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.
[pdf]
@inproceedings{Kron10Niching,
author = {Kronfeld, Marcel and Zell, Andreas},
title = {Towards Scalability in Niching Methods},
booktitle = {Proceedings of the IEEE Congress on Evolutionary Computation (CEC)},
year = {2010},
pages = {4409--4416},
address = {Barcelona, Spain},
month = jul,
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.},
isbn = {978-1-4244-6910-9},
url = {http://www.cogsys.cs.uni-tuebingen.de/publikationen/2010/Kron10Scaling.pdf}
}