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Re: [Help-glpk] glpsol (MIP) "-w" output specification, "-y" operatio

From: Michael Hennebry
Subject: Re: [Help-glpk] glpsol (MIP) "-w" output specification, "-y" operation
Date: Mon, 4 May 2009 09:55:45 -0500 (CDT)
User-agent: Alpine 1.00 (DEB 882 2007-12-20)

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)

X = SUM Bz[j, k]*j

Y = SUM Bz[j, k]*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   address@hidden
"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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