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01 integer programming
Posted:
Jun 15, 1996 11:58 AM


I'm interesting about solving this 01 integer programming problem:
Min sum(Xj), j:=1,...,n An X >= 1, where An is a matrix recursive like that:
 A1 = 1
 A(n1 I(n1) An = I(n1) A(n1)
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 donÂ´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 CÃ¡mara Facultad de Cc. MatemÃ¡ticas Universidad Complutense de Madrid Spain
Mail: mcamaral@madrid.idec.es



