Dynamic All-Different and Maximal Cliques Constraints for Fixed Job Scheduling
Résumé
The resolution of Fixed Job Scheduling (FJS) with
Constraint Programming can benefit from the initial computation
of the set of all maximal cliques over the task intervals to post
All-Different constraints over the allocation variables. However,
when direct successors are assigned during the search, single
tasks can be replaced by task chains with a longer duration and
possibly added to some of the original cliques to strengthen the
model.
We propose a new global constraint to efficiently maintain
all the maximal cliques over the task chains of an FJS problem
upon successor assignment, which can be used to add variables to
Dynamic All-Different constraints posted on the original cliques
instead of static ones. Experiments on random and real-world
instances of the Gate Allocation Problem, a classic application
of FJS, show that our approach can outperform former models
and state-of-the-art MIP solver by orders of magnitude.