Local Probing Applied to Scheduling

This paper describes local probing, an algorithm hybridiza-tion form that combines backtrack search enhanced with local consistency techniques (BT+CS) with local search (LS) via probe backtrack-ing. Generally BT+CS can be eeective at nding solutions for (or proving the infeasibility of) tightly constrained problems with complex and overlapping constraints, but lacks good optimization characteristics. By contrast, LS can be superior at optimizing problems that are loosely constrained , or that have constraints which are satissable by simple neighbourhood procedures, but it also has several weaknesses of its own. It is weaker on problems with a complex constraint satisfaction element, and cannot prove problem infeasibility, causing prolonged execution times and ambiguous search outcomes for even trivially infeasible problems. We show these divergent characteristics on a general resource constrained scheduling problem class, extended with a widely applicable objective function. We then detail a local probing hybrid that marries the strengths of constraint satisfaction techniques, including good satisfaction characteristics and proofs of problem infeasibility, with the superior optimization characteristics of LS. This local probing hybrid achieves sat-completeness, without incorporating all the constraints into the LS neighbourhood function. Finally, we discuss the principal questions that must be answered in creating local probing hybrids for other problems.