In the literature, the term premature convergence of the entire population is used with the meaning of closing the evolution before reaching the optimal point. It can be emphasized only on a test function with known landscape. If the function landscape is unknown, one can notice the population convergence only. This paper aims to answer to the question: ”how can we influence the control parameters of the genetic algorithm so that the exploration time of the parameter space be longer and the risk of premature convergence be reduced?”. The answer to the above question implies choosing a crossover operator with good performances in the landscape exploration and the use of two performance indicators for the detection of the population convergence. In choosing the control parameters of the genetic algorithm, the fitness function landscape must be taken into consideration.