Concentrating on the convergence analysis of Genetic Algorithm (GA), this study originally distinguishes two types of advantage sources: value advantage and relationship advantage. Accordingly, the quantitative feature, complete quantization feature, and the partial quantization feature in the fitness evaluation are proposed. Seven simulation experiments show that these two types of advantages have different convergence properties. For value advantage problems, GA has a good convergence. However, for a relationship advantage problem, only from the practical point of view, it is possible to get a feasible and even satisfactory solution through large-scale searching, but, in theory, however, the searching process is not convergent. Therefore, GA is not reliable to solve relationship advantage problems, to which most engineering problems involving combinatorial optimization belong. This study systematically shows convergence properties of “relationship advantage” through simulation experiments, which will be a new area for the further study on GA.