Reformulate Constraints

Type

Selection

Range

The settings listed below

Default

Multi

This option controls whether the AIMMS Presolver should try to reformulate constraints during MINLP probing. Possible values are:

  • Off

  • Single

  • Multi

The AIMMS Presolver can transform some classes of nonlinear constraints into equivalent linear constraints. For example, under some conditions it is possible to transform a constraint of the form

\[a * x + b * x * y + c * y \leq d\]

where \(x\) is a binary variable and \(y\) a continuous or integer variable, into a linear constraint. Furthermore, for a set of constraints of the form

\[\begin{split}y \leq x \\ y^2 \leq z\end{split}\]

where \(x\) is a binary variable and \(y\) and \(z\) are continuous variables, the second constraint can be transformed into its perspective counterpart resulting in a tighter relaxation. See Gu00FCnlu00FCk et al. (2010).

With setting ‘Single’ the AIMMS Presolver will only transform constraints if their counterpart consists of one constraint. With setting ‘Multi’ also constraints are transformed for which the counterpart requires more than one constraint. For inequalities the AIMMS presolver can add one additional constraint and for equalities up to three additional constraints. The suffix .ExtendedConstraint can be used to refer to these additional constraints. For example, the first additional constraint for constraint c(i) is labeled as c(i).ExtendedConstraint(‘Linearization’), the second as c(i).ExtendedConstraint(‘Linearization2’), and so on.

Setting ‘Multi’ is only applied if the GMP function GMP::Instance::CreatePresolved is used! If a normal solve statement is used then the ‘Multi’ setting is equivalent to the ‘Single’ setting.

Note

  • This option has only an effect if the option MINLP Probing is switched on.

  • For some MINLP problems it might be worthwhile to experiment with the function GMP::Instance::CreatePresolved if you are using BARON or Knitro. (The GMP-AOA algorithm already uses the function GMP::Instance::CreatePresolved underneath.)

Learn more about

References

  • Gu00FCnlu00FCk, O., and J. Linderoth, Perspective reformulations of mixed integer nonlinear programs with indicator variables, Math. Program. B 124 (2010), pp. 183-205.