Algoritmi esatti per il Job Shop Scheduling: approcci Mathematical Programming

In questa tesi ci occuperemo di fornire un modello MIP di base e di alcune sue varianti, realizzate allo scopo di comprenderne il comportamento ed eventualmente migliorarne l’efficienza. Le diverse varianti sono state costruite agendo in particolar modo sulla definizione di alcuni vincoli, oppure sui bound delle variabili, oppure ancora nell’obbligare il risolutore a focalizzarsi su determinate decisioni o specifiche variabili. Sono stati testati alcuni dei problemi tipici presenti in letteratura e i diversi risultati sono stati opportunamente valutati e confrontati. Tra i riferimenti per tale confronto sono stati considerati anche i risultati ottenibili tramite un modello Constraint Programming, che notoriamente produce risultati apprezzabili in ambito di schedulazione. Un ulteriore scopo della tesi è, infatti, comparare i due approcci Mathematical Programming e Constraint Programming, identificandone quindi i pregi e gli svantaggi e provandone la trasferibilità al modello raffrontato.

Implementation of a non ground meta interpreter for defeasible logic

Human reasoning is a fascinating and complex cognitive process that can be applied in different research areas such as philosophy, psychology, laws and financial. Unfortunately, developing supporting software (to those different areas) able to cope such as complex reasoning it’s difficult and requires a suitable logic abstract formalism. In this thesis we aim to develop a program, that has the job to evaluate a theory (a set of rules) w.r.t. a Goal, and provide some results such as “The Goal is derivable from the KB5 (of the theory)”. In order to achieve this goal we need to analyse different logics and choose the one that best meets our needs. In logic, usually, we try to determine if a given conclusion is logically implied by a set of assumptions T (theory). However, when we deal with programming logic we need an efficient algorithm in order to find such implications. In this work we use a logic rather similar to human logic. Indeed, human reasoning requires an extension of the first order logic able to reach a conclusion depending on not definitely true6 premises belonging to a incomplete set of knowledge. Thus, we implemented a defeasible logic7 framework able to manipulate defeasible rules. Defeasible logic is a non-monotonic logic designed for efficient defeasible reasoning by Nute (see Chapter 2). Those kind of applications are useful in laws area especially if they offer an implementation of an argumentation framework that provides a formal modelling of game. Roughly speaking, let the theory is the set of laws, a keyclaim is the conclusion that one of the party wants to prove (and the other one wants to defeat) and adding dynamic assertion of rules, namely, facts putted forward by the parties, then, we can play an argumentative challenge between two players and decide if the conclusion is provable or not depending on the different strategies performed by the players. Implementing a game model requires one more meta-interpreter able to evaluate the defeasible logic framework; indeed, according to Göedel theorem (see on page 127), we cannot evaluate the meaning of a language using the tools provided by the language itself, but we need a meta-language able to manipulate the object language8. Thus, rather than a simple meta-interpreter, we propose a Meta-level containing different Meta-evaluators. The former has been explained above, the second one is needed to perform the game model, and the last one will be used to change game execution and tree derivation strategies.

Meta-learning for informed model searches in Automated Machine Learning

Day by day, machine learning is changing our lives in ways we could not have imagined just 5 years ago. ML expertise is more and more requested and needed, though just a limited number of ML engineers are available on the job market, and their knowledge is always limited by an inherent characteristic of theirs: they are humans. This thesis explores the possibilities offered by meta-learning, a new field in ML that takes learning a level higher: models are trained on other models' training data, starting from features of the dataset they were trained on, inference times, obtained performances, to try to understand the relationship between a good model and the way it was obtained. The so-called metamodel was trained on data collected by OpenML, the largest ML metadata platform that's publicly available today. Datasets were analyzed to obtain meta-features that describe them, which were then tied to model performances in a regression task. The obtained metamodel predicts the expected performances of a given model type (e.g., a random forest) on a given ML task (e.g., classification on the UCI census dataset). This research was then integrated into a custom-made AutoML framework, to show how meta-learning is not an end in itself, but it can be used to further progress our ML research. Encoding ML engineering expertise in a model allows better, faster, and more impactful ML applications across the whole world, while reducing the cost that is inevitably tied to human engineers.