The number of objectives in real-world problems has increased in recent years and better algorithms are needed to deal efficiently with it. One possible improvement to such algorithms is the use of adaptive operator selection mechanisms in many-objective optimization algorithms. In this work, two adaptive operator selection mechanisms, Probability Matching (PM) and Adaptive Pursuit (AP), are incorporated into the NSGA-III framework to autonomously select the most suitable operator while solving a many-objective problem. Our proposed approaches, NSGA-III$$_backslashtext AP$$and NSGA-III$$_backslashtext PM$$, are tested on benchmark instances from the DTLZ and WFG test suits and on instances of the Protein Structure Prediction Problem. Statistical tests are performed to infer the significance of the results. The preliminary results of the proposed approaches are encouraging.