The Robust Uncapacitated Lot Sizing Model with Uncertainty Range

We study robust versions of the uncapacitated lot sizing problem, where the demand is subject to uncertainty. The robust models are guided by three parameters, namely, the total scaled uncertainty budget, the minimum number of periods in which one would like the demand to be protected against uncertainty, and the minimum scaled protection level per … Read more

Visualizing proportions and dissimilarities by Space-filling maps: a Large Neighborhood Search approach

In this paper we address the problem of visualizing a set of individuals, which have attached a statistical value given as a proportion, and a dissimilarity measure. Each individual is represented as a region within the unit square, in such a way that the area of the regions represent the proportions and the distances between … Read more

A Multi-Objective approach to visualize proportions and similarities between individuals by rectangular maps

In this paper we address the problem of visualizing the proportions and the similarities attached to a set of individuals. We represent this information using a rectangular map, i.e., a subdivision of a rectangle into rectangular portions so that each portion is associated with one individual, their areas reflect the proportions, and the closeness between … Read more

Visualizing data as objects by DC (difference of convex) optimization

In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective is the difference of two convex functions (DC). Suitable DC … Read more

An SDP approach for multiperiod mixed 0–1 linear programming models with stochastic dominance constraints for risk management

In this paper we consider multiperiod mixed 0–1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multistage case and includes both first-order and second-order constraints. We propose a stochastic … Read more

Clustering Categories in Support Vector Machines

Support Vector Machines (SVM) is the state-of-the-art in Supervised Classification. In this paper the Cluster Support Vector Machines (CLSVM) methodology is proposed with the aim to reduce the complexity of the SVM classifier in the presence of categorical features. The CLSVM methodology lets categories cluster around their peers and builds an SVM classifier using the … Read more

Polynomial time algorithms for the Minimax Regret Uncapacitated Lot Sizing Model

We study the Minimax Regret Uncapacitated Lot Sizing (MRULS) model, where the production cost function and the demand are subject to uncertainty. We propose a polynomial time algorithm which solves the MRULS model in O(n^6) time. We improve this running time to O(n^5) when only the demand is uncertain, and to O(n^4) when only the … Read more

Strongly Agree or Strongly Disagree?: Rating Features in Support Vector Machines

In linear classifiers, such as the Support Vector Machine (SVM), a score is associated with each feature and objects are assigned to classes based on the linear combination of the scores and the values of the features. Inspired by discrete psychometric scales, which measure the extent to which a factor is in agreement with a … Read more

Variable Neighborhood Search for parameter tuning in Support Vector Machines

As in most Data Mining procedures, how to tune the parameters of a Support Vector Machine (SVM) is a critical, though not sufficiently explored, issue. The default approach is a grid search in the parameter space, which becomes prohibitively time-consuming even when just a few parameters are to be tuned. For this reason, for models … Read more

Matheuristics for $\PsihBcLearning

Recently, the so-called $\psi$-learning approach, the Support Vector Machine (SVM) classifier obtained with the ramp loss, has attracted attention from the computational point of view. A Mixed Integer Nonlinear Programming (MINLP) formulation has been proposed for $\psi$-learning, but solving this MINLP formulation to optimality is only possible for datasets of small size. For datasets of … Read more