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The P-FP problem of maxing out net shields & commerce is in the NP set of solutions. (Exact solution exists, but the time is non-polynomial, takes a long time and is tedious to calculate for more than a few enteries.) It is still in this NP class after the FP is built when debating on if to move the Palace and if static analyis is taken.
A heuristic approach should be taken. These are in order for easiest to determine to hardest to determine; from least accurate to most accruate.
The simpliest approximation is if the FP isn't built yet, then find the city inside your empire that's furthest away from the Palace and build it there. That is guartined to minimize overlap. The only thing tricky about this is that you may need to consider that in Civ III, the world is a Cyclinder, and so comparing distances both clockwise and counter clockwise may be needed if your empire is like Russia. (If the FP has been built then, you would find the city furthest away from the FP as a candidate to move the Palace.)
Second approximation would take the distance portion into account, by ensuring there is at least half a ring around each location.
Third approximation would simply rule out cities that the FP can't be built in a reasonable timeframe due to being shield poor and/or not having a river or lake for fresh water access.
Fourth approximation would by simply looking at the map extra weight for productive areas, less weight for low productive areas. and if a city has both Iron & Coal in it's CR, major weight to that area, and try to ensure that it's the least important areas (Islands off the coast) that suffer from the most corruption.
A fifth approximation would look at the state of development in each city, and give more weight to the developed portions of the empire, and less weight to the undeveloped portions of the empire.
The P-FP problem of maxing out net shields & commerce is in the NP set of solutions. (Exact solution exists, but the time is non-polynomial, takes a long time and is tedious to calculate for more than a few enteries.) It is still in this NP class after the FP is built when debating on if to move the Palace and if static analyis is taken.
A heuristic approach should be taken. These are in order for easiest to determine to hardest to determine; from least accurate to most accruate.
The simpliest approximation is if the FP isn't built yet, then find the city inside your empire that's furthest away from the Palace and build it there. That is guartined to minimize overlap. The only thing tricky about this is that you may need to consider that in Civ III, the world is a Cyclinder, and so comparing distances both clockwise and counter clockwise may be needed if your empire is like Russia. (If the FP has been built then, you would find the city furthest away from the FP as a candidate to move the Palace.)
Second approximation would take the distance portion into account, by ensuring there is at least half a ring around each location.
Third approximation would simply rule out cities that the FP can't be built in a reasonable timeframe due to being shield poor and/or not having a river or lake for fresh water access.
Fourth approximation would by simply looking at the map extra weight for productive areas, less weight for low productive areas. and if a city has both Iron & Coal in it's CR, major weight to that area, and try to ensure that it's the least important areas (Islands off the coast) that suffer from the most corruption.
A fifth approximation would look at the state of development in each city, and give more weight to the developed portions of the empire, and less weight to the undeveloped portions of the empire.
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