  Creating diverse sets of high quality solutions has become an important
problem in recent years. Previous works on diverse solutions problems consider
solutions' objective quality and diversity where one is regarded as the
optimization goal and the other as the constraint. In this paper, we treat this
problem as a bi-objective optimization problem, which is to obtain a range of
quality-diversity trade-offs. To address this problem, we frame the
evolutionary process as evolving a population of populations, and present a
suitable general implementation scheme that is compatible with existing
evolutionary multi-objective search methods. We realize the scheme in NSGA-II
and SPEA2, and test the methods on various instances of maximum coverage,
maximum cut and minimum vertex cover problems. The resulting non-dominated
populations exhibit rich qualitative features, giving insights into the
optimization instances and the quality-diversity trade-offs they induce.
