The present disclosure describes a computer-implemented constraint propagation system that supports a variety of different constraint propagation and/or constraint retraction algorithms, including monotonic and/or non-monotonic algorithms. In one embodiment, the system selects particular constraint propagation and/or retraction methods based on the nature of the combinatorial optimization problem (COP) being solved and the attributes of the particular COP application involved. The system may also enable new methods for constraint propagation and/or retraction to be added with relatively little disruptive effect on other components of the system. Embodiments of the system allow the propagation of constraints to be tuned to the semantics of each constraint, the likelihood of significant variable domain reduction, and other problem specific properties. The constraint propagation system is capable of being used as part of a reconfigurable search engine.