ACO with automatic parameter selection for a scheduling problem with a group cumulative constraint

We consider a RCPSP (resource constrained project scheduling problem), the goal of which is to schedule jobs on machines in order to minimise job tardiness. This problem comes from a real industrial application, and it requires an additional constraint which is a generalisation of the classical cumulative constraint: jobs are partitioned into groups, and the number of active groups must never exceeds a given capacity (where a group is active when some of its jobs have started while some others are not yet completed). We first study the complexity of this new constraint. Then, we describe an Ant Colony Optimisation algorithm to solve our problem, and we compare three different pheromone structures for it. We study the influence of parameters on the solving process, and show that it varies from an instance to another. Hence, we identify a subset of parameter settings with complementary strengths and weaknesses, and we use a per-instance algorithm selector in order to select the best setting for each new instance to solve. We experimentally compare our approach with a tabu search approach and an exact approach on a data set coming from our industrial application.