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

TL;DR

This paper introduces an explaining version of the time-table-edge-finding propagator for cumulative resource constraints, enhancing solver explanations and demonstrating improved performance on scheduling benchmarks.

Contribution

It develops the first explaining version of the propagator, enabling better nogood learning in constraint programming solvers for scheduling problems.

Findings

Closed one open instance in PSPLib benchmark.

Improved lower bounds on 60% of remaining instances.

Closed 6 instances in total.

Abstract

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 with 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 the first explaining version of 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. Moreover, 6 of those instances were closed.