slayer task frequency

hi
set of tasks assigned by kuradal = (t1, t2, ..., t36) = T
set of tasks assignable to you = S
a task log = (l1, l2, ..., l36) = L. it's a vector or list of the number of times you

or someone got assigned each task, ti.
li
by the grouping theory, S such that ti, tj S, the ratio
a constant as L * 1
lj

(task log size) .
if we have task logs L1, L2, ..., Ln from assignable task subsets S1, S2, ..., Sn then
li
li,lj S
= ri,j = the relative frequency ratio between tasks ti, tj.
lj
li,lj S
Call the 36X36 matrix of these ratios R.
The number of tasks used to compute each ri,j =
li +
lj = wi,j.
li,lj S
li,lj S
In the optimization procedure the importance of the task frequencies f1, f2, ..., fn =
F reproducing the calculated relative frequency ratio ri,j wil be weigted by wi,j.

Call the matrix of these weights W.
the task frequencies initial guess can be: F = (1, 1, ..., 1) = 1 (or (1/n, 1/n..1/n)


so it sums to 1).
a good way to udpate and improve each component, fi, is:
n
fi
fi = fi - k
wi,j * (
- ri,j)
j=1
fj
1
(k affects convergeance rate, k =
is probably a good choice)
n
after many updates f1, f2, ..., fn = F will converge to a vector s * E, which mini-
n
n

fi
mizes
wi,j (
- ri,j)
i=1 j=1
fj
or, in other words, best repoduces the frequency ratio matrix R subject to the
frequency ratio weights matrix W.
divide the vector components by the sum of the vector components so the fre-
quencies sum to 1 (so F * 1 = 1).
I tried this method with some task logs and it worked well.
1

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