Scheduling with Soft CLP(FD) Solver*

Timetabling problems often consists from various requirements which can not be satisfied together [11]. Unsatisfiable requirements can be handled within optimization criteria as soft constraints. Such soft constraints may not be satisfied if there are some contradictions. The remaining hard constraints must be still satisfied. The set of hard and soft constraints can be naturally expressed using constraint programming [3]. Unfortunately there is no system available which would allow to use both hard and soft constraints together. There are various systems implementing soft constraints [2] but none of them allows to combine efficient constraint propagation algorithms for classical constraint satisfaction problems together with the propagation for soft constraints. Our implementation of the system for timetabling problem at Purdue University [9] was able to use both hard and soft constraints together. Hard constraints were available from SICStus Prolog CLP(FD) library [1] and soft constraints were implemented using the Soft CLP(FD) Solver [8]. This solver for soft constraints includes the specific set of soft constraints needed for the Purdue University timetabling problem. Our current intent is to generalize this proposal and implement the Soft CLP(FD) Solver as an open extendable library able to solve a wide class of problems. The new solver allows to define soft constraints as it is shown in the course timetabling example in Figure 1. Hard constraint disjoint2 ensures that all