• PhD Student:
  • Nebras Gharbi
  • Funding : OSEO
  • PhD defended on :
  • Dec 4, 2015 • Salle des thèses

Constraint Programming (CP) is a powerful paradigm used for modelling and solving combinatorial constraint problems that relies on a wide range of techniques coming from artificial intelligence, operational research, graph theory,…, etc. The basic idea of constraint programming is that the user expresses its constraints and a constraint solver seeks a solution. Constraint Satisfaction Problems (CSP), is a framework at the heart of CP problems. They correspond to decision problems where we seek for states or objects satisfying a number of constraints or criteria. These decision problems have two answers to the question they encode: true, if the problem admits a solution, false, otherwise. CSPs are the subject of intense research in both artificial intelligence and operations research. Many CSPs require the combination of heuristics and combinatorial optimization methods to solve them in a reasonable time.

With the improvement of computers, larger and larger problems can be solved. However, the size of industrial problems grow faster which requires a vast amount of memory space to store them and entail great difficulties to solve them.

In this thesis, our contributions can be divided into two main parts.

In the first part, we deal with the most used kind of constraints, which are table constraints. We proposed two compressed forms of table constraints. Both of them are based on frequent patterns search in order to avoid redundancy. However, the manner of defining pattern, the patterns-detecting process and the new compact representation differ significantly. For each form, we propose a filtering algorithm.

In the second part, we explore another way to optimize CSP solving which is the use of a parallel architecture. In fact, we enhance the solving process by establishing parallel consistencies. Different workers send to their master the result of establishing partial consistencies as new discovered facts. The master, in its turns tries to benefit from them by removing corresponding values.