Descriptif

The purpose of this course is to present constraint-based methods used in automated reasoning and search problems. Each lecture of approximatively 2h will be followed by 2h of practical work for illustrating the taught concepts and manipulating the associated tools on decision making applications. The constraint modelling language MiniZinc with its different back end constraint solvers (SAT, FD, LP, etc.) will be used as unifying framework and as basis for showing the practical complexity of different solvers on some NP hard problems.

1. Introduction to decision, optimization and constraint satisfaction problems and to the Constraint modeling language MiniZinc
   • TP Python/Jupyter preliminaries and puzzle solving in MiniZinc
2. Boolean satisfiability, SAT solvers
   • TP SAT-solver (python)
3. Polynomial complexity classes in SAT, phase transitions in random k-SAT
   • TP random k-SAT problems and graph coloring problems (python and MiniZinc-FD)
4. Constraint propagation and domain filtering algorithms 
   • TP mini constraint solver (python)
5. Search and heuristics
   
   • TP MiniZinc-FD on disjunctive scheduling
6. Global constraints
   • TP MiniZinc-FD on Air Traffic Control
7. Symmetries
   • TP MiniZinc-FD on symmetry breaking constraints
8. Arithmetic constraints
   
   • TP MiniZinc-LP Linear Programming for production planning
9. Constraint-based local search and black box continuous optimization
   • TP simulated annealing

Modalités d'évaluation : TDs + écrit final

Langue du cours : Anglais & Français

Credits ECTS : 4