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Bibliographic Details
Main Authors: Montalbano, Pierre, de Givry, Simon, Katsirelos, George
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2509.17706
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author Montalbano, Pierre
de Givry, Simon
Katsirelos, George
author_facet Montalbano, Pierre
de Givry, Simon
Katsirelos, George
contents In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost functions. Approach (i) benefits from a vast catalog of constraints. Each soft constraint propagator communicates with other soft constraints only through the variable domains, resulting in weak lower bounds. Conversely, the approach (ii) provides a global view with strong bounds, but the size of the reformulation can be problematic. We focus on approach (iii) in which soft arc consistency (SAC) algorithms produce bounds of intermediate quality. Recently, the introduction of linear constraints as local cost functions increases their modeling expressiveness. We adapt an existing SAC algorithm to handle linear constraints. We show that our algorithm significantly improves the lower bounds compared to the original algorithm on several benchmarks, reducing solving time in some cases.
format Preprint
id arxiv_https___arxiv_org_abs_2509_17706
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Virtual Arc Consistency for Linear Constraints in Cost Function Networks
Montalbano, Pierre
de Givry, Simon
Katsirelos, George
Artificial Intelligence
In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost functions. Approach (i) benefits from a vast catalog of constraints. Each soft constraint propagator communicates with other soft constraints only through the variable domains, resulting in weak lower bounds. Conversely, the approach (ii) provides a global view with strong bounds, but the size of the reformulation can be problematic. We focus on approach (iii) in which soft arc consistency (SAC) algorithms produce bounds of intermediate quality. Recently, the introduction of linear constraints as local cost functions increases their modeling expressiveness. We adapt an existing SAC algorithm to handle linear constraints. We show that our algorithm significantly improves the lower bounds compared to the original algorithm on several benchmarks, reducing solving time in some cases.
title Virtual Arc Consistency for Linear Constraints in Cost Function Networks
topic Artificial Intelligence
url https://arxiv.org/abs/2509.17706