As soon as a structure is organized, the ability to put the right people at the right time is critical to satisfy the need of a department, a school or a company. We define personnel scheduling problems as the process of building, in an optimized manner, the personnel schedules. The aims of this thesis are to propose a mean to express those problems in a simple and automatic way, avoiding the user to interact with the technical aspects of the resolution. For that matter, we propose to mix the modeling power of automata with the efficiency and modularity of constraint programming for complex problem solving. Thus, we use the expressiveness of the finite multi-valued automata to model complex scheduling rules. Then, to make use of those built automata, we introduce a new filtering algorithm for multi-valued finite automata based on Lagrangian relaxation : multicost-regular. We also introduce a soft version of this constraint that has the ability to penalize violated rules defined by the automaton : soft-multicost-regular. The constraint model is automatically built. It is solved using the constraint library CHOCO and the whole modeling-solving process has been tested on realistic instances from ASAP and NRP10 libraries. The solution search is finally improved using specialized regret-based heuristics using the structure of multicost-regular and soft-multicost-regular.
Automata and Constraint Programming for Personnel Scheduling Problems