Mining business process models from running logs is in its ascendant. Inevitably, the ever changing operational environment makes these log records diverse. Considering every mining algorithm has its pros and cons, this paper focuses on the challenge to apply a best mining algorithm against diverse logs. A novel approach, SoFi (survival of fittest integrator), is proposed to mine business process models effectively in such a diverse environment. SoFi tackles the diversity issue by utilizing domain knowledge to classify the cases in a log and applying various mining algorithms on these categories to obtain comprehensive process models as candidates for optimization. A genetic algorithm (GA) based optimizer takes these candidates as initial population for purpose of both genetic quality as well as genetic diversity. Under the principle of survival of fittest, the GA optimizer can aggregate best process fragments with context into the final process model for the entire log. Experiments on synthetic data and real cases from a telecommunication firm demonstrate the effectiveness of SoFi and comprehensive quality of mined process models in terms of replay fitness, accuracy, generalization, and simplicity.