ABSTRACT. We give a brief account of some of the traditional ways that genetic algorithms have been applied, and explain how our approach to the use of genetic algorithms for solving problems in combinatorial group theory differs. We find that, in our situation, there seems to be a correlation between successful genetic algorithms and the existence of good non-genetic, sometimes deterministic, algorithms. We use a class of equations in free groups as a test bench. In particular, it allows us to trace the convergence of co-evolution of the population of fitness functions to a deterministic solution.