Re: [Help-glpk] I need help to convert quadratic problem into linear

[glpk xypron]

Hello Mudassar,

the solution to your problem formulation leads to a CPU load
z = 76. The minimum load possible (zmin) is 52.

Your problem could be solved much faster, if you separated it into two.

First calculate the minimum possible load in a problem formulation
which does not care about the communication cost.

Second calculate the minimum possible communication cost for the
maximum CPU load (zmax) that you allow.

Solving the complete problem (with the two symmetry breaking constraints
which I proposed yesterday, and option --cuts) takes my computer
310 seconds.

Determining the minimum possible load takes 27 seconds.
Determining the minimum communication cost for zmax = 76 takes
81 seconds.

If you put a tighter constraint on the load, the solution is calculated
faster, e.g for zmax = zmin = 52: 5 seconds.

Did you think about replacing communication cost by communication time?

TotalTime >= CPU time
TotalTime >= Communication / Bandwidth
Minimize TotalTime.

In this case, you might first calculate the minimum CPU time for
unlimited bandwidth. Minimize communication for minimum CPU time,
and check if bandwidth is a problem.

If yes, minizme processing time for minimum bandwidth and check if
CPU time is limiting.

If yes, minimize total time.

Best regards

Xypron

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