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Documents authored by Schaus, Pierre


Document
Boosting Decision Diagram-Based Branch-And-Bound by Pre-Solving with Aggregate Dynamic Programming

Authors: Vianney Coppé, Xavier Gillard, and Pierre Schaus

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


Abstract
Discrete optimization problems expressible as dynamic programs can be solved by branch-and-bound with decision diagrams. This approach dynamically compiles bounded-width decision diagrams to derive both lower and upper bounds on unexplored parts of the search space, until they are all enumerated or discarded. Assuming a minimization problem, relaxed decision diagrams provide lower bounds through state merging while restricted decision diagrams obtain upper bounds by excluding states to limit their size. As the selection of states to merge or delete is done locally, it is very myopic to the global problem structure. In this paper, we propose a novel way to proceed that is based on pre-solving a so-called aggregate version of the problem with a limited number of states. The compiled decision diagram of this aggregate problem is tractable and can fit in memory. It can then be exploited by the original branch-and-bound to generate additional pruning and guide the compilation of restricted decision diagrams toward good solutions. The results of the numerical study we conducted on three combinatorial optimization problems show a clear improvement in the performance of DD-based solvers when blended with the proposed techniques. These results also suggest an approach where the aggregate dynamic programming model could be used in replacement of the relaxed decision diagrams altogether.

Cite as

Vianney Coppé, Xavier Gillard, and Pierre Schaus. Boosting Decision Diagram-Based Branch-And-Bound by Pre-Solving with Aggregate Dynamic Programming. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{coppe_et_al:LIPIcs.CP.2023.13,
  author =	{Copp\'{e}, Vianney and Gillard, Xavier and Schaus, Pierre},
  title =	{{Boosting Decision Diagram-Based Branch-And-Bound by Pre-Solving with Aggregate Dynamic Programming}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{13:1--13:17},
  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.2023.13},
  URN =		{urn:nbn:de:0030-drops-190500},
  doi =		{10.4230/LIPIcs.CP.2023.13},
  annote =	{Keywords: Discrete Optimization, Decision Diagrams, Aggregate Dynamic Programming}
}
Document
Probabilistic Inference by Projected Weighted Model Counting on Horn Clauses

Authors: Alexandre Dubray, Pierre Schaus, and Siegfried Nijssen

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


Abstract
Weighted model counting, that is, counting the weighted number of satisfying assignments of a propositional formula, is an important tool in probabilistic reasoning. Recently, the use of projected weighted model counting (PWMC) has been proposed as an approach to formulate and answer probabilistic queries. In this work, we propose a new simplified modeling language based on PWMC in which probabilistic inference tasks are modeled using a conjunction of Horn clauses and a particular weighting scheme for the variables. We show that the major problems of inference for Bayesian Networks, network reachability and probabilistic logic programming can be modeled in this language. Subsequently, we propose a new, relatively simple solver that is specifically optimized to solve the PWMC problem for such formulas. Our experiments show that our new solver is competitive with state-of-the-art solvers on the major problems studied.

Cite as

Alexandre Dubray, Pierre Schaus, and Siegfried Nijssen. Probabilistic Inference by Projected Weighted Model Counting on Horn Clauses. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{dubray_et_al:LIPIcs.CP.2023.15,
  author =	{Dubray, Alexandre and Schaus, Pierre and Nijssen, Siegfried},
  title =	{{Probabilistic Inference by Projected Weighted Model Counting on Horn Clauses}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{15:1--15:17},
  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.2023.15},
  URN =		{urn:nbn:de:0030-drops-190520},
  doi =		{10.4230/LIPIcs.CP.2023.15},
  annote =	{Keywords: Model Counting, Bayesian Networks, Probabilistic Networks}
}
Document
Short Paper
Partitioning a Map into Homogeneous Contiguous Regions: A Branch-And-Bound Approach Using Decision Diagrams (Short Paper)

Authors: Nicolas Golenvaux, Xavier Gillard, Siegfried Nijssen, and Pierre Schaus

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


Abstract
Regionalization is a crucial spatial analysis technique used for partitioning a map divided into zones into k continuous areas, optimizing the similarity of zone attributes within each area. This technique has a variety of applications in fields like urban planning, environmental management, and geographic information systems. The REDCAP algorithm is a well-known approach for addressing the regionalization problem. It consists of two main steps: first, it generates a spatially contiguous tree (SCT) representing the neighborhood structure of the set of spatial objects using a contiguity-constrained hierarchical clustering method. Second, it greedily removes k-1 edges from the SCT to create k regions. While this approach has proven to be effective, it may not always produce the most optimal solutions. We propose an alternative method for the second step, an exact dynamic programming (DP) formulation for the k-1 edges removal problem. This DP is solved using a multi-valued decision diagram (MDD)-based branch and bound solver leading to a more optimal solution. We compared our proposed method with the REDCAP state-of-the-art technique on real data and synthetic ones, using different instances of the regionalization problem and different supervised and unsupervised metrics. Our results indicate that our approach provides higher quality partitions than those produced by REDCAP at acceptable computational costs. This suggests that our method could be a viable alternative for addressing the regionalization problem in various applications.

Cite as

Nicolas Golenvaux, Xavier Gillard, Siegfried Nijssen, and Pierre Schaus. Partitioning a Map into Homogeneous Contiguous Regions: A Branch-And-Bound Approach Using Decision Diagrams (Short Paper). In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 45:1-45:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{golenvaux_et_al:LIPIcs.CP.2023.45,
  author =	{Golenvaux, Nicolas and Gillard, Xavier and Nijssen, Siegfried and Schaus, Pierre},
  title =	{{Partitioning a Map into Homogeneous Contiguous Regions: A Branch-And-Bound Approach Using Decision Diagrams}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{45:1--45:10},
  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.2023.45},
  URN =		{urn:nbn:de:0030-drops-190825},
  doi =		{10.4230/LIPIcs.CP.2023.45},
  annote =	{Keywords: Regionalization, Redcap, Skater, Multivalued Decision Diagrams}
}
Document
Solving the Constrained Single-Row Facility Layout Problem with Decision Diagrams

Authors: Vianney Coppé, Xavier Gillard, and Pierre Schaus

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


Abstract
The Single-Row Facility Layout Problem is an NP-hard problem dealing with the ordering of departments with given lengths and pairwise traffic intensities in a facility. In this context, one seeks to minimize the sum of the distances between department pairs, weighted by the corresponding traffic intensities. Practical applications of this problem include the arrangement of rooms on a corridor in hospitals or offices, airplanes and gates in an airport or machines in a manufacture. This paper presents two novel exact models for the Constrained Single-Row Facility Layout Problem, a recent variant of the problem including positioning, ordering and adjacency constraints. On the one hand, the state-of-the-art mixed-integer programming model for the unconstrained problem is extended to incorporate the constraints. On the other hand, a decision diagram-based approach is described, based on an existing dynamic programming model for the unconstrained problem. Computational experiments show that both models outperform the only mixed-integer programming model in the literature, to the best of our knowledge. While the two models have execution times of the same order of magnitude, the decision diagram-based approach handles positioning constraints much better but the mixed-integer programming model has the advantage for ordering constraints.

Cite as

Vianney Coppé, Xavier Gillard, and Pierre Schaus. Solving the Constrained Single-Row Facility Layout Problem with Decision Diagrams. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{coppe_et_al:LIPIcs.CP.2022.14,
  author =	{Copp\'{e}, Vianney and Gillard, Xavier and Schaus, Pierre},
  title =	{{Solving the Constrained Single-Row Facility Layout Problem with Decision Diagrams}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{14:1--14:18},
  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.2022.14},
  URN =		{urn:nbn:de:0030-drops-166433},
  doi =		{10.4230/LIPIcs.CP.2022.14},
  annote =	{Keywords: Discrete Optimization, Mixed-Integer Programming, Decision Diagrams, Constrained Single-Row Facility Layout Problem}
}
Document
Sequence Variables for Routing Problems

Authors: Augustin Delecluse, Pierre Schaus, and Pascal Van Hentenryck

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


Abstract
Constraint Programming (CP) is one of the most flexible approaches for modeling and solving vehicle routing problems (VRP). This paper proposes the sequence variable domain, that is inspired by the insertion graph introduced in [Bent and Van Hentenryck, 2004] and the subset bound domain for set variables. This domain representation, which targets VRP applications, allows for an efficient insertion-based search on a partial tour and the implementation of simple, yet efficient filtering algorithms for constraints that enforce time-windows on the visits and capacities on the vehicles. Experiment results demonstrate the efficiency and flexibility of this CP domain for solving some hard VRP problems, including the Dial-A-Ride, the Patient Transportation, and the asymmetric TSP with time windows.

Cite as

Augustin Delecluse, Pierre Schaus, and Pascal Van Hentenryck. Sequence Variables for Routing Problems. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{delecluse_et_al:LIPIcs.CP.2022.19,
  author =	{Delecluse, Augustin and Schaus, Pierre and Van Hentenryck, Pascal},
  title =	{{Sequence Variables for Routing Problems}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{19:1--19:17},
  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.2022.19},
  URN =		{urn:nbn:de:0030-drops-166485},
  doi =		{10.4230/LIPIcs.CP.2022.19},
  annote =	{Keywords: Constraint Programming, Dial-A-Ride, Patient Transportation, TSPTW, Vehicle Routing, Sequence Variables, Insertion Variables}
}
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