Application-oriented Mixed Integer Non-Linear Programming

In the most recent years there is a renovate interest for Mixed Integer Non-Linear Programming (MINLP) problems. This can be explained for different reasons: (i) the performance of solvers handling non-linear constraints was largely improved; (ii) the awareness that most of the applications from the real-world can be modeled as an MINLP problem; (iii) the challenging nature of this very general class of problems. It is well-known that MINLP problems are NP-hard because they are the generalization of MILP problems, which are NP-hard themselves. However, MINLPs are, in general, also hard to solve in practice. We address to non-convex MINLPs, i.e. having non-convex continuous relaxations: the presence of non-convexities in the model makes these problems usually even harder to solve. The aim of this Ph.D. thesis is to give a flavor of different possible approaches that one can study to attack MINLP problems with non-convexities, with a special attention to real-world problems. In Part 1 of the thesis we introduce the problem and present three special cases of general MINLPs and the most common methods used to solve them. These techniques play a fundamental role in the resolution of general MINLP problems. Then we describe algorithms addressing general MINLPs. Parts 2 and 3 contain the main contributions of the Ph.D. thesis. In particular, in Part 2 four different methods aimed at solving different classes of MINLP problems are presented. Part 3 of the thesis is devoted to real-world applications: two different problems and approaches to MINLPs are presented, namely Scheduling and Unit Commitment for Hydro-Plants and Water Network Design problems. The results show that each of these different methods has advantages and disadvantages. Thus, typically the method to be adopted to solve a real-world problem should be tailored on the characteristics, structure and size of the problem. Part 4 of the thesis consists of a brief review on tools commonly used for general MINLP problems, constituted an integral part of the development of this Ph.D. thesis (especially the use and development of open-source software). We present the main characteristics of solvers for each special case of MINLP.

Aging of nuclear power plant cables: in search of non-destructive diagnostic quantities

The safety systems of nuclear power plants rely on low-voltage power, instrumentation and control cables. Inside the containment area, cables operate in harsh environments, characterized by relatively high temperature and gamma-irradiation. As these cables are related to fundamental safety systems, they must be able to withstand unexpected accident conditions and, therefore, their condition assessment is of utmost importance as plants age and lifetime extensions are required. Nowadays, the integrity and functionality of these cables are monitored mainly through destructive test which requires specific laboratory. The investigation of electrical aging markers which can provide information about the state of the cable by non-destructive testing methods would improve significantly the present diagnostic techniques. This work has been made within the framework of the ADVANCE (Aging Diagnostic and Prognostics of Low-Voltage I\&C Cables) project, a FP7 European program. This Ph.D. thesis aims at studying the impact of aging on cable electrical parameters, in order to understand the evolution of the electrical properties associated with cable degradation. The identification of suitable aging markers requires the comparison of the electrical property variation with the physical/chemical degradation mechanisms of polymers for different insulating materials and compositions. The feasibility of non-destructive electrical condition monitoring techniques as potential substitutes for destructive methods will be finally discussed studying the correlation between electrical and mechanical properties. In this work, the electrical properties of cable insulators are monitored and characterized mainly by dielectric spectroscopy, polarization/depolarization current analysis and space charge distribution. Among these techniques, dielectric spectroscopy showed the most promising results; by means of dielectric spectroscopy it is possible to identify the frequency range where the properties are more sensitive to aging. In particular, the imaginary part of permittivity at high frequency, which is related to oxidation, has been identified as the most suitable aging marker based on electrical quantities.

High sensitivity analysis of BRAF mutations in neoplastic and non-neoplastic thyroid lesions

The clonal distribution of BRAFV600E in papillary thyroid carcinoma (PTC) has been recently debated. No information is currently available about precursor lesions of PTCs. My first aim was to establish whether the BRAFV600E mutation occurs as a subclonal event in PTCs. My second aim was to screen BRAF mutations in histologically benign tissue of cases with BRAFV600E or BRAFwt PTCs in order to identify putative precursor lesions of PTCs. Highly sensitive semi-quantitative methods were used: Allele Specific LNA quantitative PCR (ASLNAqPCR) and 454 Next-Generation Sequencing (NGS). For the first aim 155 consecutive formalin-fixed and paraffin-embedded (FFPE) specimens of PTCs were analyzed. The percentage of mutated cells obtained was normalized to the estimated number of neoplastic cells. Three groups of tumors were identified: a first had a percentage of BRAF mutated neoplastic cells > 80%; a second group showed a number of BRAF mutated neoplastic cells < 30%; a third group had a distribution of BRAFV600E between 30-80%. The large presence of BRAFV600E mutated neoplastic cell sub-populations suggests that BRAFV600E may be acquired early during tumorigenesis: therefore, BRAFV600E can be heterogeneously distributed in PTC. For the second aim, two groups were studied: one consisted of 20 cases with BRAFV600E mutated PTC, the other of 9 BRAFwt PTCs. Seventy-five and 23 histologically benign FFPE thyroid specimens were analyzed from the BRAFV600E mutated and BRAFwt PTC groups, respectively. The screening of BRAF mutations identified BRAFV600E in “atypical” cell foci from both groups of patients. “Unusual” BRAF substitutions were observed in histologically benign thyroid associated with BRAFV600E PTCs. These mutations were very uncommon in the group with BRAFwt PTCs and in BRAFV600E PTCs. Therefore, lesions carrying BRAF mutations may represent “abortive” attempts at cancer development: only BRAFV600E boosts neoplastic transformation to PTC. BRAFV600E mutated “atypical foci” may represent precursor lesions of BRAFV600E mutated PTCs.