Does user_objective_scale and user_bound_scale modify output dec vars and solution values instead of only internal scaling?

[yellowdrac]

Hi everybody,

According to the documentation, user_objective_scale and user_bound_scale should only affect internal calculations, with the solution values automatically returned in the original scale. However, I'm observing that the solution values (variables and objective function) appear to be scaled in the output.

I thought it was

1 Model is passed with original scale
2 Scaling options are applied (e.g., user_objective_scale = 4)
3 HiGHS performs internal calculations with scaled values
4 Solution is returned in original (unscaled) scale

The solution values appear to be affected by the scaling factors, suggesting they are not being automatically de-scaled before being returned to the user.

Is this the intended behavior, or should the solution values be automatically returned in the original scale as the documentation suggests? Is possible that I am not mapping correclty the output but I just want confirmation about this

[yellowdrac]

[jajhall]

Will do.

[jajhall]

Is this the intended behavior, or should the solution values be automatically returned in the original scale as the documentation suggests? Is possible that I am not mapping correctly the output but I just want confirmation about this

I've verified that when scaling up/down with user_bound_scale and user_objective_scale the solution is returned in the original unscaled space.

Note that if user_bound_scale or user_objective_scale is sufficiently small then HiGHS may not return the same solution as when they are zero. Specifically, extreme values could lead to the feasible region being within epsilon of the origin, or all dual values being less than epsilon in magnitude, so a different vertex is optimal.

[yellowdrac]

Hi @jajhall ,

Thank you for the clarification! I just realized that the issue is not with the final solution - that one does come back properly scaled.
The problem I'm experiencing is with the intermediate solutions generated during the MIP solving process, specifically the solutions passed through the MIP improving solution callback.

Could you confirm whether the automatic de-scaling applies not only to the final output solution, but also to each intermediate solution that is passed through the MIP improving solution callback?

Thanks again for your help!

[jajhall]

Could you confirm whether the automatic de-scaling applies not only to the final output solution, but also to each intermediate solution that is passed through the MIP improving solution callback?

Indeed, the solutions passed through the MIP improving solution callback will not be unscaled. That would be tricky to achieve since, within a particular solver, the values of user_bound_scale and user_objective_scale are unknown

[yellowdrac]

@jajhall Thank you for the clarification, I understand that part now.
Is there any way to know which variables are unscaled so we can handle the de-scaling on our side? My understanding is that not all variables are scaled, correct?

This would help us properly de-scale the intermediate solutions in the callback...

[jajhall]

@jajhall Thank you for the clarification, I understand that part now. Is there any way to know which variables are unscaled so we can handle the de-scaling on our side? My understanding is that not all variables are scaled, correct?

This would help us properly de-scale the intermediate solutions in the callback...

In a MIP, all the continuous variables will be scaled, but none of the integer variables (since that would change the integer solution space).