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Is there a way to get the branch and bound algorithm to converge to a solution "close" to an initial value?

One way I can think of, is to adding a "distance from initial value" term to the cost function. However, this makes the linear problem quadratic.

To give you a brief understanding of the problem I am working on:

Machines are to be allocated to various factories in certain packaging formats. Thus when the required capacity increases, my code throws up solutions where too many machines get relocated.

How do I get to the optimum solution which is closest to the current machine configuration?

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1 Answer 1

up vote 2 down vote accepted

You can keep the linearity. Just minimize the sum of the absolute values the differences. Instead of

min abs(x)

use

min (zp + zm)
s.t.  
    x = zp - zm
    zp >= 0
    zm >= 0
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Thanks for the idea. Also found a useful bag of tricks on the AIMMS website –  Shamps May 4 '12 at 12:00
    
Yes, that is a good document. This trick with the absolute values is 6.1 in it. Anyway, good luck! –  Ali May 4 '12 at 14:16
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