The phase-transition niche for evolutionary algorithms in timetabling

Abstract

Constraint satisfaction problems tend to display phase transitions with respect to the effort required by specific problem solving strategies. So far, little is known concerning the causes of phase transitions, or the relative differences between performance of different algorithms around them, especially with respect to stochastic iterative methods such as evolutionary search. Also, work so far on phase transitions concentrates on homogeneous random problems, rather than problems displaying elements of structure typical of more realistic problems. We investigate some of these issues, and uncover some new phase transition regions on timetabling style problems, occurring in the context of varying degrees of problem homogenity as well as (the more standard) graph connectivity. Further, we find that a simple evolutionary algorithm outperforms a simple Stochastic Hillclimber in regions strongly associated with certain phase transitions, and not others. Finally, we discuss various clues to the underlying causes of these phase transitions.