through numerical experiments, the advantages and disadvantages of these approaches. Then we propose a new method which combines the good features of both. The resulting algorithm, which we call Non-dominated Sorting Memetic Algorithm (NSMA), besides enjoying interesting theoretical properties, excels in all of the numerical tests we performed on several, widely employed, test functions., Comment: 30 pages, 8 figures

In this paper we propose a new optimization model for maximum likelihood estimation of causal and invertible ARMA models. Through a set of numerical experiments we show how our proposed model outperforms, both in terms of quality of the fitted model as well as in the computational time, the classical estimation procedure based on Jones reparametrization. We also propose a regularization term in the model and we show how this addition improves the out of sample quality of the fitted model. This improvement is achieved thanks to an increased penalty on models close to the non causality or non invertibility boundary., Comment: 11 pages