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.

Costrutti ed Applicazioni di Programmazione Generica in Linguaggi Object-Oriented

Generic programming is likely to become a new challenge for a critical mass of developers. Therefore, it is crucial to refine the support for generic programming in mainstream Object-Oriented languages — both at the design and at the implementation level — as well as to suggest novel ways to exploit the additional degree of expressiveness made available by genericity. This study is meant to provide a contribution towards bringing Java genericity to a more mature stage with respect to mainstream programming practice, by increasing the effectiveness of its implementation, and by revealing its full expressive power in real world scenario. With respect to the current research setting, the main contribution of the thesis is twofold. First, we propose a revised implementation for Java generics that greatly increases the expressiveness of the Java platform by adding reification support for generic types. Secondly, we show how Java genericity can be leveraged in a real world case-study in the context of the multi-paradigm language integration. Several approaches have been proposed in order to overcome the lack of reification of generic types in the Java programming language. Existing approaches tackle the problem of reification of generic types by defining new translation techniques which would allow for a runtime representation of generics and wildcards. Unfortunately most approaches suffer from several problems: heterogeneous translations are known to be problematic when considering reification of generic methods and wildcards. On the other hand, more sophisticated techniques requiring changes in the Java runtime, supports reified generics through a true language extension (where clauses) so that backward compatibility is compromised. In this thesis we develop a sophisticated type-passing technique for addressing the problem of reification of generic types in the Java programming language; this approach — first pioneered by the so called EGO translator — is here turned into a full-blown solution which reifies generic types inside the Java Virtual Machine (JVM) itself, thus overcoming both performance penalties and compatibility issues of the original EGO translator. Java-Prolog integration Integrating Object-Oriented and declarative programming has been the subject of several researches and corresponding technologies. Such proposals come in two flavours, either attempting at joining the two paradigms, or simply providing an interface library for accessing Prolog declarative features from a mainstream Object-Oriented languages such as Java. Both solutions have however drawbacks: in the case of hybrid languages featuring both Object-Oriented and logic traits, such resulting language is typically too complex, thus making mainstream application development an harder task; in the case of library-based integration approaches there is no true language integration, and some “boilerplate code” has to be implemented to fix the paradigm mismatch. In this thesis we develop a framework called PatJ which promotes seamless exploitation of Prolog programming in Java. A sophisticated usage of generics/wildcards allows to define a precise mapping between Object-Oriented and declarative features. PatJ defines a hierarchy of classes where the bidirectional semantics of Prolog terms is modelled directly at the level of the Java generic type-system.