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0-1 integer programming
Posted:
Jun 15, 1996 11:58 AM
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From: mcamaral@madrid.idec.es (Miguel Angel Camara)
I'm interesting about solving this 0-1 integer programming
problem:
Min sum(Xj), j:=1,...,n
An X >= 1, where An is a matrix recursive like that:
- A1 = 1
- A(n-1 I(n-1)
An =
I(n-1) A(n-1)
where In is de identity matrix of order n.
- n= 2**k, where k:= 1, 2, 3, 4......
- Xj = (0,1).
- An(i,j) = (0,1)
Example: n=8=2**3
Min X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8
|1 1 1 0 1 0 0 0| X1 1
|1 1 0 1 0 1 0 0| X2 1
|1 0 1 1 0 0 1 0| X3 1
|0 1 1 1 0 0 0 1| X4 1
|1 0 0 0 1 1 1 0| X5 >= 1
|0 1 0 0 1 1 0 1| X6 1
|0 0 1 0 1 0 1 1| X7 1
|0 0 0 1 0 1 1 1| X8 1
That is:
X1 + X2 + X3 + X5 >= 1
X1 + X2 + X4 + X6 >= 1
X1 + X3 + X4 + X7 >= 1
+ X2 + X3 + X4 + X8 >= 1
X1 + X5 + X6 + X7 >= 1
+ X2 + X5 + X6 + X8 >= 1
+ X3 + X5 + X7 + X8 >= 1
+ X4 + X6 + X7 + X8 >= 1
The matrix An is symetric, and his determin sometimes is 0.
I'm practising and solving this problem with the aditiv
algorithm of Balas, and his results about the complexity of time don+t
satisfy me. This problem for n=32=2**5 was executed in 6 hours
aproximately in one Pentium 100 Mhz. I'm interesting to solve the
maximum number of variables about this problem.
All suggestions or recomendations about this problem, or
bibliography to see will be gratefully.
Regards. I hope your mail or news.
Miguel Angel Cbmara
Facultad de Cc. Matembticas
Universidad Complutense de Madrid
Spain
Mail: mcamaral@madrid.idec.es
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