Constraining Special-Purpose Domain Types

Abstract

With an open-ended constraint solver it is possible to introduce new facilities for modeling a problem. To illustrate this approach, we present as a case study how OpenSolver [2] can be configured as a solver for the job-shop scheduling problem (JSSP). OpenSolver is configured using plug-ins for several aspects of constraint solving. Here we use special-purpose domain types (sets of domains that can be associated with a variable) and reduction operators.

A JSSP instance consists of several jobs that themselves consist of a number of activities. Activities are characterized by a resource that is needed to process the activity, and by how long the activity claims this resource. The constraints are: all activities of a job must be processed in a specified order, and no two activities can use the same resource simultaneously. The goal is to find starting times for all activities such that the total processing time (makespan) is minimal.

A CP model for this problem uses a variable for the starting time and completion time of each activity [1]. When doing a complete search for the minimal makespan, branching is on the order in which resources are assigned to the activities that require them. The nodes of the search tree correspond to partial schedules, for which constraint propagation verifies feasibility. Search can be implemented by posting and retracting precedence constraints.