The paper presents the novel approach to solve some problems occurred in application of the genetic algorithm to the determination of the optimal tire pattern sequence in order to reduce the tire air-pumping noise which is generated by the repeated compression and expansion of the air cavity between tire pattern and road surface. The genetic algorithm has been used to find the optimal tire pattern sequence having a low level of tire air-pumping noise using the image based air-pumping model. In the genetic algorithm used in the previous researches, there are some problems in the encoding structure and the selection of objective function. The paper proposed single encoding element with five integers, divergent objective function based on evolutionary process and the optimal evolutionary rate based on Shannon entropy to solve the problems. The results of the proposed genetic algorithm with evolutionary process are compared with those of the randomized algorithm without evolutionary process on the two-dimensional normal distribution. It is confirmed that the genetic algorithm is more effective to reduce the peak value of the predicted tire air-pumping noise and the consistency and cohesion of the obtained simulation results are also improved in terms of probability.