Experimental Evaluation of Interchangeability in Soft CSPs

In [8], Freuder defined interchangeability for classical Constraint Satisfaction Problems (CSPs). Recently [2], we extended the definition of interchangeability to Soft CSPs and we introduced two notions of relaxation based on degradation # and on threshold # ( neighborhood interchangeability ( NI )and # neighborhood interchangeability (#NI )). In this pae

Generalizing Consistency and other Constraint Properties to Quantified Constraints

Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the usual notion of solution inappropriate. As a consequence, basic properties of Constraint Satisfaction Problems (CSP), such as consistency or substitutability, are not completely understood in the quantified case. These properties are important because they are the basis of most of the reasoning methods used to solve classical (existentially quantified) constraints, and one would like to benefit from similar reasoning methods in the resolution of quantified constraints. In this paper, we show that most of the properties that are used by solvers for CSP can be generalized to quantified CSP. This requires a re-thinking of a number of basic concepts; in particular, we propose a notion of outcome that generalizes the classical notion of solution and on which all definitions are based. We propose a systematic study of the relations which hold between these properties, as well as complexity results regarding the decision of these properties. Finally, and since these problems are typically intractable, we generalize the approach used in CSP and propose weaker, easier to check notions based on locality, which allow to detect these properties incompletely but in polynomial time

On the Computation of Local Interchangeability in Soft Constraint Satisfaction Problems

Freuder in (1991) de?ned interchangeability for classical Constraint Satisfaction Problems (CSPs). Recently (2002), we extended the de?nition of interchangeability to Soft CSPs and we introduced two notions of relaxations based on degradation ? and on threshold ? (?neighborhood interchangeability (?NI )and ?neighborhood interchangeability ?NI ). In this paper we study the presence of these relaxed version of interchangeability in random soft CSPs. We give a description of the implementation we used to compute interchangeabilities and to make the tests. The experiments show that there is high occurrence of ?NI and ?NI interchangeability around optimal solution in Fuzzy CSP and weighted CSPs. Thus, these algorithms can be used succesfully in solution update applications. Moreover, it is also showed that NI interchangeability can well approximate full interchangeability (FI )

A constraint-based framework for configuration

The research presented here aims at providing a comprehensive framework for solving configuration problems, based on the Constraint Satisfaction paradigm. This thesis is addressing the two main issues raised by a configuration task: modeling the problem and solving it efficiently. Our approach subsumes previous approaches, incorporating both Simplification and further extension, offering increased representational power and efficiency. Modeling. We advance the idea of local, context independent models for the types of objects in the application domain, and show how the model of an artifact can be built as a composition of local models of the constituent parts. Our modeling technique integrates two mechanisms for dealing with complexity, namely composition and abstraction. Using concepts such as locality, aggregation and inheritance, it offers support and guidance as to the appropriate content and organization of the domain knowledge, thus making knowledge specification and representation less error prone, and knowledge maintenance much easier. There are two specific aspects which make modeling configuration problems challenging: the complexity and heterogeneity of relations that must be expressed, manipulated and maintained, and the dynamic nature of the configuration process. We address these issues by introducing Composite Constraint Satisfaction Problems, a new, nonstandard class of problems which extends the classic Constraint Satisfaction paradigm. Efficiency. For the purpose of the work presented here, we are only interested in providing a guaranteed optimal solution to a configuration problem. To achieve this goal, our research focused on two complementary directions. The first one led to a powerful search algorithm called Maintaining Arc Consistency Extended (MACE). By maintaining arc consistency and taking advantage of the problem structure, MACE turned out to be one of the best general purpose CSP search algorithms to date. The second research direction aimed at reducing the search effort involved in proving the optimality of the proposed solution by making use of information which is specific to individual configuration problems. By adding redundant specialized constraints, the algorithm improves dramatically the lower bound computation. Using abstraction through focusing only on relevant features allows the algorithm to take advantage of context-dependent interchangeability between component instances and discard equivalent solutions, involving the same cost as solutions that have already been explored

Broken Triangles Revisited

International audienceA broken triangle is a pattern of (in)compatibilities between assignments in a binary CSP (constraint satisfaction problem). In the absence of certain broken triangles, satisfiability-preserving domain reductions are possible via merging of domain values. We investigate the possibility of maximising the number of domain reduction operations by the choice of the order in which they are applied, as well as their interaction with arc consistency operations. It turns out that it is NP-hard to choose the best order

Interchangeability with thresholds and degradation factors for Soft CSPs

Substitutability and interchangeability in constraint satisfaction problems (CSPs) have been used as a basis for search heuristics, solution adaptation and abstraction techniques. In this paper, we consider how the same concepts can be extended to soft constraint satisfaction problems (SCSPs). We introduce two notions: threshold alpha and degradation factor delta for substitutability and interchangeability, ( (alpha) substitutability/interchangeability and (delta) substitutability/interchangeabi-lity respectively). We show that they satisfy analogous theorems to the ones already known for hard constraints. In (alpha) interchangeability, values are interchangeable in any solution that is better than a threshold alpha, thus allowing to disregard differences among solutions that are not sufficiently good anyway. In (delta) interchangeability, values are interchangeable if their exchange could not degrade the solution by more than a factor of delta. We give efficient algorithms to compute ( (delta) / (alpha) )interchangeable sets of values for a large class of SCSPs, and show an example of their application. Through experimental evaluation based on random generated problem we measure first, how often neighborhood interchangeable values are occurring, second, how well they can approximate fully interchangeable ones, and third, how efficient they are when used as preprocessing techniques for branch and bound search

Global SPACING Constraint (Technical Report)

We propose a new global SPACING constraint that is useful in modeling events that are distributed over time, like learning units scheduled over a study program or repeated patterns in music compositions. First, we investigate theoretical properties of the constraint and identify tractable special cases. We propose efficient DC filtering algorithms for these cases. Then, we experimentally evaluate performance of the proposed algorithms on a music composition problem and demonstrate that our filtering algorithms outperform the state-of-the-art approach for solving this problem