On inferring cumulative constraints
This work addresses a bottleneck in constraint programming for scheduling, offering incremental improvements in performance and solution quality for specific benchmarks.
The paper tackles the problem of inefficient propagation in cumulative constraints for scheduling by introducing a preprocessing method that infers additional constraints to capture multi-resource interactions, resulting in improved search performance and tighter objective bounds on favorable instances, with experiments discovering 25 new lower bounds and five new best solutions.
Cumulative constraints are central in scheduling with constraint programming, yet propagation is typically performed per constraint, missing multi-resource interactions and causing severe slowdowns on some benchmarks. I present a preprocessing method for inferring additional cumulative constraints that capture such interactions without search-time probing. This approach interprets cumulative constraints as linear inequalities over occupancy vectors and generates valid inequalities by (i) discovering covers, the sets of tasks that cannot run in parallel, (ii) strengthening the cover inequalities for the discovered sets with lifting, and (iii) injecting the resulting constraints back into the scheduling problem instance. Experiments on standard RCPSP and RCPSP/max test suites show that these inferred constraints improve search performance and tighten objective bounds on favorable instances, while incurring little degradation on unfavorable ones. Additionally, these experiments discover 25 new lower bounds and five new best solutions; eight of the lower bounds are obtained directly from the inferred constraints.