In recent years, Multi-Objective Evolutionary Algorithms (moeas) that consider diversity as an objective have been used to tackle single-objective optimisation problems. The ability to deal with premature convergence has been greatly improved with these schemes. However, they usually increase the number of free parameters that need to be tuned. To improve results and avoid the tedious hand-tuning of algorithms, the use of automated parameter control approaches that are able to adapt parameter values during the course of an evolutionary run are becoming more common in the field of Evolutionary Computation (ec). This research focuses on the application of parameter control approaches to diversity-based moeas. Two external parameter control methods are investigated; a novel method based on Fuzzy Logic and a recently proposed Hyper-heuristic. These are compared to an internal control method that uses self-adaptation. An extensive comparison of the three methods is carried out using a set of single-objective benchmark problems of diverse complexity. Analyses include comparisons to a wide range of schemes with fixed parameters and to a single-objective approach. The results show that the fuzzy logic and hyper-heuristic methods are able to find similar or better solutions than the fixed parameter methods for a significant number of problems, with considerable savings in computational resources and time, whereas the self-adaptive strategy provides little benefit. Finally, we also demonstrate that the controlled diversity-based moea outperforms the single-objective scheme in most cases, thus showing the benefits of solving single-objective problems through diversity-based multi-objective schemes.