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Digital archive of theses discussed at the University of Pisa


Thesis etd-10152010-094014

Thesis type
Tesi di dottorato di ricerca
Thesis title
Artificial Intelligence Techniques for Automatic Reformulation and Solution of Structured Mathematical Models
Academic discipline
Course of study
tutor Frangioni, Antonio
  • frame logic
  • modeling
  • optimization
  • reformulation
Graduation session start date
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