That may by OK if tweaking the model to get a preferred outcome is OK.  But if our goal is keep out gerrymandering then we are probably better off without placing tweak variables in the objective function.  Using the same units of measurement for all of the variables in the objective function avoids the need for such tweak variables.

If we are going to introduce tweak variables then I think it is better to place them in the constraints.  Each constraint is for a single unit of measure so different units would have their own set of constraints.  Constraints can be iteratively tightened/loosened to find the boundary conditions that define which combination of constraints are infeasible for a given map input.  A well-defined formal procedure for doing this systematically can remove subjectivity.

For example, the maximum difference between district population size constraint can be reduced to the minimum feasible amount first.  Then another constraint, such as the district continuity constraint, can be added and iteratively tightened to find the feasibility boundary.  After the feasibility boundary is found the constraint can be loosened by some pre-determined method to provide slack for optimizing the objective.  This works best if the number of constraints is kept to a minimum.

It is better to avoid non-linearity in the model and to keep integers out of the objective function.  Non-linear integer optimization is more difficult than integer linear optimization which is more difficult than non-integer linear optimization.  All other things being equal the less complicated the optimization model the more opportunity for mathematically sophisticated citizens to be competitive re-districting participants and the more consistently the re-districting result will be close to reaching the objective and thus satisfy the public and the courts that the process is fair.

Also, from this perspective it is better to provide proportional representation opportunity by implementing a PR election method within multi member districts than to add additional constraints in an effort to corral a majority of some minority into a single member district.  Optimizing for compact districts is not neutral, it can favor or disfavor minority representation depending on the geographic and demographic details.  Of course, geographic and demographic details impact PR election methods also, but with multiple districts the overall impact may be more balanced.

Adam Tarr wrote:

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.