The aim of the simulation study presented is to make a comparison between two different approaches to adaptive control of the bioreactor performance applied to a continuous baker's yeast culture. The first approach, self-tuning extremum control, is based on a dynamic model identification with a classical gradient optimization technique. This method is not time consuming and has a good adaptability but requires a continuous, on-line measurement of the most relevant process variables which can be rarely satisfied. Therefore, a second, different approach, the ISOPE optimizing procedure is proposed, utilising only occasional in-situ, off-line or laboratory measurement of the key process variable and shows similar or better performance as the previous approach. Comparative simulation results for two cases of objective functions are presented. Each approach has been applied to maximize the cellular productivity by manipulating with the dilution rate and, respectively, to minimize a deviation between the real process output value and its set point by manipulating with the air flow rate. The performances are evalueted in terms of optimization speed and accuracy, reoptimization capability (or adaptability) and long term operational stability. The ISOPE optimizing procedure was shown to be able to reoptimize the culture when planned disturbances were introduced.