optimizing visited value per distance travelled (sightseeing, tourist problem):
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is it possible to turn tastiness and distance into one weight?
- weight w = (target tastiness / edge length, edge length)
- (a, x) + (a, y) = (a, x + y)
- (a, x) + (b, x) = ((a + b)/2 , 2x)
- (a, x) + (b, y) = ((x·a + y·b)/(x+y), x+y) = (2x/(x+y) ·a, (x+y)/2) + (2y/(x+y) ·b, (x+y)/2)
- weights are compared only in the first component
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essential insights: