How can we determine the mathematical property of a high-dimensional benchmark problem?
Take, for example, the n-dimension Rosebrock equation. It is a unimodal equation with localized behaviour in 2 dimensions (We can tell this from the 2D plot). However, if the dimension is taken greater than 3, the equation shows multimodal behaviour. In short, the mathematical characteristic may change according to the dimension change. How can we determine the mathematical characteristic of an equation with different dimensions using a small number of analysis results obtained in the design space?
The n-dimensional Rosebrock equation is shared from the link below.
https://www.sfu.ca/~ssurjano/rosen.html
As a method, we thought that the effect of the parameters in the high-dimensional equation on the result could be examined and the results would be decided by plotting the two-dimensional results for the two most dominant variables. But we are not sure whether it will give correct results for every equation. We will analyze the results by conducting experiments. Other than that, do you have any other suggestions?
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