Abstract
This paper is an extension of work originally presented at the 2nd International Conference of the Portuguese Society for Engineering Education and aims to describe an interdisciplinarity teaching experiment involving three subjects of the scientific area of Mathematics and a fourth one in the area of Management. Using only one project, the students developed skills, in an integrated way, in the fields of the subjects involved. The structure of the project is described in detail. It is shown how the knowledge obtained in the different subjects is needed and how it connects together to answer the proposed challenges. We report the progress of the students' work, the main difficulties and the skills developed during this process. We conclude with a reflection on the main problems and gains that may arise in similar projects.

Abstract
In this work, we describe an interdisciplinary teaching experiment involving three subjects of the scientific area of Mathematics and a fourth one in the area of Management. Using only one project, the students developed skills, in an integrated way, in the fields of the subjects involved. The structure of the project is described in detail. It is shown how the knowledge obtained in the different subjects is needed and how it connects together to answer the proposed challenges. We report the progress of the students' work, the main difficulties and the skills developed during this process. We conclude with a reflection on the main problems and gains that may arise in projects of this kind.

Abstract
In this work, we introduce in the first part new developments in Principal Component Analysis (PCA) and in the second part a new method to select variables (genes in our application). Our focus is on problems where the values taken by each variable do not all have the same importance and where the data may be contaminated with noise and contain outliers, as is the case with microarray data. The usual PCA is not appropriate to deal with this kind of problems. In this context, we propose the use of a new correlation coefficient as an alternative to Pearson's. This leads to a so-called weighted PCA (WPCA). In order to illustrate the features of our WPCA and compare it with the usual PCA, we consider the problem of analyzing gene expression data sets. In the second part of this work, we propose a new PCA-based algorithm to iteratively select the most important genes in a microarray data set. We show that this algorithm produces better results when our WPCA is used instead of the usual PCA. Furthermore, by using Support Vector Machines, we show that it can compete with the Significance Analysis of Microarrays algorithm.

Abstract
The Unit Commitment (UC) problem is a wellknown combinatorial optimization problem arising in operations planning of power systems. It is typically formulated as nonlinear mixed-integer programming problem and has been solved in the literature by a huge variety of optimization methods, ranging from exact methods (such as dynamic programming, branch-and-bound) to heuristic methods (genetic algorithms, simulated annealing, particle swarm). Here, we start by formulating the UC problem as a mixed-integer optimal control problem, with both binary-valued control variables and real-valued control variables. Then, we use a variable time transformation method to convert the problem into an optimal control problem with only real-valued controls. Finally, this problem is transcribed into a finite-dimensional nonlinear programming problem to be solved using an optimization solver.

Abstract
A Biased Random Key Genetic Algorithm (BRKGA) is proposed to find solutions for the unit commitment problem. In this problem, one wishes to schedule energy production on a given set of thermal generation units in order to meet energy demands at minimum cost, while satisfying a set of technological and spinning reserve constraints. In the BRKGA, solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0, 1]. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as in the crossover strategy. Tests have been performed on benchmark large-scale power systems of up 100 units for a 24 hours period. The results obtained have shown the proposed methodology to be an effective and efficient tool for finding solutions to large-scale unit commitment problems. Furthermore, form the comparisons made it can be concluded that the results produced improve upon the best known solutions.

Abstract
A Biased Random Key Genetic Algorithm (BRKGA) is proposed to find solutions for the unit commitment problem. In this problem, one wishes to schedule energy production on a given set of thermal generation units in order to meet energy demands at minimum cost, while satisfying a set of technological and spinning reserve constraints. In the BRKGA, solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0, 1]. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as in the crossover strategy. Tests have been performed on benchmark large-scale power systems of up to 100 units for a 24 hours period. The results obtained have shown the proposed methodology to be an effective and efficient tool for finding solutions to large-scale unit commitment problems. Furthermore, from the comparisons made it can be concluded that the results produced improve upon some of the best known solutions.