Search in weighted constraint satisfaction problems
A wide variety of real-world optimisation problems can be modelled as Weighted Constraint Satisfaction Problems (WCSPs). Such problems are NP-hard and require an exponential amount of time to find the optimal solution. This thesis concentrates on the University Examination Timetabling Problem. A general abstraction of this problem has been used, as there are many institution-specific rules which could be incorporated into the problem. The use of this problem type allows WCSPs to be investigated using realistic problem data and allows a comparison with previously published results for the problem instances used. We have examined some existing variable ordering heuristics and defined new ones. An analysis methodology has been defined that allows the characteristics of good solutions to be identified. Different methods of identifying difficult to solve sub-problems and the use of such methods in variable ordering has been investigated. Incorporating the weight, or preference, associated with constraints into variable ordering heuristics has been found to be beneficial to finding solutions of low cost. The analysis methodology has been used to examine the relationship between solutions of different quality and the knowledge derived has been used to define, and justify, two new variable ordering heuristics. The usefulness of different value ordering heuristics has been examined. Value selection on the error incurred with past assignments and the use of look-ahead have been investigated. Variable ordering heuristics have been extended to try and exploit the advantages of such value ordering heuristics. The use of stochasticity with such orderings has been investigated and has led to a new class of hybrid value ordering heuristics being defined. Finally two hybrid search algorithms have been defined that attempt to concentrate search upon the sections of the problem instance which have the largest effect upon the overall quality of solutions found. Such methods are shown to be at least competitive with standard tree based search techniques.