Originally posted by: SystemAdmin

Hi CPLEX experts,

I have a question regarding the computational performances over different coefficient scales in the objective function. I know in the objective function, if some of the coefficients are small numbers like 0.001, while others could take values as large as 10e+8, then this could hurt LP solving, B&C and other heuristic algorithms (although not knowing enough details). But what would happen if all the coefficients in the obj. function have the scale of 10e+8? Will this have a different performance from the case in which we rescale all the coefficients in the obj. function to be 10e+4 (From my experience, I think it is)? If so, what is the theoretical reason behind this phenomena? Many thanks in advance.
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Originally posted by: SystemAdmin

Yes, scaling the objective function can have an influence on numerical stability, and as a consequence also on solving time. I think it is typically the best to have objective coefficients being in the order of 1.

The objective coefficients enter into some equation system solves as right hand side (in particular in the dual simplex). Thus, big values will potentially lead to big solution values (for the dual). Since the tolerances in CPLEX are absolute values (which are tuned to work best for calculations on values in the order of 1), having very big numbers is certainly not the best approach...

Tobias
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Originally posted by: SystemAdmin

I see. Thanks.
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