Dynamic Constraint Weighting for Over-Constrained Problems

Many real-world constraint satisfaction problems (CSPs) can be over-constrained but contain a set of mandatory or hard constraints that have to be satisfied for a solution to be acceptable. Recent research has shown that constraint weighting local search algorithms can be very effective in solving a variety of CSPs. However, little work has been done in applying such algorithms to over-constrained problems with hard constraints. The difficulty has been finding a weighting scheme that can weight unsatisfied constraints and still maintain the distinction between the mandatory and non-mandatory constraints. This paper presents a new weighting strategy that simulates the transformation of an over-constrained problem with mandatory constraints into an equivalent problem where all constraints have equal importance, but the hard constraints have been repeated. In addition, two dynamic constraint weighting schemes are introduced that alter the number of simulated hard constraint repetitions according to feedback received during the search. The dynamic constraint weighting algorithms are compared with two algorithms that maintain a fixed number of hard constraint repetitions, using a test bed of over-constrained timetabling and nurse rostering problems. The results show the dynamic strategies outperform both fixed repetition approaches.