Testing Surrogate-Based Optimization with the Fortified Branin-Hoo
Extended to Four Dimensions
- URL: http://arxiv.org/abs/2107.08035v1
- Date: Fri, 16 Jul 2021 17:56:32 GMT
- Title: Testing Surrogate-Based Optimization with the Fortified Branin-Hoo
Extended to Four Dimensions
- Authors: Charles F. Jekel, Raphael T. Haftka
- Abstract summary: This paper examines the effect of fortifying the Branin-Hoo function on surrogate-based optimization.
It is found that the difference between the ordinary function and the fortified one was much more pronounced for the four-dimensional function.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Some popular functions used to test global optimization algorithms have
multiple local optima, all with the same value, making them all global optima.
It is easy to make them more challenging by fortifying them via adding a
localized bump at the location of one of the optima. In previous work the
authors illustrated this for the Branin-Hoo function and the popular
differential evolution algorithm, showing that the fortified Branin-Hoo
required an order of magnitude more function evaluations. This paper examines
the effect of fortifying the Branin-Hoo function on surrogate-based
optimization, which usually proceeds by adaptive sampling. Two algorithms are
considered. The EGO algorithm, which is based on a Gaussian process (GP) and an
algorithm based on radial basis functions (RBF). EGO is found to be more frugal
in terms of the number of required function evaluations required to identify
the correct basin, but it is expensive to run on a desktop, limiting the number
of times the runs could be repeated to establish sound statistics on the number
of required function evaluations. The RBF algorithm was cheaper to run,
providing more sound statistics on performance. A four-dimensional version of
the Branin-Hoo function was introduced in order to assess the effect of
dimensionality. It was found that the difference between the ordinary function
and the fortified one was much more pronounced for the four-dimensional
function compared to the two dimensional one.
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