Adam wrote: 
"Only if there is only one input variable in the objective function.  As soon as
you have more than one input variable, there is some implicit weight being applied to each input.  All I'm doing is making it explicit."

With a map grid as input, it seems to me that the perimeter length qualifies as a single variable objective function.  If there is a compelling justification for not using a single variable, linear, continuous objective function then I am not aware of it.  In particular, the goal of district continuity is well-suited to be represented by a constraint.

Adam wrote: 
"We can't really avoid discrete operations here.  People are not continuous.
More to the point, I think it's a good idea to not allow census blocks to be
split into more than one district.  This means you must work in groups of
several thousand people."

In the U.S. context, my understanding is that courts have been strict with
their interpretation of one person one vote.  In particular, I think there
is a US Supreme Court decision defining one man one vote for Congressional
districts.  U.S. census blocks vary considerably in population size, and that variance is presumably even larger for voting eligible population.