Note
Often, you can change the formulation of a MILP to make it more easily solvable. For suggestions on how to change your formulation, see Williams [1].
After you run intlinprog once, you might want to change some
options and rerun it. The changes you might want to see include:
Lower run time
Lower final objective function value (a better solution)
Smaller final gap
More or different feasible points
Here are general recommendations for option changes that are most likely to help the solution process. Try the suggestions in this order:
For a faster and more accurate solution, increase the
CutMaxIterations option from its default
10 to a higher number such as 25.
This can speed up the solution, but can also slow it.
For a faster and more accurate solution, change the
CutGeneration option to
'intermediate' or 'advanced'. This
can speed up the solution, but can use much more memory, and can slow the
solution.
For a faster and more accurate solution, change the
IntegerPreprocess option to
'advanced'. This can have a large effect on the
solution process, either beneficial or not.
For a faster and more accurate solution, change the
RootLPAlgorithm option to
'primal-simplex'. Usually this change is not
beneficial, but occasionally it can be.
To try to find more or better feasible points, increase the
HeuristicsMaxNodes option from its default
50 to a higher number such as
100.
To try to find more or better feasible points, change the
Heuristics option to either
'intermediate' or
'advanced'.
To try to find more or better feasible points, change the
BranchRule option to
'strongpscost' or, if that choice fails to improve
the solution, 'maxpscost'.
For a faster solution, increase the
ObjectiveImprovementThreshold option from its default
of zero to a positive value such as 1e-4. However, this
change can cause intlinprog to find fewer integer
feasible points or a less accurate solution.
To attempt to stop the solver more quickly, change the
RelativeGapTolerance option to a higher value than
the default 1e-4. Similarly, to attempt to obtain a more
accurate answer, change the RelativeGapTolerance option
to a lower value. These changes do not always improve results.
Often, some supposedly integer-valued components of the solution
x(intcon) are not precisely integers.
intlinprog considers as integers all solution values within
IntegerTolerance of an integer.
To round all supposed integers to be precisely integers, use the round function.
x(intcon) = round(x(intcon));
Caution
Rounding can cause solutions to become infeasible. Check feasibility after rounding:
max(A*x - b) % see if entries are not too positive, so have small infeasibility max(abs(Aeq*x - beq)) % see if entries are near enough to zero max(x - ub) % positive entries are violated bounds max(lb - x) % positive entries are violated bounds
intlinprog does not enforce that solution components be
integer valued when their absolute values exceed 2.1e9. When your
solution has such components, intlinprog warns you. If you
receive this warning, check the solution to see whether supposedly integer-valued
components of the solution are close to integers.
intlinprog does not allow components of the problem, such as
coefficients in f, A, or
ub, to exceed 1e15 in absolute value. If you
try to run intlinprog with such a problem,
intlinprog issues an error.
If you get this error, sometimes you can scale the problem to have smaller coefficients:
For coefficients in f that are too large, try
multiplying f by a small positive scaling factor.
For constraint coefficients that are too large, try multiplying all bounds and constraint matrices by the same small positive scaling factor.
[1] Williams, H. Paul. Model Building in Mathematical Programming. Wiley, 2013.