Application of the hardness theory when solving the timetabling problem with genetic algorithms

This paper describes an investigation for applying the hardness theory, developed for constraint type problems, when solving the timetabling problem in particular. The main idea is to compare the performance of the genetic algorithm when evaluating the individuals in the population by either the normal penalty function or by the hardness-based measure. The reported experiments consider instances of the timetabling problem with only edge constraints, and the hardness-based function is evaluated by considering the difficulty to solve the remaining subproblem in each chromosome, that is, by taking only the violated constraints and the events involving those constraints at a particular stage. Results obtained show that the applicability of the hardness theory with respect to the fitness function is very limited for the timetabling problem, since features such as the combination of the number of events on the unsolved subproblem, the number of constraints among those events, and the number of time slots, makes it very difficult to adjust the proper conditions for which the theory is able to work