🤖 AI Summary
This work addresses the inefficiency of traditional scheduling approaches in handling cumulative constraints, which often neglect interactions among multiple resources. The authors propose a novel preprocessing method that systematically integrates cover-set identification with inequality lifting techniques to model cumulative constraints as linear inequalities over occupation vectors. This approach automatically infers and injects new constraints that explicitly capture multi-resource coupling relationships—without requiring additional search or probing. By significantly enhancing constraint propagation, the method effectively identifies incompatibilities among tasks that preclude parallel execution. Evaluated on standard RCPSP and RCPSP/max benchmark instances, the technique not only markedly improves solving performance but also establishes 25 new lower bounds—eight of which directly result from the inferred constraints—and yields five new optimal solutions.
📝 Abstract
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.