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On Inferring Cumulative Constraints

Author Konstantin Sidorov

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Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Theory of computation → Discrete optimization
  • Mathematics of computing → Integer programming
Keywords
  • Constraint programming
  • scheduling
  • cumulative
  • lifting
  • valid inequalities

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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 exhibiting more stable performance on unfavorable instances than the prior work. Additionally, these experiments discover 25 new lower bounds and five new best solutions; seven of the lower bounds are obtained directly from the inferred constraints.

Cite As Get BibTex

Konstantin Sidorov. On Inferring Cumulative Constraints. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 50:1-50:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CP.2026.50

Author Details

Konstantin Sidorov
  • Delft University of Technology, The Netherlands

Funding

Supported by the TU Delft AI Labs program as part of the XAIT lab.

Acknowledgements

I would like to thank Imko Marijnissen for the enlightening discussions that sparked the development of the technique presented in this paper, and the anonymous reviewers for improving the presentation of the approach and empirical results.

Supplementary Materials

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