There is no single cure for such a general question. The question remains difficult even for the single objective optimization. The convergence and the diversity are the hardest to harmonize. Sorry for vague answer, but the trial and error and an experience of other researchers is still the best approach.
The diversity depends on the solving method used. By example, some algorithms of the Integration of Variables Method (see "The Integration of Variables method" and "Analysis and Synthesis of Engineering Systems" in my researchgate profile). In the convergence criterion could be included, as an additional component reaching some diversity in the final population.
Correcting the previous answer: The diversity depends on the solving method used. By example, some algorithms of the Integration of Variables Method provide acceptable diversity.
the convergence and diversity are opose aspects of multicriterial optimization but you can harmonize this aspects with many different methods that included weight variables behind the solutions.