A Partial Taxonomy of Substitutability and Interchangeability

Substitutability, interchangeability and related concepts in Constraint Programming were introduced approximately twenty years ago and have given rise to considerable subsequent research. We survey this work, classify, and relate the different concepts, and indicate directions for future work, in particular with respect to making connections with research into symmetry breaking. This paper is a condensed version of a larger work in progress.Comment: 18 pages, The 10th International Workshop on Symmetry in Constraint Satisfaction Problems (SymCon'10

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

Neighborhood Interchangeability and Dynamic Bundling for Non-binary CSPs

1. Interchangeability: An algorithm for computing interchangeability in non-binary CSPs. 2. Dynamic bundling: Integration of the above with backtrack search for solving non-binary CSPs. 3. Experiments demonstrating the benefits of dynamic bundling ·Finding multiple, robust solutions. ·Decreasing computational cost of search

Neighborhood Interchangeability and Dynamic Bundling for Non-binary CSPs

1. Interchangeability: An algorithm for computing interchangeability in non-binary CSPs. 2. Dynamic bundling: Integration of the above with backtrack search for solving non-binary CSPs. 3. Experiments demonstrating the benefits of dynamic bundling ·Finding multiple, robust solutions. ·Decreasing computational cost of search

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 )

Techniques for Bundling the Solution Space of Finite Constraint Satisfaction Problems

We study the backtrack-search procedure with forward checking (FCBT) for finding all solutions to a finite Constraint Satisfaction Problem (CSP). We describe how to use dynamic interchangeability to enhance the performance of search and represent the solution space in a compact manner. We evaluate this strategy (FC-DNPI) in terms of the numbers of nodes visited, constraints checked, and solution bundles generated by comparing it, theoretically and empirically, to other search strategies. We show that FC-DNPI is equivalent to search with the Cross Product Representation (FC-CPR) of [Hubbe and Freuder 1992] in terms of the numbers of solution bundles and constraint checks, while it reduces the number of nodes visited. We establish that both strategies are always superior to FC-BT in terms of all three criteria and dynamic bundling is always beneficial. Further, we compare FC-DNPI to the search procedure of [Haselböck 1993], which exploits static, pre-computed interchangeability relations. We show that the former never generates more solution bundles nor expands more nodes than the latter, and often reduces the number of constraint checks. We also propose, without evaluating them, amendments to the strategy of [Haselböck 1993] to improve its performance and reduce the number of constraint checks

Multi-Dimensional Models Facilitate Automatic Reformulation: The Case Study of the SET Game

In this paper we describe a reformulation strategy for solving multidimensional Constraint Satisfaction Problems (CSPs). This strategy operates by iteratively considering, in isolation, each one of the uni-dimensional constraints in the problem, and exploits the approximate symmetries induced by the selected constraint on the domains in order to enforce this constraint on the simplified problem. We use the game of SET, a combinatorial card game, as a toy problem to motivate our strategy and to explain and illustrate its operation. However, we believe that our approach is applicable to more complex domains of scientific and industrial importance, and deserves more thorough investigations in the future. Our approach sheds a new light on the dynamic reformulation of multidimensional CSPs. Importantly, it advocates that modeling tools for Constraint Programming should allow the user to specify the constraints directly on the attributes of the domain objects (i.e., variables and values) so that their multi-dimensionality can be exploited during problem solving

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

Lightweight Detection of Variable Symmetries for Constraint Satisfaction

International audienceIn this paper, we propose to automatically detect vari- able symmetries of CSP instances by computing for each constraint scope a partition exhibiting locally symmetric variables. From this local information obtained in polyno- mial time, we can build a so-called lsv-graph whose auto- morphisms correspond to (global) variable symmetries. In- terestingly enough, our approach allows us to disregard the representation (extension, intension, global) of constra ints. Besides, the size of the lsv-graph is linear with respect to the number of constraints (and their arity)