Evolutionary algorithm in group theory

In the study of group theory, coset enumeration is a major technique for determining the order of finitely presented groups. ACE is an important computer implemented coset enumeration system. It provides a wide choice of parameter settings, which can derive different strategies for enumeration. In this paper, an evolutionary algorithm is used to optimize parameter settings for ACE to discover better enumerations for several classic groups. The results show that the evolutionary algorithm discovers ACE parameter settings that construct previously unknown enumerations that are more optimal than enumerations discovered by hand or using brute-force search techniques.