Parallel constraint solving for combinatorial problems

Abstract

With parallelism becoming the standard in computer design, research on parallel constraint solving technique is of vital importance for enhancing the performance of constraint solving. In this dissertation, we reviewed the literature on exploiting parallelism in constraint solving to help gain insight into the rationale of different types of parallel constraint solving approaches. On this basis, we analyzed the effectiveness of parallel constraint solving, with the focus on obtaining a first solution when solving computationally hard combinatorial problems. We have shown that a well-designed search space splitting method and constraint programming model can enable the embarrassingly parallel search (EPS) to solve some open instances of the social golfer problem that have not been solved by a sequential algorithm. We also observed superlinear speedups when solving these instances, which confirms our theoretical analysis. Besides, we examined two practical constraint optimization problems, including the traveling tournament problem with predefined venues and the talent scheduling problem. Our proposed constraint models outperformed the existing models on the same instances, and the EPS approach could always attain better feasible solutions in terms of the optimal objective value by using more parallel processors. To explore the use of massively parallel processing, we proposed the parallel stochastic portfolio search, which is a simple and non-intrusive way to parallelize different incarnations of a sequential solver. When comparing the existing portfolio to our portfolio approach by solving the same constraint satisfaction problems using the same constraint models, our technique could solve harder and larger instances. The successes of our new parallel approaches are attributed to early diversity; i.e., some diversity early in the search introduced by parallelism can offset early mistakes caused by weak heuristic choices. Unlike the other techniques (e.g., limited discrepancy search) used to overcome early mistakes, the studied two parallel constraint solving approaches not only can explore more nodes simultaneously but also does not sacrifice the guarantee of completeness. We also presented a hypertree decomposition method that builds a degenerate decomposition tree for a given constraint network, in which each node of the decomposition tree possesses and executes a subset of constraints of the given constraint network. The usefulness of our proposed parallel techniquedepends on whether we can find an efficient way to join the results of each node.