TITLE:
Cluster Search Algorithm for Finding Multiple Optima
AUTHORS:
John Guenther, Herbert K. H. Lee
KEYWORDS:
Bayesian Statistics, Treed Gaussian Process, Emulator, DBSCAN, Optimization
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.7,
April
28,
2016
ABSTRACT: The black box functions found in computer experiments often result
in multimodal optimization programs. Optimization that focuses on a
single best optimum may not achieve the goal of getting the best answer for the
purposes of the experiment. This paper builds upon an algorithm introduced in
[1] that is successful for finding multiple optima within the input space of
the objective function. Here we introduce an alternative cluster search
algorithm for finding these optima, making use of clustering. The cluster
search algorithm has several advantages over the earlier algorithm. It gives a
forward view of the optima that are present in the input space so the user has
a preview of what to expect as the optimization process continues. It employs
pattern search, in many instances, closer to the minimum’s location in input
space, saving on simulator point computations. At termination, this algorithm
does not need additional verification that a minimum is a duplicate of a
previously found minimum, which also saves on simulator point computations.
Finally, it finds minima that can be “hidden” by close larger minima.