# On Global Warming (Softening Global Constraints)

@article{Hoeve2004OnGW, title={On Global Warming (Softening Global Constraints)}, author={Willem Jan van Hoeve and G. Pesant and Louis-Martin Rousseau}, journal={ArXiv}, year={2004}, volume={cs.AI/0408023} }

We describe soft versions of the global cardinality constraint and the regular constraint, with efficient filtering algorithms maintaining domain consistency. For both constraints, the softening is achieved by augmenting the underlying graph. The softened constraints can be used to extend the meta-constraint framework for over-constrained problems proposed by Petit, Regin and Bessiere.

## 15 Citations

Global Constraint Catalogue: Past, Present and Future

- Mathematics, Computer ScienceConstraints
- 2006

The catalogue of global constraints is reviewed, focusing on the graph-based description of global constraints. A number of possible enhancements are proposed as well as several research paths for…

Underestimating the cost of a soft constraint is dangerous: revisiting the edit-distance based soft regular constraint

- Mathematics, Computer ScienceJ. Heuristics
- 2013

This work uses the edit-distance based SoftRegular constraint as an example to show that a propagation algorithm that sometimes underestimates the cost may guide the search to incorrect (non-optimal) solutions to an over-constrained problem.

Efficient Propagators for Global Constraints

- Mathematics, Computer Science
- 2006

New propagators for the ALL-DIFFERENT constraint, the GCC, and the INTER-DISTANCE constraint are presented i.e., new filtering algorithms that reduce the search space according to these constraints.

Contraint-Based Combinators for Local Search

- Mathematics, Computer ScienceConstraints
- 2005

This paper shows that constraint combinators, such as logical and cardinality operators, reification, and first-class expressions can all be viewed as differentiable objects.

Global Constraint Catalog

- Mathematics
- 2005

This report presents a catalog of global constraints where
each constraint is explicitly described in terms of graph properties
and/or automata. When available, it also presents some typical usage…

Scheduling with Soft CLP(FD) Solver

- Computer Science
- 2006

The implementation of the Soft CLP(FD) solver is presented and the representatives of the problems which can be solved with the solver are presented.

Soft constraint processing

- 2005

This (not so) short text presents some results I’m aware of in the field of soft constraint network processing. Given the short (four hours) format of the school (and the relatively short time I used…

Constraint Programming

- Computer Science, MathematicsIntelligenza Artificiale
- 2006

Publisher Summary Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence (AI), operations…

4 Constraint Programming

Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, operations research, algorithms, graph…

Handbook of Constraint Programming

- Computer ScienceHandbook of Constraint Programming
- 2006

Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.

## References

SHOWING 1-10 OF 19 REFERENCES

Cost Evaluation of Soft Global Constraints

- Computer ScienceCPAIOR
- 2004

This paper shows that existing definitions of costs associated with soft global constraints are not sufficient to deal with all the usual global constraints. We propose more expressive definitions:…

A Hyper-arc Consistency Algorithm for the Soft Alldifferent Constraint

- Computer ScienceCP
- 2004

An algorithm is presented that achieves hyper-arc consistency for the soft alldifferent constraint by proving and exploiting the equivalence with a minimum-cost flow problem.

Specific Filtering Algorithms for Over-Constrained Problems

- Computer ScienceCP
- 2001

This paper presents a paradigm that places no restrictions on the constraint filtering algorithms used by associating specific filtering algorithms with constraints that may be violated in over-constrained problems.

Valued Constraint Satisfaction Problems: Hard and Easy Problems

- Mathematics, Computer ScienceIJCAI
- 1995

A simple algebraic framework is considered, related to Partial Constraint Satisfaction, which subsumes most of these proposals and is used to characterize existing proposals in terms of rationality and computational complexity.

Meta-constraints on violations for over constrained problems

- Computer ScienceProceedings 12th IEEE Internationals Conference on Tools with Artificial Intelligence. ICTAI 2000
- 2000

This paper classify the most usual types of rules, and it is shown that some of them are not expressible in existing frameworks, and introduces a new paradigm in which all these rules can be encoded, through meta-constraints.

A Regular Language Membership Constraint for Finite Sequences of Variables

- Computer Science, MathematicsCP
- 2004

A filtering algorithm is described and analyzed achieving generalized arc consistency for this constraint requiring that the corresponding sequence of values taken by these variables belong to a given regular language, thereby generalizing some other known global constraints.

Node and arc consistency in weighted CSP

- Computer ScienceAAAI/IAAI
- 2002

This paper specialize this definition to weighted CSP and introduces a stronger form of arc consistency (AC*) along with a <i>O(n <sup>2</sup>d<sup>3</Sup>)</i> algorithm, and empirically demonstrate that AC* is likely to be much better than AC in terms of pruned values.

Semirings for Soft Constraint Solving and Programming

- Computer Science, MathematicsLecture Notes in Computer Science
- 2004

This chapter discusses SCSPs for Modelling Attacks to Security Protocols, Soft Concurrent Constraint Programming, and Interchangeability in Soft CSPs.

Partial Constraint Satisfaction

- Mathematics, Computer ScienceIJCAI
- 1989

A general model of partial constraint satisfaction is proposed and standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction.

Generalized Arc Consistency for Global Cardinality Constraint

- Computer ScienceAAAI/IAAI, Vol. 1
- 1996

This paper presents an efficient way of implementing generalized arc consistency for a gcc based on a new theorem of flow theory and shows how this algorithm can efficiently be combined with other filtering techniques.