Flow-Based Propagators for the SEQUENCE and Related Global Constraints

Maher, Michael J.; Narodytska, Nina; Quimper, Claude-Guy; Walsh, Toby

doi:10.1007/978-3-540-85958-1_11

Cited by 25 publications

(32 citation statements)

References 18 publications

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“…Even if powerful specialized algorithms exist for this constraint (see e.g. [7]), the automaton resulting from the reformulation can be integrated with other pattern requirements as we will show in Section 4. Finally, one should notice the work (see e.g.…”

Section: Path-finding and Decomposition: Two Approaches For Regularmentioning

confidence: 99%

Sequencing and Counting with the multicost-regular Constraint

Menana

Demassey

2009

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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Abstract. This paper introduces a global constraint encapsulating a regular constraint together with several cumulative costs. It is motivated in the context of personnel scheduling problems, where a schedule meets patterns and occurrence requirements which are intricately bound. The optimization problem underlying the multicost-regular constraint is NP-hard but it admits an efficient Lagrangian relaxation. Hence, we propose a filtering based on this relaxation. The expressiveness and the efficiency of this new constraint is experimented on personnel scheduling benchmark instances with standard work regulations. The comparative empirical results show how multicost-regular can significantly outperform a decomposed model with regular and global-cardinality constraints.

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Section: Path-finding and Decomposition: Two Approaches For Regularmentioning

confidence: 99%

Sequencing and Counting with the multicost-regular Constraint

Menana

Demassey

2009

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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“…Moreover, this last algorithm is able to handle arbitrary sets of AMONG constraints on consecutive variables (denoted GEN-SEQUENCE), however in O(n 4 ). Last, a flow-based algorithm achieving AC in O(n 2 ) was introduced in [10]. Here again, the algorithm can be adapted, using more general linear programming tools to handle the GEN-SEQUENCE constraint in O(n 2 log n) in the worst case.…”

Section: Csp and Sequence Constraintsmentioning

confidence: 99%

“…It was observed in [18] and [10] that we can consider Boolean variables and v = {1}, since the following decomposition of AMONG (or ATMOST) does not hinder propagation as it is Berge-acyclic [6]:…”

Section: The Atmostseqcard Constraintmentioning

confidence: 99%

“…However, there might often exist more efficient algorithm for the particular case at hand. For instance, filtering algorithms have been proposed for the AMONGSEQ constraint in [6,10,19,18]. This constraint ensures that all subsequences of size q have at least l but no more than u values in a set v. This constraint is often applied to car-sequencing and crew-rostering problems.…”

Section: Introductionmentioning

confidence: 99%

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An Optimal Arc Consistency Algorithm for a Chain of Atmost Constraints with Cardinality

Siala

Hébrard

Huguet

2012

Lecture Notes in Computer Science

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Abstract. The ATMOSTSEQCARD constraint is the conjunction of a cardinality constraint on a sequence of n variables and of n − q + 1 constraints ATMOST u on each subsequence of size q. This constraint is useful in car-sequencing and crew-rostering problems. In [18], two algorithms designed for the AMONGSEQ constraint were adapted to this constraint with a O(2 q n) and O(n 3 ) worst case time complexity, respectively. In [10], another algorithm with a O(n 2 log n) worst case time complexity and similarly adaptable to filter ATMOSTSEQCARD in O(n log n) was proposed. In this paper, we introduce an algorithm for achieving Arc Consistency on the ATMOSTSEQCARD constraint with a O(n) (hence optimal) worst case time complexity. We then empirically study the efficiency of our propagator on instances of the car-sequencing and crew-rostering problems.

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“…Several decompositions for this constraint have been introduced, two of which successively improved the best known asymptotic bound for propagating the constraint [19,20]. Some of these decompositions are based on mapping the problem into a linear program that represent a network flow.…”

Section: Sequencementioning

confidence: 99%