Scheduling with Structured Preferences

Abstract

AbstractThe problem of finding a feasible schedule for a partially ordered set of tasks can be formulated as a Disjunctive Temporal Problem (DTP). While there exist extensions to DTPs that augment them by associating numeric costs to the violation of individual temporal constraints, they still make the restrictive assumption that the costs associated with constraints are independent of one another. In this paper we propose a further extension, which enables the designer to specify (directional) dependencies between the preferences associated with the constraints. Such preferences are represented by exploiting Utility Difference Networks (UDNs) that allow for the definition of structured objective functions based on the notion of conditional difference independence (CDI). Thanks to such conditional independencies, the specification of the utilities and the computation of the utility of (partial) solutions explored during the search for an optimal solution, turn out to be very similar to how probabilities are handled within a Bayesian Network. The paper presents a branch-and-bound algorithm for solving this new class of problems, analyzes its computational complexity and reports some encouraging experimental results.KeywordsDisjunctive Temporal Problem (DTP)Temperature ProblemJoint AlgorithmTemporal Constraint Satisfaction Problem (TCSPs)Mixed Logical Linear Program (MLLP)These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.