## 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

Supervisors

**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.

Practitioners are usually able to formulate such models in their "natural" form; however, solving them often

requires finding an appropriate reformulation to reveal structures in the model which make it possible to

apply efficient, specialized approaches. The search for the "best" formulation of a given problem, the one which

allows the application of the solution algorithm that best exploits the available computational resources, is currently

a painstaking process which requires considerable work by highly skilled personnel. Experts in solution algorithms are

required for figuring out which (formulation, algorithm) pair is better used, considering issues like the appropriate

selection of the several obscure algorithmic parameters that each solution methods has. This process is only going to

get more complex, as current trends in computer technology dictate the necessity to develop complex parallel approaches

capable of harnessing the power of thousands of processing units, thereby adding another layer of complexity in the form

of the choice of the appropriate (parallel) architecture. All this renders the use of mathematical models exceedingly

costly and difficult for many potentially fruitful applications. The \name{} environment, proposed in this Thesis, aims

at devising a software system for automatizing the search for the best combination of (re)formulation, solution

algorithm and its parameters (comprised the computational architecture), until now a firm domain of human intervention,

to help practitioners bridging the gap between mathematical models cast in their natural form and existing solver

systems. I-DARE deals with deep and challenging issues, both from the theoretical and from an implementative viewpoint:

1) the development of a language that can be effectively used to formulate large-scale structured mathematical

models and the reformulation rules that allow to transform a formulation into a different one; 2) a core subsystem

capable of automatically reformulating the models and searching in the space of (formulations, algorithms,

configurations) able to "the best" formulation of a given problem; 3) the design of a general interface for numerical

solvers that is capable of accommodate and exploit structure information.

To achieve these goals I-DARE will propose a sound and articulated integration of different programming paradigms and

techniques like, classic Object-Oriented programing and Artificial Intelligence (Declarative Programming, Frame-Logic,

Higher-Order Logic, Machine Learning). By tackling these challenges, I-DARE may have profound, lasting and disruptive

effects on many facets of the development and deployment of mathematical models and the corresponding solution

algorithms.

Practitioners are usually able to formulate such models in their "natural" form; however, solving them often

requires finding an appropriate reformulation to reveal structures in the model which make it possible to

apply efficient, specialized approaches. The search for the "best" formulation of a given problem, the one which

allows the application of the solution algorithm that best exploits the available computational resources, is currently

a painstaking process which requires considerable work by highly skilled personnel. Experts in solution algorithms are

required for figuring out which (formulation, algorithm) pair is better used, considering issues like the appropriate

selection of the several obscure algorithmic parameters that each solution methods has. This process is only going to

get more complex, as current trends in computer technology dictate the necessity to develop complex parallel approaches

capable of harnessing the power of thousands of processing units, thereby adding another layer of complexity in the form

of the choice of the appropriate (parallel) architecture. All this renders the use of mathematical models exceedingly

costly and difficult for many potentially fruitful applications. The \name{} environment, proposed in this Thesis, aims

at devising a software system for automatizing the search for the best combination of (re)formulation, solution

algorithm and its parameters (comprised the computational architecture), until now a firm domain of human intervention,

to help practitioners bridging the gap between mathematical models cast in their natural form and existing solver

systems. I-DARE deals with deep and challenging issues, both from the theoretical and from an implementative viewpoint:

1) the development of a language that can be effectively used to formulate large-scale structured mathematical

models and the reformulation rules that allow to transform a formulation into a different one; 2) a core subsystem

capable of automatically reformulating the models and searching in the space of (formulations, algorithms,

configurations) able to "the best" formulation of a given problem; 3) the design of a general interface for numerical

solvers that is capable of accommodate and exploit structure information.

To achieve these goals I-DARE will propose a sound and articulated integration of different programming paradigms and

techniques like, classic Object-Oriented programing and Artificial Intelligence (Declarative Programming, Frame-Logic,

Higher-Order Logic, Machine Learning). By tackling these challenges, I-DARE may have profound, lasting and disruptive

effects on many facets of the development and deployment of mathematical models and the corresponding solution

algorithms.

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