An Attempt to Dynamically Break Symmetries in the Social Golfers Problem

Abstract

A number of different satisfaction and optimisation combinatorial problems have recently been approached with constraint programming over the domain of finite sets, for increased declarativity and efficiency. Such problems where one tries to find sets of values that satisfy some conditions, often present much symmetry on variables and values. In particular, the social golfers problem encompasses many possible symmetries. Allowing symmetric solutions increases search space unnecessarily, thus multiplying solution time. Therefore, ordering constraints have been proposed and incorporated in set solvers. However, such constraints are imposed statically in the global problem model and are unable to detect symmetries that still occur in sub-problems after a partial labelling. In this paper we discuss how to overcome this and present an approach that sequentially labels variables avoiding such symmetries by dynamically disallowing the assignment of other values from the same equivalence class in the golfers problem. Experimental results show that this approach outperforms previous ones, recently achieved by the constraint programming community, namely over sets. Unfortunately, the current method is incomplete and may loose solutions. Nevertheless, results are correct and show that similar techniques can be used efficiently to obtain faster solutions.