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Tesi etd-10152010-094014


Thesis type
Tesi di dottorato di ricerca
Author
PEREZ SANCHEZ, LUIS
URN
etd-10152010-094014
Title
Artificial Intelligence Techniques for Automatic Reformulation and Solution of Structured Mathematical Models
Settore scientifico disciplinare
INF/01
Corso di studi
INFORMATICA
Commissione
tutor Frangioni, Antonio
Parole chiave
  • optimization
  • modeling
  • frame logic
  • reformulation
Data inizio appello
17/12/2010;
Consultabilità
completa
Riassunto analitico
Complex, hierarchical, multi-scale industrial and natural systems generate increasingly large mathematical models.<br>Practitioners are usually able to formulate such models in their &#34;natural&#34; form; however, solving them often<br>requires finding an appropriate reformulation to reveal structures in the model which make it possible to<br>apply efficient, specialized approaches. The search for the &#34;best&#34; formulation of a given problem, the one which<br>allows the application of the solution algorithm that best exploits the available computational resources, is currently<br>a painstaking process which requires considerable work by highly skilled personnel. Experts in solution algorithms are<br>required for figuring out which (formulation, algorithm) pair is better used, considering issues like the appropriate<br>selection of the several obscure algorithmic parameters that each solution methods has. This process is only going to<br>get more complex, as current trends in computer technology dictate the necessity to develop complex parallel approaches<br>capable of harnessing the power of thousands of processing units, thereby adding another layer of complexity in the form<br>of the choice of the appropriate (parallel) architecture. All this renders the use of mathematical models exceedingly<br>costly and difficult for many potentially fruitful applications. The \name{} environment, proposed in this Thesis, aims<br>at devising a software system for automatizing the search for the best combination of (re)formulation, solution<br>algorithm and its parameters (comprised the computational architecture), until now a firm domain of human intervention,<br>to help practitioners bridging the gap between mathematical models cast in their natural form and existing solver<br>systems. I-DARE deals with deep and challenging issues, both from the theoretical and from an implementative viewpoint:<br>1) the development of a language that can be effectively used to formulate large-scale structured mathematical<br>models and the reformulation rules that allow to transform a formulation into a different one; 2) a core subsystem<br>capable of automatically reformulating the models and searching in the space of (formulations, algorithms,<br>configurations) able to &#34;the best&#34; formulation of a given problem; 3) the design of a general interface for numerical<br>solvers that is capable of accommodate and exploit structure information. <br>To achieve these goals I-DARE will propose a sound and articulated integration of different programming paradigms and<br>techniques like, classic Object-Oriented programing and Artificial Intelligence (Declarative Programming, Frame-Logic,<br>Higher-Order Logic, Machine Learning). By tackling these challenges, I-DARE may have profound, lasting and disruptive<br>effects on many facets of the development and deployment of mathematical models and the corresponding solution<br>algorithms.
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