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IntegralityFocus
Integrality focus
| Type: | int | |
|---|---|---|
| Default value: | 0 | |
| Minimum value: | 0 | |
| Maximum value: | 1 |
One unfortunate reality in MIP is that integer variables don't always
take exact integral values. While this typically doesn't create
significant problems, in some situations the side-effects can be quite
undesirable. The best-known example is probably a trickle
flow, where a continuous variable that is meant to be zero when an
associated binary variable is zero instead takes a non-trivial value.
More precisely, given a constraint 
, where 
is a
non-negative continuous variable, 
is a binary variable, and 
is
a constant that captures the largest possible value of , the
constraint is intended to enforce the relationship that must be
zero if is zero. With the default
integer feasibility tolerance,
the binary variable is allowed to take a value as large as 
while still being considered as taking value zero. If the value
is large, then the 
upper bound on the variable can be
substantial.
Reducing the value of the IntFeasTol
parameter can mitigate the effects of such trickle flows, but often at
a significant cost, and often with limited success. The
IntegralityFocus parameter provides a better alternative.
Setting this parameter to 1 requests that the solver work harder to
try to avoid solutions that exploit integrality tolerances. More
precisely, the solver tries to find solutions that are still (nearly)
feasible if all integer variables are rounded to exact integral
values. We should say that the solver won't always succeed in finding
such solutions, and that this setting introduces a modest performance
penalty, but the setting will significantly reduce the frequency and
magnitude of such violations.
For examples of how to query or modify parameter values from our different APIs, refer to our Parameter Examples.
