Explaining Time-Table-Edge-Finding Propagation for the Cumulative Resource Constraint

Cumulative resource constraints can model scarce resources in scheduling problems or a dimension in packing and cutting problems. In order to efficiently solve such problems by a constraint programming solver, it is important to have strong and fast propagators for cumulative resource constraints. One such propagator is the recently developed time-table-edge-finding propagator which considers the current resource profile during the edge-finding propagation. Recently lazy clause generation solvers, i.e., constraint programming solvers incorporating nogood learning, have proved to be excellent at solving scheduling and cutting problems. For such solvers, concise and accurate explanations of the reasons for propagation are essential for strong nogood learning. In this paper, we develop a first explaining version for time-table-edge-finding propagation and show preliminary results on resource-constrained project scheduling problems from various standard benchmark suites. On the standard benchmark suite PSPLib, we were able to close one open instance and to improve the lower bound of about 60% of the remaining open instances and, even, close 6 of them.