Linear programming is a very well known and deeply applied field of optimization theory. One of its most famous and used algorithms is the so called Simplex algorithm, independently proposed by Kantorovič and Dantzig, between the end of the 30s and the end of the 40s. Even if extremely powerful, the Simplex algorithm suffers of one initialization issue: its starting point must be a feasible basic solution of the problem to solve. To overcome it, two approaches may be used: the two-phases method and the Big-M method, both presenting positive and negative aspects. In this work we aim to propose a non-Archimedean and non-parametric variant of the Big-M method, able to overcome the drawbacks of its classical counterpart (mainly, the difficulty in setting the right value for the constant M). We realized such extension by means of the novel computational methodology proposed by Sergeyev, known as Grossone Methodology. We have validated the new algorithm by testing it on three linear programming problems.

This paper presents a method, based on classification techniques, for automatic detection and diagnosis of defects of rolling element bearings. The experimental data set consists of vibration signals recorded by four accelerometers on a mechanical device including rolling element bearings: the signals were collected both with all faultless bearings and after substituting one faultless bearing with an artificially damaged one. Four defects and, for one of them, three severity levels are considered. Classification accuracy higher than 99% was achieved in all the experiments performed on the vibration signals represented in the frequency domain, thus proving the high sensitivity of our method to different types of defects and to different degrees of fault severity. The degree of robustness of our method to noise is also assessed by analyzing how the classification performance varies with the signal-to-noise ratio and using statistical classifiers and neural networks.

Numerous problems arising in engineering applications can have several objectives to be satisfied. An important class of problems of this kind is lexicographic multi-objective problems where the first objective is incomparably more important than the second one which, in its turn, is incomparably more important than the third one, etc. In this paper, Lexicographic Multi-Objective Linear Programming (LMOLP) problems are considered. To tackle them, traditional approaches either require solution of a series of linear programming problems or apply a scalarization of weighted multiple objectives into a single-objective function. The latter approach requires finding a set of weights that guarantees the equivalence of the original problem and the single-objective one and the search of correct weights can be very time consuming. In this work a new approach for solving LMOLP problems using a recently introduced computational methodology allowing one to work numerically with infinities and infinitesimals is proposed. It is shown that a smart application of infinitesimal weights allows one to construct a single-objective problem avoiding the necessity to determine finite weights. The equivalence between the original multi-objective problem and the new single-objective one is proved. A simplex-based algorithm working with finite and infinitesimal numbers is proposed, implemented, and discussed. Results of some numerical experiments are provided

This paper presents a flexible approach to forecasting of energy production in solar photovoltaic (PV) installations, using time series analysis and neural networks. Our goal is to develop a one day-ahead forecasting model based on an artificial neural network with tapped delay lines. Despite some methods already exist for energy forecasting problems, the main novelty of our approach is the proposal of a tool for the technician of a PV installation to correctly configure the forecasting model according to the particular installation characteristics. The correct configuration takes into account the number of hidden neurons, the number of delay elements, and the training window width, i.e., the appropriate number of days, before the predicted day, employed for the training. The irradiation along with the sampling hour are used as input variables to predict the daily accumulated energy with a percentage error less than 5%.