The optimization problem of triviality search in group presentations

This paper transforms the triviality search problem in group presentations into an optimization problem by defining decision variables, objective functions, and constraints, and conducts an in-depth analysis of the scale and complexity of the proposed model, highlighting its computational challenges. A genetic algorithm-based solution framework is designed to efficiently search for Andrews-Curtis transformation sequences, and its effectiveness for specific group presentations is validated, successfully solving the Andrews-Curtis transformation sequence search problem. This study not only provides a novel methodology for addressing the triviality search problem but also demonstrates the practical application of optimization techniques in group theory, offering new insights for future research in this field.