The retention of diversity of genetic information is an important aspect of many population-based evolutionary optimizers. With the increasing relevance of dynamic optimization, where live data is streamed directly into a running optimization system, this algorithmic facet gains new importance. This study compares five different strategies for handling diversity in genetic algorithms in a dynamic open-ended optimization scenario. Using the traveling salesman problem as a benchmark, the algorithmic variations are compared and analyzed with respect to their performance and retained diversity. Results indicate that convergence patterns behave differently from static optimization and several algorithm features that are well understood for static optimization may have unintended consequences in dynamic scenarios.