On inferring cumulative constraints

TL;DR

This paper introduces a preprocessing technique that infers additional cumulative constraints in scheduling problems, capturing resource interactions more effectively and improving solver performance without increasing search complexity.

Contribution

It presents a novel method to infer cumulative constraints as linear inequalities, enhancing constraint propagation and solution quality in scheduling problems.

Findings

Improved search performance on benchmark problems

Discovered 25 new lower bounds and five best solutions

Inferred constraints directly contributed to lower bounds

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.