## 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 "natural" 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 "best" 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 "the best" 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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