Applying Ad-hoc Global Constraints with the $${\tt case}$$ Constraint to Still-Life

Abstract

The Still-Life problem is challenging for CP techniques because the basic constraints of the game of Life are loose and give poor propagation for Still-Life. In this paper, we show how ad hoc global $${\tt case}$$ constraints can be customized to construct various models to provide much stronger propagation with CP solvers. Since we use custom ad hoc constraints of high arity where the number of tuples to define the constraint are large, the actual constraint representation becomes important to avoid excessive space consumption. We demonstrate how to use BDDs to construct good representations for the $${\tt case}$$ constraint which is critical for efficiency. Our results seem comparable to hybrid CP/IP models even though we are only using propagation albeit on ad hoc global constraints. This paper shows an extensive example of how to systematically build models using different kinds of ad hoc constraints. It also demonstrates the solving potential of ad hoc global constraints.