4 Search Results for "Khalil, Elias B."

Document
DOI: 10.4230/LIPIcs.CP.2024.22
Learning Lagrangian Multipliers for the Travelling Salesman Problem

Authors: Augustin Parjadis, Quentin Cappart, Bistra Dilkina, Aaron Ferber, and Louis-Martin Rousseau

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient propagators in constraint programming (such as the weighted circuit constraint). However, the conventional process of deriving Lagrangian multipliers (e.g., using subgradient methods) is often computationally intensive, limiting its practicality for large-scale or time-sensitive problems. To address this challenge, we propose an innovative unsupervised learning approach that harnesses the capabilities of graph neural networks to exploit the problem structure, aiming to generate accurate Lagrangian multipliers efficiently. We apply this technique to the well-known Held-Karp Lagrangian relaxation for the traveling salesman problem. The core idea is to predict accurate Lagrangian multipliers and to employ them as a warm start for generating Held-Karp relaxation bounds. These bounds are subsequently utilized to enhance the filtering process carried out by branch-and-bound algorithms. In contrast to much of the existing literature, which primarily focuses on finding feasible solutions, our approach operates on the dual side, demonstrating that learning can also accelerate the proof of optimality. We conduct experiments across various distributions of the metric traveling salesman problem, considering instances with up to 200 cities. The results illustrate that our approach can improve the filtering level of the weighted circuit global constraint, reduce the optimality gap by a factor two for unsolved instances up to a timeout, and reduce the execution time for solved instances by 10%.
Cite as

Augustin Parjadis, Quentin Cappart, Bistra Dilkina, Aaron Ferber, and Louis-Martin Rousseau. Learning Lagrangian Multipliers for the Travelling Salesman Problem. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{parjadis_et_al:LIPIcs.CP.2024.22,
  author =	{Parjadis, Augustin and Cappart, Quentin and Dilkina, Bistra and Ferber, Aaron and Rousseau, Louis-Martin},
  title =	{{Learning Lagrangian Multipliers for the Travelling Salesman Problem}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.22},
  URN =		{urn:nbn:de:0030-drops-207076},
  doi =		{10.4230/LIPIcs.CP.2024.22},
  annote =	{Keywords: Lagrangian relaxation, unsupervised learning, graph neural network}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.25
Combining Constraint Programming Reasoning with Large Language Model Predictions

Authors: Florian Régin, Elisabetta De Maria, and Alexandre Bonlarron

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
Constraint Programming (CP) and Machine Learning (ML) face challenges in text generation due to CP’s struggle with implementing "meaning" and ML’s difficulty with structural constraints. This paper proposes a solution by combining both approaches and embedding a Large Language Model (LLM) in CP. The LLM handles word generation and meaning, while CP manages structural constraints. This approach builds on GenCP, an improved version of On-the-fly Constraint Programming Search (OTFS) using LLM-generated domains. Compared to Beam Search (BS), a standard NLP method, this combined approach (GenCP with LLM) is faster and produces better results, ensuring all constraints are satisfied. This fusion of CP and ML presents new possibilities for enhancing text generation under constraints.
Cite as

Florian Régin, Elisabetta De Maria, and Alexandre Bonlarron. Combining Constraint Programming Reasoning with Large Language Model Predictions. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{regin_et_al:LIPIcs.CP.2024.25,
  author =	{R\'{e}gin, Florian and De Maria, Elisabetta and Bonlarron, Alexandre},
  title =	{{Combining Constraint Programming Reasoning with Large Language Model Predictions}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.25},
  URN =		{urn:nbn:de:0030-drops-207109},
  doi =		{10.4230/LIPIcs.CP.2024.25},
  annote =	{Keywords: Solver and Tools, ML-augmented CP, Constrained Text Generation, ML alongside CO}
}
Document
DOI: 10.4230/LIPIcs.CP.2024.30
Learning Precedences for Scheduling Problems with Graph Neural Networks

Authors: Hélène Verhaeghe, Quentin Cappart, Gilles Pesant, and Claude-Guy Quimper

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract
The resource constrained project scheduling problem (RCPSP) consists of scheduling a finite set of resource-consuming tasks within a temporal horizon subject to resource capacities and precedence relations between pairs of tasks. It is NP-hard and many techniques have been introduced to improve the efficiency of CP solvers to solve it. The problem is naturally represented as a directed graph, commonly referred to as the precedence graph, by linking pairs of tasks subject to a precedence. In this paper, we propose to leverage the ability of graph neural networks to extract knowledge from precedence graphs. This is carried out by learning new precedences that can be used either to add new constraints or to design a dedicated variable-selection heuristic. Experiments carried out on RCPSP instances from PSPLIB show the potential of learning to predict precedences and how they can help speed up the search for solutions by a CP solver.
Cite as

Hélène Verhaeghe, Quentin Cappart, Gilles Pesant, and Claude-Guy Quimper. Learning Precedences for Scheduling Problems with Graph Neural Networks. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{verhaeghe_et_al:LIPIcs.CP.2024.30,
  author =	{Verhaeghe, H\'{e}l\`{e}ne and Cappart, Quentin and Pesant, Gilles and Quimper, Claude-Guy},
  title =	{{Learning Precedences for Scheduling Problems with Graph Neural Networks}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{30:1--30:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.30},
  URN =		{urn:nbn:de:0030-drops-207150},
  doi =		{10.4230/LIPIcs.CP.2024.30},
  annote =	{Keywords: Scheduling, Precedence graph, Graph neural network}
}
Document
DOI: 10.4230/LIPIcs.CP.2023.14
Fast Matrix Multiplication Without Tears: A Constraint Programming Approach

Authors: Arnaud Deza, Chang Liu, Pashootan Vaezipoor, and Elias B. Khalil

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

Abstract
It is known that the multiplication of an N × M matrix with an M × P matrix can be performed using fewer multiplications than what the naive NMP approach suggests. The most famous instance of this is Strassen’s algorithm for multiplying 2× 2 matrices in 7 instead of 8 multiplications. This gives rise to the constraint satisfaction problem of fast matrix multiplication, where a set of R < NMP multiplication terms must be chosen and combined such that they satisfy correctness constraints on the output matrix. Despite its highly combinatorial nature, this problem has not been exhaustively examined from that perspective, as evidenced for example by the recent deep reinforcement learning approach of AlphaTensor. In this work, we propose a simple yet novel Constraint Programming approach to find algorithms for fast matrix multiplication or provide proof of infeasibility otherwise. We propose a set of symmetry-breaking constraints and valid inequalities that are particularly helpful in proving infeasibility. On the feasible side, we find that exploiting solver performance variability in conjunction with a sparsity-based problem decomposition enables finding solutions for larger (feasible) instances of fast matrix multiplication. Our experimental results using CP Optimizer demonstrate that we can find fast matrix multiplication algorithms for matrices up to 3× 3 with R = 23 in a short amount of time.
Cite as

Arnaud Deza, Chang Liu, Pashootan Vaezipoor, and Elias B. Khalil. Fast Matrix Multiplication Without Tears: A Constraint Programming Approach. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{deza_et_al:LIPIcs.CP.2023.14,
  author =	{Deza, Arnaud and Liu, Chang and Vaezipoor, Pashootan and Khalil, Elias B.},
  title =	{{Fast Matrix Multiplication Without Tears: A Constraint Programming Approach}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{14:1--14:15},
  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.2023.14},
  URN =		{urn:nbn:de:0030-drops-190518},
  doi =		{10.4230/LIPIcs.CP.2023.14},
  annote =	{Keywords: fast matrix multiplication, computer-assisted proofs, constraint programming, constraint satisfaction problem}
}
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