Evolutionary computation in coset enumeration.

摘要

In computational group theory, coset enumeration is an important technique for investigating finitely presented groups. We make a novel application of evolutionary computation to increase the efficiency of coset enumeration program. The program we work with is ACE, developed by Havas and Ramsay. In principle, coset enumeration will succeed whenever a presented group is finite. However, the space available during the enumeration determines the maximum number of coset defined. ACE has a wide choice of parameter settings, which can determine different strategies for enumeration. To discover good parameter combinations in order to produce space saving strategies is a challenging topic for research. Evolutionary computation is a heuristic search method based on principles of evolution and heredity. We apply evolutionary computation on top of ACE trying to find ideal parameter settings. This approach yields some significant results.