Is there any statistical measure comparing different sets of location configurations?

[Tae-Jung_JonathanKwon]

Hello,

My question may seem confusing but here is what I'd want to do;

I have a given set of facility locations as shown below, ;

And based on a predefined optimization criterion, I optimized the whole network and obtained the following configuration;

I understand that whatever the optimization criterion I used, I can simply look at the criterion value for both and say that the optimized network is "better". But I am need of another statistical measure that will tell how similar or different the new network (i.e., 2nd figure) is when compared to the existing network (i.e., 1st figure). Below is the figure showing both configurations;

I am not so sure if that performance or benchmarking measure is available to quantitatively describe how similar/different the optimized network is to the existing one, but it will be useful when I have different sets of optimization results using different criteria and see which criterion would give the solution that best matches the existing one.

Any comments or thoughts are greatly appreciated.

[DarrenWiens2]

Can you compare statewide point density variance? It looks like the main difference is that point density is more variable (more clumps and voids) in the optimized surface than the more even original surface.

[Tae-Jung_JonathanKwon]

I am not sure if that will provide a definite measure for comparing how close the optimized network is to the existing one. There are several different optimized configurations obtained through utilizing different optimization criteria and the intent here is to quantitatively assess which optimization criterion would provide a solution that is most similar to the existing network... will the point density estimation do the job in this case?? Thanks for your answer though...