Another Domain?

[Matt Gokey <mgokey@xxxxxxxxxx>]

A few weeks ago I posted a message introducing a roughly defined idea,
the gist of which was to try to sample the search space of go using
"atomic moves" made up of multiple single stone moves and "searching"
using these moves.  The main goal being to find the hot spots on the
board.  I would have liked to have gotten more feedback from everyone
and in this case I don't think no news is good news!  Being new to this
problem domain, I guess my thinking probably is not that mature, but I
would like any feedback - negative or positive and with reasons, as this
will help me better understand the domain.  And acting in the role of a
teacher, you may find that your own understanding becomes clearer too.
Of course, one never knows, one day some new blood (perhaps not mine)
may shed light on an old problem - its happened many times throughout
history....

To implement a form of this idea for Go would require a pretty good
playing engine which already makes use of patterns and heuristics, does
board subdivision, perhaps have a Fuseki and Joseki database, etc.
Since I don't have the time or knowledge to do this much work now, I am
trying to find or devise a simpler problem domain that does not require
as difficult a base but that exemplifies characteristics similar to
certain aspects of Go that I could use to experiment and determine
whether the idea has merit.

What would the requirements be of this simpler domain?
        1.   Should be a non-trivial problem.
        2.   An easy evaluation function would be nice.
        3.   The problem should have natural subdivisions or sub goals
which are not strictly defined and which are partly independent from
each other.
        4.   The moves (change from one node to the next) can be
combined to satisfy a sub goal.
        5.   Large enough tree to be sampled like this without
blanketing the tree.

Any ideas?

Matt