Interchangeability in constraint satisfaction problems

2003

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 δ and on threshold α (δ neighborhood interchangeability (δ NI)and α neighborhood interchangeability (α NI)). In this paper we extend the study introduced in [11] and we analyze the presence of the relaxed version of interchangeability in random soft CSPs. We give a short description of the implementation we used to compute interchangeabilities and to make the tests. The experiments show that there is high occurrence of α NI and δ NI interchangeability around optimal solution in fuzzy CSPs and weighted CSPs. Thus, these algorithms can be used successfully in solution update applications. Moreover, it is also showed that NI interchangeability can well approximate full interchangeability (FI).

Lecture Notes in Computer Science, 2002

Combinatorial optimization is a powerful paradigm for representing complex problems. It has a wide range of applications such as planning, scheduling, resource sharing, in many domains such as transportation, production, mass marketing, network management, human resources management. Constraint satisfaction techniques provide efficient algorithms to prune search spaces.

2001

While there are many general methods for case retrieval, case adaptation usually requires problem-specific knowledge and it is still an open problem. In this paper we propose a general method for solving case adaptation problems for the large class of problems which can be formulated as Constraint Satisfaction Problems. This method is based on the concept of interchangeability between values in problem solutions. The method is able to determine how change propagates in a solution set and generate a minimal set of choices which need to be changed to adapt an existing solution to a new problem. The paper presents the proposed method, algorithms and test results for a resource allocation domain.

1998

We address in this paper the adaptation of a case when a complete constraint model of the underlying problem is given. The idea is to apply methods from constraint based reasoning that allows the detection of "similar" solutions, which can be used to adapt a selected case to a new situation. We consider applications like configuration where a complete constraint model is available.

PROCEEDINGS OF THE NATIONAL …, 1998

ACM SIGAPP Applied Computing Review, 2013

Onto-substitutability has been shown to be intrinsic to how a domain value is considered redundant in Constraint Satisfaction Problems (CSPs). A value is onto-substitutable if any solution involving that value remains a solution when that value is replaced by some other value. We redefine onto-substitutability to accommodate binary relationships and study its implication. Joint interchangeability, an extension of onto-substitutability to its interchangeability counterpart, emerges as one of the results. We propose a new way of removing interchangeable values by constructing a new value as an intermediate step, as well as introduce virtual interchangeability, a local reasoning that leads to joint interchangeability and allows values to be merged together. Algorithms for removing onto-substitutable values are also proposed. 1

2005

The concept of interchangeability characterizes the possibilities for making local changes to CSP solutions. Often, interchangeability is only partial and also requires changing values assigned to other variables, called the dependent set. As partial interchangeability (PI) can only be computed by solving the whole problem, it needs to be approximated. We introduce the new concept of neighborhood tuple interchangeability (NTI) and show that it correctly approximates partial interchangeability (PI). We propose an algorithm for computing smallest dependent sets for NTI.

Annals of Mathematics and Artificial Intelligence, 2013

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 α and degradation factor δ for substitutability and interchangeability, ( α substitutability/interchangeability and δ substitutability/interchangeabi-lity respectively). We show that they satisfy analogous theorems to the ones already known for hard constraints. In α interchangeability, values are interchangeable in any solution that is better than a threshold α, thus allowing to disregard differences among solutions that are not sufficiently good anyway. In δ interchangeability, values are interchangeable if their exchange could not degrade the solution by more than a factor of δ. We give efficient algorithms to compute ( δ / α )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.

Lecture notes in computer science, 2001

1999

Case adaptation is a complex problem for which no general method has been found. We consider the restricted domain of problems which can be formulated as constraint satisfaction, and propose a general method using dimensionality reduction based on constraint solving and interchangeability.