Using genetic algorithms to generate Steiner triple systems

摘要

Steiner systems, particularly triple systems, are usually generated by mathematicians using techniques from the theory of groups and quasi-groups. When pencil-and-paper enumeration becomes infeasible, mathematicians have used computers to carry out exhaustive searches. This paper presents some results of using genetic algorithms, which do not use exhaustive search, to generate Steiner systems. A specialized mutation operator was effective in generating Steiner triple systems. Future research will focus on improving the genetic algorithm to generate higher order Steiner systems whose existence is not currently known.