Evolutionary optimisation of methodist preaching timetables

Abstract

Methodist churches are arranged into local circuits with, for example, some 30 churches existing in a local area covering about 1,000 square miles. A central element of Methodist religious life at a particular church is the frequent delivery of sermons and similar activities by preachers who are not based at that particular church. Periodically, it is the job of a senior member of the Methodist movement in a local area and his or her staff to draft a preaching timetable. This may involve, for example, about 40 or 50 ministers (of different seniorities and types), 30 or 40 churches, and the need to fill each of 3 or 4 preaching slots every Sunday at each church in the region. The problem of finding a suitable preaching timetable involves a variety of idiosyncratic constraints which make it an interesting variation on the general timetabling problem. Here we look at various simple approaches to the problem, which draw on the two main styles of approach to stochastic iterative timetabling (direct and indirect representations), and compare three well-known search techniques: evolutionary algorithms, simulated annealing, and hillclimbing. In the context of finding a successful approach to a problem with development time at a premium (hence: using simple implementations) we find strong support for the superiority of an “indirect” timetable representation over a direct one. We also find that simulated annealing is generally the more robust method over a range of problems, with all other methods except hillclimbing performing strongly in particular cases.