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DoA

What are the next starts i should choose to reduce gemstones type difference, the discrete optimization point of view.

Let us consider the gemstones as a vector y = (y1, y2, y3, y4) in N4, where the components respectively respresent the number of margonite gemstones, stygian gemstones, torment gemstones, titan gemstones.

Then, we consider successful runs by the following functions going from N4 to N4:

f1(x) = x + k(1, 2, 3, 4)

f2(x) = x + k(4, 1, 2, 3)

f3(x) = x + k(3, 4, 1, 2)

f4(x) = x + k(2, 3, 4, 1)

Where k = 2 in Hard Mode (HM), and where the functions respectively represent start city, start veil, start gloom, start foundry.


Now, let g be a finite number ni of composition of functions fi, (i in {1,...,4}). We consider g to be solution if it is the minimal number of composition which gives the minimum possible difference of gemstones. This gives the following minimization problem:

argming (max(i, j) |gi(y) - gj(y)| + d||n||1), where d is small.

Let us set h(i,j)(y) = |gi(y) - gj(y)|. This is a polyhedral function with respect to n:

h(i,j)(n, y) = |yi - yj + k<D(i,j),n>|

Continuous setting

Let us now consider z in R. The discrete problem is equivalent to this one:

minz z + <n, 1>

under:

z >= yi - yj + k<D(i,j),n>

z >= yj - yi + k<D(j,i),n>

for all couple (i,j) in {(1, 2), (2, 3), (3, 4), (1, 3), (2, 4), (1, 4)}

Contact

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In game character name Kunvie Zhan