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On global warming: Flowbased soft global constraints
, 2006
"... In case a CSP is overconstrained, it is natural to allow some constraints, called soft constraints, to be violated. We propose a generic method to soften global constraints that can be represented by a flow in a graph. Such constraints are softened by adding violation arcs to the graph and then co ..."
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Cited by 39 (6 self)
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In case a CSP is overconstrained, it is natural to allow some constraints, called soft constraints, to be violated. We propose a generic method to soften global constraints that can be represented by a flow in a graph. Such constraints are softened by adding violation arcs to the graph and then computing a minimumweight flow in the extended graph to measure the violation. We present efficient propagation algorithms, based on different violation measures, achieving domain consistency for the alldifferent constraint, the global cardinality constraint, the regular constraint and the same constraint.
Global Constraint Catalogue: Past, Present and Future
, 2006
"... The catalogue of global constraints is reviewed, focusing on the graphbased description of global constraints. A number of possible enhancements are proposed as well as several research paths for the development of the area. ..."
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Cited by 26 (2 self)
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The catalogue of global constraints is reviewed, focusing on the graphbased description of global constraints. A number of possible enhancements are proposed as well as several research paths for the development of the area.
On Global Warming (Softening Global Constraints)
 In Proc. of the 6th International Workshop on Preferences and Soft Constraints
, 2004
"... We describe soft versions of the global cardinality constraint and the regular constraint, with e#cient 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 ..."
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Cited by 7 (1 self)
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We describe soft versions of the global cardinality constraint and the regular constraint, with e#cient 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 metaconstraint framework for overconstrained problems proposed by Petit, Regin and Bessiere.
Set Variables and Local Search
"... Many combinatorial (optimisation) problems have natural models based on, or including, set variables and set constraints. This modelling device has been around for quite some time in the constraint programming area, and proved its usefulness in many applications. This paper introduces set variable ..."
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Cited by 6 (6 self)
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Many combinatorial (optimisation) problems have natural models based on, or including, set variables and set constraints. This modelling device has been around for quite some time in the constraint programming area, and proved its usefulness in many applications. This paper introduces set variables and set constraints also in the local search area. It presents a way of representing set variables in the local search context, where we deal with concepts like transition functions, neighbourhoods, and penalty costs. Furthermore, some common set constraints and their penalty costs are defined. These constraints are later used to model three problems and some initial experimental results are reported.
Soft Constraints of Difference and Equality
"... In many combinatorial problems one may need to model the diversity or similarity of sets of assignments. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type we can use soft variants of the well known AllDifferent and AllEq ..."
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Cited by 3 (0 self)
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In many combinatorial problems one may need to model the diversity or similarity of sets of assignments. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type we can use soft variants of the well known AllDifferent and AllEqual constraints. We present a taxonomy of six soft global constraints, generated by combining the two latter ones and the two standard cost functions, which are either maximised or minimised. We characterise the complexity of achieving arc and bounds consistency on these constraints, resolving those cases for which NPhardness was neither proven nor disproven. In particular, we explore in depth the constraint ensuring that at least k pairs of variables have a common value. We show that achieving arc consistency is NPhard, however bounds consistency can be achieved in polynomial time through dynamic programming. Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor of 1 2 with a linear time greedy algorithm. Finally, we provide a fixed parameter tractable algorithm with respect to the number of values appearing in more than two distinct domains. Interestingly, this taxonomy shows that enforcing equality is harder than enforcing difference. 1.
Toward Understanding SolutionGuided MultiPoint Constructive Search for CSPs
"... Abstract. SolutionGuided MultiPoint Constructive Search (SGMPCS) is a complete, constructive search technique that has been shown to outperform standard constructive search techniques on a number of constraint optimization and constraint satisfaction problems. In this paper, we perform a case stu ..."
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Abstract. SolutionGuided MultiPoint Constructive Search (SGMPCS) is a complete, constructive search technique that has been shown to outperform standard constructive search techniques on a number of constraint optimization and constraint satisfaction problems. In this paper, we perform a case study of the application of SGMPCS to a constraint satisfaction model of the multidimensional knapsack problem. We show that SGMPCS performs poorly. We then develop a descriptive model of its performance using fitnessdistance analysis. It is demonstrated that SGMPCS search performance is partially dependent upon the correlation between the heuristic evaluation of the guiding solutions and their distance to the nearest satisfying solution. This is the first work to develop a descriptive model of SGMPCS search behaviour. The descriptive model points to a clear direction in improving the performance of constructive search for constraint satisfaction problems: the development of heuristic evaluations for partial solutions. 1