Solving High School Timetabling with Satisfiability Modulo Theories

High School Timetabling (HSTT) is a well known and wide spread problem. The problem consists of coordinating resources (e.g. teachers, rooms), time slots and events (e.g. lectures) with respect to various constraints. Unfortunately, HSTT is hard to solve and just finding a feasible solution for simple variants of HSTT has been proven to be NP-complete. In addition, timetabling requirements vary from country to country and because of this many variations of HSTT exist. Recently, researchers have proposed a general HSTT problem formulation in an attempt to standardize the problem from different countries and school systems. In this paper, for the first time we provide a new detailed modeling of the general HSTT as a Satisfiability Modulo Theory (SMT) problem in the bit vector form. In addition, we present preliminary experimental results and compare to the winner of the Third International Timetabling Competition 2011 (ITC), using both artificial and real-world instances, all of which were taken from ITC 2011 benchmark repository. Our current approach provides feasible solutions for some examples, which in some cases could not have been obtained with the competition winner algorithm within 24 hours.