Multi-Objective Boolean Optimization: complexity with compiled constraints and SAT-based resolution • Emmanuel Lonca
- Co-Supervisor :
- Anne Parrain
- Funding : Artois
- PhD defended on :
- Salle des thèses
Decision aiding aims at helping a decision-maker to pick up a solution among several others. The usefulness of such approaches is as prominent as the size of the problems under consideration increases.
The need of decision aiding techniques is salient when the problem does not just consist in deciding whether a solutions exists, but to find one of the best solutions according to a given criterion. In this case, the problem goes from a decision problem (decide whether a solution exists) to a single criterion optimization problem (find one of the best solutions according to a criterion). A decision-maker may even want to consider multiple criteria, which turns the initial decision problem into a multicriteria optimization problem. The main issue arising in such cases lies in the fact that the criteria under consideration are often antagonistic, which implies that there is no solution which is the best for each of the objectives. In this case, a good compromise solution is looked for.
In this thesis, we first focus on the complexity of optimization requests based on a set of propositional languages. We then study the practical aspects of the resolution of such problems, using pieces of software designed for dealing with combinatorial decision problems, namely SAT solvers.