Applied Partial Constraint Satisfaction Using Weighted Iterative Repair

Many real-world constraint satisfaction problems (CSPs) can be over-constrained or too large to solve using a standard constructive/ backtracking approach. Instead, faster heuristic techniques have been proposed that perform a partial search of all possible solutions using an iterative repair or hill-climbing approach. The main problem with such approaches is that they can become stuck in local minima. Consequently, various strategies or metaheuristics have been developed to escape from local minima. This paper investigates the application of one such meta-heuristic, weighted iterative repair, to solving a real-world problem of scheduling nurses at an Australian hospital. Weighted iterative repair has already proved successful in solving various binary CSPs. The current research extends this work by looking at a non-binary problem formulation, and partial constraint satisfaction involving hard and soft constraints. This has lead to the development of a soft constraint heuristic to improve the level of soft constraint optimisation and an extension of the original weighted iterative repair that avoids certain forms of cyclic behaviour. It is also demonstrated that weighted iterative repair can learn from repeatedly solving the same problem. and that restarting the algorithm on the same problem can result in faster execution times. The overall results show that weighted iterative repair finds better quality solutions than a standard iterative repair, whilst approaching near optimal solutions in less time than an alternative integer programming approach.