On Mon, 4 May 2009, Johannes Waldmann wrote:
To get tighter relaxations, use the smallest big M's that will work.
This effectively limits the range of values for the unknowns.
No, it limits the ranges of the big M's:
Z = max(X, Y)
X in Lx..Ux
Y in Ly..Uy
b in 0..1
Z >= X
Z >= Y
Z <= X + (Uy-Lx)*b
Z <= Y + (Ux-Ly)*(1-b)
If that range is very small, then I can directly use a binary encoding
for numbers, and use a SAT solver - in fact that's what I've been doing
for some time. I was hoping that MIP gives another feasible approach.
If the numbers are really small:
Z = SUM Bz[j, k]*max(j, k)
j,k
X = SUM Bz[j, k]*j
j,k
Y = SUM Bz[j, k]*k
j,k
I think that this is *linearly* equivalent to the preceeding,
but it has a lot more binaries, so I can't recommend it.
Rather obviously (X, Y, Z) is constrained
to the convex hull of its feasible values.
But as they say, "there's no free lunch".
--
Michael [email protected]
"Pessimist: The glass is half empty.
Optimist: The glass is half full.
Engineer: The glass is twice as big as it needs to be."
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