Towards scalability in niching methods

Abstract

The scaling properties of multimodal optimization methods have seldom been studied, and existing studies often concentrated on the idea that all local optima of a multimodal function can be found and their number can be estimated a priori. We argue that this approach is impractical for complex, high-dimensional target functions, and we formulate alternative criteria for scalable multimodal optimization methods. We suggest that a scalable niching method should return the more local optima the longer it is run, without relying on a fixed number of expected optima. This can be fulfilled by sequential and semi-sequential niching methods, several of which are presented and analyzed in that respect. Results show that, while sequential local search is very successful on simpler functions, a clustering-based particle swarm approach is most successful on multi-funnel functions, offering scalability even under deceptive multimodality, and denoting it a starting point towards effective scalable niching.