Elicitation strategies for fuzzy constraint problems with missing preferences: algorithms and experimental studies

Fuzzy constraints are a popular approach to handle preferences and over-constrained problems in scenarios where one needs to be cautious, such as in medical or space applications. We consider here fuzzy constraint problems where some of the preferences may be missing. This models, for example, settings where agents are distributed and have privacy issues, or where there is an ongoing preference elicitation process. In this setting, we study how to find a solution which is optimal irrespective of the missing preferences. In the process of finding such a solution, we may elicit preferences from the user if necessary. However, our goal is to ask the user as little as possible. We define a combined solving and preference elicitation scheme with a large number of different instantiations, each corresponding to a concrete algorithm which we compare experimentally. We compute both the number of elicited preferences and the "user effort", which may be larger, as it contains all the preference values the user has to compute to be able to respond to the elicitation requests. While the number of elicited preferences is important when the concern is to communicate as little information as possible, the user effort measures also the hidden work the user has to do to be able to communicate the elicited preferences. Our experimental results show that some of our algorithms are very good at finding a necessarily optimal solution while asking the user for only a very small fraction of the missing preferences. The user effort is also very small for the best algorithms. Finally, we test these algorithms on hard constraint problems with possibly missing constraints, where the aim is to find feasible solutions irrespective of the missing constraints.Comment: Principles and Practice of Constraint Programming, 14th International Conference, CP 2008, Sydney, Australia, September 14-18, 2008. Proceeding

A Cost-based Model and Algorithms for Interleaving Solving and Elicitation of CSPs

In Constraint Satisfaction Problems it is usually assumed that the CSP is available before the solving process begins, that is, the elicitation of the problem is completed before we attempt to solve the problem. As discussed in the work on Open Constraints and Interactive CSPs, there are situations where it can be advantageous and natural to interleave the elicitation and the solving. In particular, it may be expensive, in terms of time or other costs, to elicit certain constraints or parts of the constraints, and, we may very well not need all the complete constraints to be available in order for us to find a solution. In this paper we consider algorithms which take these costs into account. Constraints may be initially incomplete: it may be unknown whether certain tuples satisfy the constraint or not. We assume that we can determine such an unknown tuple, i.e., find out whether this tuple is in the constraint or not, but doing so incurs a known cost, which may vary between tuples. We also assume that we know the probability of an unknown tuple satisfying a constraint. An optimal algorithm for this situation is defined to be one which incurs minimal expected cost in finding a solution. We define algorithms for this problem, based on backtracking search. Specifically, we consider a simple iterative algorithm based on a cost limit on which unknowns may be determined, and a more complex algorithm which delays determining an unknown in order to estimate better whether doing so is worthwhile. We show experimentally the benefit in terms of cost of using the more sophisticated algorithms