Control Parameters That Influence the AOA Algorithm
Control parameters
The multistart module defines several parameters that influence the outer approximation algorithm. These parameters have a similar functionality as options of a solver, e.g., CPLEX. The most important parameters, with their default setting, are shown in this table.
Parameter |
Default |
Range |
Subsection |
|---|---|---|---|
|
20 |
{0,maxint} |
|
|
0 |
{0,maxint} |
|
|
0 |
{0,1} |
|
|
1 |
{0,1} |
|
|
0 |
{0,1} |
|
|
1 |
{0,1} |
|
|
0 |
{0,1} |
|
|
1e-5 |
{0,1} |
|
|
1 |
{0,1} |
The parameters that are not self-explanatory are explained in this section; the last column in the table refers to the subsection that discusses the corresponding parameter.
Specifying a Time Limit
Parameter TimeLimit
The parameter TimeLimit can be used to set a limit on the total
elapsed time (in seconds) used by the outer approximation algorithm. The
default value of 0 has a special meaning; in that case there is no time
limit.
Using the AIMMS Presolver
Parameter UsePresolver
By default the outer approximation algorithm starts by applying the
AIMMS Presolver to the MINLP model. By preprocessing the MINLP model,
the model might become smaller and easier to solve. The parameter
UsePresolver can be used to switch off the preprocessing step.
Combining Outer Approximation with Multistart
Parameter UseMultistart
If the parameter UseMultistart is switched on then the outer
approximation algorithm will use the multistart algorithm to solve the
nonlinear subproblems. For non-convex models this can have a positive
effect on the quality of the solution that is returned by the outer
approximation algorithm. The multistart algorithm is described in
section The AIMMS Multistart Algorithm. The parameters
MultistartNumberOfSamplePoints and
MultistartNumberOfSelectedSamplePoints can be used to specify the
number of sample and selected sample points, respecively, as used by the
multistart algorithm.
Multistart module
To use the multistart algorithm, the system module Multi Start
should be added to your project. You can install this module using the
Install System Module command in the AIMMS Settings menu.
Terminate If Solution of Relaxed Model Is Integer
Parameter TerminateAfterFirstNLPIsInteger
By default the outer approximation algorithm will terminate if it finds
an integer solution for the initial NLP problem, which is obtained from
the MINLP model by relaxing the integer variables. By switching off the
parameter TerminateAfterFirstNLPIsInteger you can enforce the
algorithm to continue.
Solving a Convex Model
Parameter IsConvex
The parameter IsConvex can be used to indicate that the model is
convex. In that case the outer approximation algorithm will no longer
stop after the iteration limit is hit, as specified by the parameter
IterationMax. Instead, the algorithm will stop if the gap between
the objective values of the master MIP problem and the nonlinear
subproblem is sufficiently small, as controlled by the parameter
RelativeOptimalityTolerance. Note that AIMMS cannot identify whether
a model is convex or not.
Starting Point Strategy for NLP Subproblems
Parameter NLPUseInitialValues
The parameter NLPUseInitialValues specifies the starting point
strategy used for solving the NLP subproblems. For nonconvex nonlinear
problems the starting point often has a big influence on the solution
that the NLP solver will find. By default the AOA algorithm will use the
initial values as provided by the user for all NLP subproblems that are
solved. By setting this parameter to 0, the algorithm will use the
solution of the previous master MIP problem as the starting point for
the next NLP subproblem (and for the initial NLP it will use the initial
values provided by the user). Note: if one of the parameters
UseMultistart or IsConvex equals 1 then NLPUseInitialValues
is automatically set to 0.