摘要 : 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 c... 展开 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, (_αsubstitutability/interchangeability and ~δsubstitutability/interchangeabi-lity respectively). We show that they satisfy analogous theorems to the ones already known for hard constraints. In _αinterchangeability, 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. 收起