Exchanging nogoods : an efficient cooperative search for solving constraint satisfaction problems Research Report Number LSIS

We propose a new cooperative concurrent search for solving the constraint satisfaction problem. Our approach consists in running independently many solvers (each one being associated with a process). These solvers exploit the algorithm Forward-Checking with Nogood Recording and they differ from each other in the heuristics they use for ordering variables and values. The cooperation is then based on exchanging nogoods (i.e. instantiations which cannot be extended to a solution). It is realized by two cooperation forms. On the one hand, we record every produced nogood in a shared memory. Thanks to these nogoods, each solver can then prune its own search tree. On the other hand a solver communicates directly a nogood to some other solvers by sending a message. We propose three different schemes for implementing the second cooperation form. Two of them reduce the communication cost by only sending to a solver the nogoods which are useful for it. Furthermore, we add to each solver a interpretation phase whose role is to limit the size of the search tree according to the received nogoods. Finally, we explain why a trade-off between cooperation and concurrency is required, before proposing such a trade-off. From a practical point of view, the interest of our approach is shown experimentally on random instances and on real-world instances. First, we establish that exchanging nogoods appears to be an efficient cooperation form. In particular, on random instances, we obtain linear or superlinear speed-up for consistent problems, like for inconsistent ones, up to about ten solvers. Then, we compare our approach with some classical state-of-the-art enumerative algorithms. In a multiprocessor system, our approach with at least two or four solvers is faster than these classical algorithms. In a monoprocessor system, in most cases, it is equivalent to or better than Forward-Checking with Nogood Recording but it is often worse than the other classical algorithms. However, in a few cases, in particular for some real-world instances, it outperforms the classical algorithms.