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DOI: 10.4230/LIPIcs.CP.2025.5

Transition Dominance in Domain-Independent Dynamic Programming

Authors: J. Christopher Beck, Ryo Kuroiwa, Jimmy H. M. Lee, Peter J. Stuckey, and Allen Z. Zhong

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

Abstract

Domain-independent dynamic programming (DIDP) is a model-based paradigm for dynamic programming (DP) that enables users to define DP models based on a state transition system. Heuristic search-based solvers have demonstrated strong performance in solving combinatorial optimization problems. In this paper, we formally define transition dominance in DIDP, where one transition consistently leads to better solutions than another, allowing the search process to safely ignore dominated transitions. To facilitate the efficient use of transition dominance, we introduce an interface for defining transition dominance and propose the use of state functions to cache values, thereby avoiding redundant computations when verifying transition dominance. Experimental results on DP models across multiple problem classes indicate that incorporating transition dominance and state functions yields a 5 to 10 times speed-up on average for different search algorithms within the DIDP framework compared to the baseline.

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J. Christopher Beck, Ryo Kuroiwa, Jimmy H. M. Lee, Peter J. Stuckey, and Allen Z. Zhong. Transition Dominance in Domain-Independent Dynamic Programming. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beck_et_al:LIPIcs.CP.2025.5,
  author =	{Beck, J. Christopher and Kuroiwa, Ryo and Lee, Jimmy H. M. and Stuckey, Peter J. and Zhong, Allen Z.},
  title =	{{Transition Dominance in Domain-Independent Dynamic Programming}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{5:1--5:23},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-238661},
  doi =		{10.4230/LIPIcs.CP.2025.5},
  annote =	{Keywords: Dominance, Dynamic Programming, Combinatorial Optimization}
}

Document

DOI: 10.4230/LIPIcs.CP.2022.31

Exploiting Functional Constraints in Automatic Dominance Breaking for Constraint Optimization

Authors: Jimmy H. M. Lee and Allen Z. Zhong

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)

Abstract

Dominance breaking is an effective technique to reduce the time for solving constraint optimization problems. Lee and Zhong propose an automatic dominance breaking framework for a class of constraint optimization problems based on specific forms of objectives and constraints. In this paper, we propose to enhance the framework for problems with nested function calls which can be flattened to functional constraints. In particular, we focus on aggregation functions and exploit such properties as monotonicity, commutativity and associativity to give an efficient procedure for generating effective dominance breaking nogoods. Experimentation also shows orders-of-magnitude runtime speedup using the generated dominance breaking nogoods and demonstrates the ability of our proposal to reveal dominance relations in the literature and discover new dominance relations on problems with ineffective or no known dominance breaking constraints.

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Jimmy H. M. Lee and Allen Z. Zhong. Exploiting Functional Constraints in Automatic Dominance Breaking for Constraint Optimization. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lee_et_al:LIPIcs.CP.2022.31,
  author =	{Lee, Jimmy H. M. and Zhong, Allen Z.},
  title =	{{Exploiting Functional Constraints in Automatic Dominance Breaking for Constraint Optimization}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.31},
  URN =		{urn:nbn:de:0030-drops-166607},
  doi =		{10.4230/LIPIcs.CP.2022.31},
  annote =	{Keywords: Constraint Optimization Problems, Dominance Breaking}
}

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Documents authored by Lee, Jimmy H. M.

Transition Dominance in Domain-Independent Dynamic Programming

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Exploiting Functional Constraints in Automatic Dominance Breaking for Constraint Optimization

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