Mixed-Integer Sequential Quadratic Programming (MISQP)

The MISQP method can be used with the MOP solver or a direct solver call. It allows you to generate a new sample set to provide a more refined approach than the Screening method. MISQP is available for both continuous and discrete input parameters, which is why mixed is in its name. MISQP can handle only one output parameter goal. Other output parameters can be defined as constraints.

Further information about methods of multidisciplinary optimization used in optiSLang can be found here.

Node Settings

To access the options shown in the following table, double-click the Mixed-Integer Sequential Quadratic Programming (MISQP) system on the Scenery pane and in the Settings tab, click Change settings.

Option	Default Value	Description
Maximum Number of Iterations	50	Stop criterion. Maximum number of iterations that the algorithm is to execute. If convergence happens before this number is reached, the iterations stop. This also provides an idea of the maximum possible number of samples that are needed for the full cycle. For MISQP, the number of samples can be approximated according to the Finite Difference Approximation gradient calculation method as follows: number of iterations * (2*number of inputs +1)
Maximum Convergence Percentage	0.0001	Stop criterion. Tolerance to which the Karush-Kuhn-Tucker (KKT) optimality criterion is generated during the MISQP process. A smaller value indicates more convergence iterations and a more accurate (but slower) solution. A larger value indicates fewer convergence iterations and a less accurate (but faster) solution.
Initial Finite Difference Delta	0.001	Defines the relative variation used to alter the current point to compute gradients. Used in conjunction with Maximum convergence percentage (%) to ensure that the delta in MISQP's calculation of finite differences is large enough to be seen above the noise in the simulation problem. This wider sampling produces results that are more clearly differentiated so that the difference is less affected by solution noise and the gradient direction is clearer. The value should be larger than both the value for Initial Finite Difference Delta (%) and the noise magnitude of the model. However, smaller values produce more accurate results, so set Initial Finite Difference Delta (%) only as high as necessary to be seen above simulation noise.
Derivative Approximation	Central	Defines the method of approximating the gradient of the objective function. Choices are: Central: Increases the accuracy of the gradient calculations by sampling from both sides of the sample point but increases the number of design point evaluations by 50%. This method makes use of the initial point, as well as the forward point and rear point. This is the default method. Forward: Uses fewer design point evaluations but decreases the accuracy of the gradient calculations. This method makes use of only two design points, the initial point and forward point, to calculate the slope forward.

Additional Options

To access the options shown in the following table, in any tab, click Show additional options.

Option	Description
Limit maximum in parallel	Controls the resource usage of nodes in the system. When the check box is cleared (default), a value is chosen to ensure the best possible utilization of the child nodes. When the check box is selected, set the value manually to specify how many designs are sent to child nodes, limiting the maximum degree of parallelism for all children. Ansys recommends keeping the check box clear.
Auto-save behavior	Select one of the following options: No auto-save Actor execution finished Every n-th finished design (then select the number of designs from the text field) Iteration finished (for optimization, reliability) The project, including the database, is auto-saved (depending on defined interval) after calculating this node/system (either when the calculation succeeds or fails). By default, all parametric and algorithm systems have Every nth finished design 1 design(s) selected, all other nodes have No auto-save selected.

Option

Description

Limit maximum in parallel

Controls the resource usage of nodes in the system.

When the check box is cleared (default), a value is chosen to ensure the best possible utilization of the child nodes. When the check box is selected, set the value manually to specify how many designs are sent to child nodes, limiting the maximum degree of parallelism for all children. Ansys recommends keeping the check box clear.

Auto-save behavior

Select one of the following options:

No auto-save
Actor execution finished
Every n-th finished design (then select the number of designs from the text field)
Iteration finished (for optimization, reliability)

The project, including the database, is auto-saved (depending on defined interval) after calculating this node/system (either when the calculation succeeds or fails).

By default, all parametric and algorithm systems have Every nth finished design 1 design(s) selected, all other nodes have No auto-save selected.

Supported versions

The following versions of MISQP are supported and tested: 2021 R2 and later.