Open Constraint Optimization

Constraint satisfaction has been applied with great success in closed-world scenarios, where all options and constraints are known from the beginning and fixed. With the internet, many of the traditional CSP applications in resource allocation, scheduling and planning pose themselves in open-world settings, where options and constraints must be gathered from different agents in a network. We define open constraint optimization as a model of such tasks. Under the assumption that options are discovered in decreasing order of preference, it becomes possible to guarantee optimality even when domains and constraints are not completely known. We propose several algorithms for solving open constraint optimization problems by incrementally gathering options through the network. We report empirical results on their performance on random problems, and analyze how to achieve optimality with a minimal number of queries to the information sources. 1 Constraint Optimization in Distributed Systems Constraint satisfaction and optimization has been applied with great success to resource allocation, scheduling, planning and configuration. Traditionally, these problems are solved in a closed-world setting: all variable domains and constraints are assumed to be completely known, then the problem is solved by a search algorithm. With increasing use of the internet, many of the problems that constraint programming techniques are good at now pose themselves in a distributed setting. For example, in personnel allocation, it is possible to obtain staff from partner companies. In configuration, it is possible to locate part suppliers through the internet. Furthermore, problems may also involve agents with different and possibly conflicting interests, for example when allocating production resources among different factories. Figure 1 illustrates the context we assume: a set of m agents wish to find an assignment to a set of variables that is optimal with respect to their preferences. A central CSP solver is tasked to find this solution, and queries the agents for their options and preferences using queries more(xi,di). Agents will return their options starting with the one they would most prefer as a solution, and then in F. Rossi (Ed.): CP 2003, LNCS 2833, pp. 303–317, 2003. c © Springer-Verlag Berlin Heidelberg 2003 304 Boi Faltings and Santiago Macho-Gonzalez