Recently worked with Dale Nimmo and our honours student Andrew on optimizing abundance (or the geometric mean of abundance) based on land types. I found it a really interesting problem, as trying to using a general solver generally just didn’t work. The optimization is essentially with respect to the objective:

∏_i=1…n (∑w_j x_ij)

and so non-linear. However by representing the geometric mean as the sum of logs and, in turn, the logarithmic function as the max min of linear functions then we’re able to solve it linearly. I also looked at a bilevel approach for maximizing Shannon’s diversity.

The code is available here:

http://www.deakin.edu.au/~sjames/R_files/LAND-USE.R

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