Locating Multiple Optima with Dynamic Design Space Partitioning


Example:

The Branin-Hoo function is a popular benchmark test function for global optimization algorithms.  The contours are shown in the figure below, where the three global optima are represented by yellow stars.


In this video, dynamic design space partitioning is used to locate the three global optima. A local surrogate is used in each sub-region.  The initial size of the DOE is 12.  There is initially 1 sub-region, with a minimum of 1 and maximum of 6 allowed.  It is observed that the centers of the sub-regions stabilize around all optima.

Description of symbols
Yellow stars: True optima
Black circles: Centers of sub-regions (centers of agents sub-region)
White triangles: Points added in iteration
Black x: current database of all points