Does presolve of Highs generate new variables?

[linpeng0105]

Does presolve of Highs generate new variables? For example, merging two variables to generate a new variable? In addition, for the same variable, will the variable name change?

[jajhall]

No, when variables (or constraints) are removed - possibly by combining two variables (or constraints) - one of the original variables (or constraints) is retained, with its original name.

Hence all names in the presolved problem are subsets of names in the original problem.

[linpeng0105]

Following up on the previous discussion, I have a related question:

For a variable $x_k$ with the same name in both the Original Model and the Presolved Model, does it represent the same mathematical entity in both models?

For example:

If I modify the bounds or variable type (e.g., integer → continuous) of $x_k$ in both models, would the equivalence between the two models still hold?

Or does the Presolved Model’s $x_k$ potentially represent a transformed/aggregated version of the original variable (due to presolve steps like substitutions or merging), making such modifications unsafe for equivalence?

In other words, are variable names in the Presolved Model guaranteed to retain not just their "name" but also their semantic definition from the Original Model?

This is critical for understanding whether post-presolve modifications to variables (by name) preserve equivalence. Thank you!

[jajhall]

If you modify anything in the original model, then you can't consider making any corresponding modification to the presolved model, since the logical arguments that led to the presolve reductions may no longer be true.

If you modify a model, you must run presolve from scratch to generate a new presolved model

[linpeng0105]

So I can understand it this way. I want to modify the model: the value range of variable $x_k$. I cannot modify it on the preserved model and must modify it on the original model. This is because modifying the same variable on the preserved model and on the original model is not equivalent.

[jajhall]

It's not just that the same variable in the original model and the presolved model aren't equivalent in this way. If you make any change in the original model, in general the validity of presolve reductions will change, so even the dimensions of the presovled model may change