[EM] District continuity preserving re-districting

[atarr at purdue.edu]

Quoting Niemzinski at ecybermind.net:

> I wasn't clear.  With a single objective optimization the best re-districting
> is
> the one that achieves the smallest (or largest for maximization) objective. 
> The problem with multi-objective optimization for re-districting isn't that
> it
> can't be done.  The problem with it in this context is how do you determine
> which re-districting is "best"?



It's actually relatively simple.  You just need to design an objective function 
that thakes all of your criterion into account.  Say you have some function 
which calculates the P = summed "population moment of inertia" of the 
districts, and the S = summed "severed transportation network links" of the 
districts.  Both of these criterion should be minimized.

A reasonable objective function would be a*P + b*S, where a and b are chosen to 
give the two criteria the relative importance desired.

Another reasonable objective function (I'd prefer this) would be (P^a)*(S^b), 
again choosing a and b to give each criteria the relative importance desired.

And you could introduce the constraints mentioned by Matt.  Then set up some 
sort of iterative nonlinear optimization program to search for a solution.

Of course, all I've done is abstract out your "how do you determine
which re-districting is 'best'?" question into the "what values should 'a' and 
'b' have" question, but that's an easily defined problem, and you can tweak the 
numbers if you don't like the results.