Gadi Solotorevsky

Modeling and solving distributed constraint satisfaction problems (DCSPs)

Constraint satisfaction problems (CSP) are part of many real world domains, such as computer vision and scheduling problems. Often, CSPs are solved in real life by several agents, each of them working on a part of the problem [3, 4]. A distributed CSP can be viewed as a set of constraint networks(CN), each CN being solved by a different agent, where the CNs are connected by constraints. A major assumption of the present paper is that checking constraints inside the distributed components has a much lower cost than checking constraints across different components. The latter check involves some kind of message passing that the solving algorithm would like to minimize. The processing of CNs have been studied extensively in the last decade [1, 2], usually within the standard model which is sequential. Several at tempts have been made at studying the processing of CNs in parallel The most relevant study of distributed CSPs has been made by Yokoo [5]. The basic difference between our approach and Yokoos approach is that our algorithms try to take advantage of the differences between the DCSPs components. The model of a DCSP of the present paper uses agents that are connected by a communication network (i.e., no common memory, just message passing). The number of agents is equal or larger by a small constant, to the number of subproblems in the given division of the DCSP. Based on this we state the following goals for our multi-agent algorithms:

Employee Timetabling, Constraint Networks and Knowledge-Based Rules: A Mixed Approach

Employee timetabling problems (ETP) usually involve an organization with a set of tasks that need to be fulfilled by a set of employees, each with his/her own qualifications, constraints and preferences. The organization usually enforces some overall constraints and attempts to achieve some global objectives such as a just or equitable division of work. Examples for such problems are: assignment of nurses to shifts in a hospital, or assignment of phone operators to shifts and stations in a service-oriented call-center. One possible approach for solving ETPs is to use constraint processing techniques. Another approach is to model human knowledge into knowledge-based systems for timetabling. The present paper presents an approach to representing and processing employee timetabling problems (ETP) by a combination of explicit representations of some constraints in the network and rule-based processing in which specific heuristics for generic constraints of ETPs are embedded. The mixed-mode approach has been implemented in the form of a commercial software package for defining and solving real world ETPs. Example of a real world ETP is followed through the presentation and is used to experimentally compare standard CSP techniques with the proposed mixed-mode approach.

Combining rules and constraints for employee timetabling

Employee Timetabling Problems (ETP) are all around us. One possible approach for solving ETPs is to use constraint processing techniques. Another approach is to model human knowledge which is commonly used for solving such problems into knowledge‐based systems for timetabling. It is difficult to represent the complex constraints of timetabling explicitly in constraint networks. On the other hand, knowledge‐based representations of constraints are implicit and cannot support most of the heuristics of constraint‐based processing that have been developed over the last decade. The present article presents on approach to representing and processing employee timetabling problems by a combination of explicit representations of some constraints and rule‐based processing with heuristics for generic ETP constraints. This mixed‐mode approach has been implemented in the form of a software package for defining and solving real‐word ETPs. A general description of the design and organization of this software tool is given. Results for solving a typical real‐world employee timetabling problem are presented and a comparison with the use of standard CSP (Constraint Satisfaction Problems) techniques is made.

CSPs with counters: a likelihood-based heuristic

Abstract. Counter constraints are a naturalrepresentation of constraints on the finite capacity of resources in resource-allocation type problems. They are a generic family of non-binary constraints that limit the number of variables that may be assigned particular values. Counter constraints can be represented by binary constraints, at a cost. We analyse the cost, show how a counter can be represented as a linear number of binary constraints, and demonstrate empirically that even with the optimal reduction,an explicit representation of counters is preferable to their representation as a set of binary constraints. For counter constraints, value ordering is essential. An heuristic for value ordering on constraint satisfaction problems (CSP), based on the estimated likelihoodof a solution, is presented. The proposed value ordering heuristic is useful for counter constraints, as well as for binary CSPs, where it can be used to approximate the number of solutions consistent with a particular value assignment ...

Bayes networks for estimating the number of solutions of constraint networks

The problem of counting the number of solutions to a constraint network (CN) (also called constraint satisfaction problems, CSPs) is rephrased in terms of probability updating in Bayes networks. Approximating the probabilities in Bayes networks is a problem which has been studied for a while, and may well provide a good approximation to counting the number of solutions. We use a simple approximation based on independence, and show that it is correct for tree‐structured CNs. For other CNs, it is less optimistic than a spanning‐tree approximation suggested in prior work. Experiments show that the Bayes nets estimation is more accurate on the average, compared to competing methods (the spanning‐tree, as well as a scheme based on a product of all compatible pairs of values). We present empirical evidence that our approximation may also be a useful (value ordering) search heuristic for finding a single solution to a constraint satisfaction problem.