The paradox of multimodal optimization: Concepts vs. species in single and multi-objective problems

It is well-known that decision-makers are often interested in searching for multiple alternative solutions. A major goal of multimodal optimization is to find such alternatives by searching for multiple peaks in the landscape. However, as claimed and demonstrated here with respect to that goal, the notion of multi-modal optimization is problematic on a fundamental level. Moreover, as discussed here, the notion of multimodal optimization is, for the most of it, restricted to single objective optimization. Following the above argumentation, this paper provides some overview on the set-base concept approach and describes how this approach can be used to produce meaningful solution alternatives for the decision-makers both for single and multi-objective problem. It is concluded that, when decision-makers are interested in finding multiple solutions, the use of the set-based concept approach is a valid alternative to multimodal optimization.