polygon - Calculating Fitness function for Polygonal Map Generation -

i'm working on thesis regarding procedural map generation , using fitness functions calculate capability of algorithms used , resultant procedural maps.

i'm basing work off of amitp's polygonal map generation, found unity version use sources, updated recent version, corrected missing sections , stripped away eye candy goes beyond scope of thesis. problem run fitness functions on it.

some notes on map:

• the map isn't intended have practical resources or bases (which 1 of major problems in regards calculating fitness functions, since ones found assume presences of such elements)
• the focus evaluate @ least couple of algorithms (perlin 1 of them, second 1 i'm not sure yet - radial process included, have yet find paper discussing algorithm validate use) how "fit , healthy" maps result these algorithms are.

as fitness functions, sourced following paper: toward multiobjective procedural map generation (julian togelius). these focus around fairness, interestingness , playability - not applicable components line of work, it's metric evaluation i've been able locate far.

• base distance (average weighted distance between bases). considering map without bases (or discrete resources matter), tough 1 use.
• base on ground (average elevation per base ground). same above.
• map asymmetry (average elevation difference between strategically chosen cells , counterparts opposite on x , y axis). weird use due nature of polygonals' map generation amitp - elevation increases inland, , map polygonal, therefore there no direct opposites on x, y or other midway axis.
• resource distance (1- [max dist - min dist]). above, no discrete resources speak of. entire map considered wide variety of resources in case.
• resource clustering (how abundant / scarce resources are) per above.

so i'm stuck @ point... attempting evaluate somehow, potential fitness , health of map, functions find not relate kind of polygonal map generation present i'm able work with, , attempts @ transferring approach gridded system, while not fruitless near expected outcome.

my question

how can adapt these above fitness functions fit polygonal map, shown below, or alternatively locate alternative fitness functions (which scholarly valid) utilize instead calculating such results.

coming own functions may not valid, if there no background study somehow validating use of such metrics, though can't entirely rule out possibility backup.

the togelius paper looking @ maps rts type games. amit's guide making game agnostic maps. if want examine them through rts lens, you'll need convert them rts maps. (this true of procedural content generation - typically need modify general technique use in specific genre/game/context.)

alternatively, attempt evaluate maps generic maps, you'll still need compare them to. instance, take couple of different pcg island map generators & compare output real islands.

either way, without additional context coming quantitative measure of map's 'goodness' arbitrary. can see ways might adapt togelius metric other genres, don't think generalize in meaningful way measuring generic maps.