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DOI: 10.4230/LIPIcs.CP.2025.36

Balancing Latin Rectangles with LLM-Generated Streamliners

Authors: Florentina Voboril, Vaidyanathan Peruvemba Ramaswamy, and Stefan Szeider

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract

We present an integration of Large Language Models (LLMs) with streamlining techniques to find well-balanced Latin rectangles. Our approach combines LLM-generated streamlining constraints that effectively partition the search space, directing constraint solvers toward structured subspaces containing high-quality solutions. Our methodology extends LLM-generated streamliners, as Voboril et al. (2024) introduced for decision problems, to the optimization context through techniques that incrementally refine the objective function value. We propose two complementary strategies to orchestrate sets of streamliners: an incremental mechanism that utilizes improving solutions to initialize subsequent search processes, and an evolutionary framework that maintains and refines effective streamliner populations. Our experiments demonstrate that our approach successfully reduces established minimum imbalance values for partially spatially balanced Latin rectangles across multiple problem dimensions. The results validate the efficacy of combining LLMs with constraint programming methodologies for tackling problems characterized by complex global constraints.

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Florentina Voboril, Vaidyanathan Peruvemba Ramaswamy, and Stefan Szeider. Balancing Latin Rectangles with LLM-Generated Streamliners. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{voboril_et_al:LIPIcs.CP.2025.36,
  author =	{Voboril, Florentina and Peruvemba Ramaswamy, Vaidyanathan and Szeider, Stefan},
  title =	{{Balancing Latin Rectangles with LLM-Generated Streamliners}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.36},
  URN =		{urn:nbn:de:0030-drops-238970},
  doi =		{10.4230/LIPIcs.CP.2025.36},
  annote =	{Keywords: Balanced Latin Rectangles, Streamliners, Large Language Models, Warmstarts, Evolutionary Search}
}

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Short Paper

DOI: 10.4230/LIPIcs.CP.2023.48

Proven Optimally-Balanced Latin Rectangles with SAT (Short Paper)

Authors: Vaidyanathan Peruvemba Ramaswamy and Stefan Szeider

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract

Motivated by applications from agronomic field experiments, Díaz, Le Bras, and Gomes [CPAIOR 2015] introduced Partially Balanced Latin Rectangles as a generalization of Spatially Balanced Latin Squares. They observed that the generation of Latin rectangles that are optimally balanced is a highly challenging computational problem. They computed, utilizing CSP and MIP encodings, Latin rectangles up to 12 × 12, some optimally balanced, some suboptimally balanced. In this paper, we develop a SAT encoding for generating balanced Latin rectangles. We compare experimentally encoding variants. Our results indicate that SAT encodings perform competitively with the MIP encoding, in some cases better. In some cases we could find Latin rectangles that are more balanced than previously known ones. This finding is significant, as there are many arithmetic constraints involved. The SAT approach offers the advantage that we can certify that Latin rectangles are optimally balanced through DRAT proofs that can be verified independently.

Cite as

Vaidyanathan Peruvemba Ramaswamy and Stefan Szeider. Proven Optimally-Balanced Latin Rectangles with SAT (Short Paper). In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 48:1-48:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{peruvembaramaswamy_et_al:LIPIcs.CP.2023.48,
  author =	{Peruvemba Ramaswamy, Vaidyanathan and Szeider, Stefan},
  title =	{{Proven Optimally-Balanced Latin Rectangles with SAT}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{48:1--48:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-300-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{280},
  editor =	{Yap, Roland H. C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.48},
  URN =		{urn:nbn:de:0030-drops-190855},
  doi =		{10.4230/LIPIcs.CP.2023.48},
  annote =	{Keywords: combinatorial design, SAT encodings, certified optimality, arithmetic constraints, spatially balanced Latin rectangles}
}

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Documents authored by Peruvemba Ramaswamy, Vaidyanathan

Balancing Latin Rectangles with LLM-Generated Streamliners

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Proven Optimally-Balanced Latin Rectangles with SAT (Short Paper)

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