Parameter control involves dynamically adjusting the parameter values of the evolutionary algorithm throughout the optimization process, including parameters like mutation rate and operator selection. Self-adaptation can improve the performance and robustness of the algorithm, however, parameter control mechanisms themselves need to be designed and configured carefully. In this article, we review the cumulative step size adaptation method originally proposed for single-objective optimization over continuous variables and recast it for deployment in multiobjective optimization over unbounded integer space. We contribute a systematic investigation of its hyperparameters which shows that while (1) the very best configurations remain problem-specific, (2) the performance of the algorithm is largely independent of the self-adaptation scheme’s parameterization and initial configuration.