Xopt (User-Defined Optimization Engine)

In HyperStudy, you can link to an external optimizer to use in the optimization approach. This is called a User method. In this section, you will find detailed information on how to setup and use the “User” optimization method in HyperStudy.

When you select User method in HyperStudy, HyperOpt is invoked to manage the optimization process using the external optimizer. HyperOpt manages the optimization by providing information on problem definition to the external optimizer, initializing solver runs using input variable values obtained from the external optimizer, and providing results from analyses to the external optimizer. The external optimizer performs the optimization using problem definition and analysis result information provided by HyperOpt. It determines when the optimization has converged and relates this to HyperOpt, which then terminates the study.

In order for a user-defined optimizer to interface with HyperStudy/HyperOpt, four things are required:

The user-defined optimizer must be able to interpret the problem definition as exported by HyperStudy, to the extrnopt.dat file.
The format of the extrnopt.dat file is:
```
Number_of_variables
Number_of_constraints
Variable_number,initial_value,lower_bound,upper_bound
Variable_number,initial_value,lower_bound,upper_bound
...
Constraint_number,ibound,constraint_value
Constraint_number,ibound,constraint_value
...
```
where:

Number_of_variables

Total number of input variables.

There must be a "Variable_number,initial_value,lower_bound,upper_bound" line for each input variable.

Number_of_constraints

Total number of constraints.

There must be a "Constraint_number,ibound,constraint_value" line for each constraint.

Variable_number

An integer value.

Each input variable is assigned a variable number, starting from 1. This number is used to identify the variable.

initial_value

Initial value for the input variable.

lower_bound

Lower limit for the input variable.

upper_bound

Upper limit for the input variable.

Constraint_number

An integer value.

Each constraint is assigned a constraint number, starting from 1. This number is used to identify the constraint.

ibound

Either 1 or -1, this specifies whether the constraint is an upper bound or lower bound constraint, respectively.

constraint_value

Bound value for the constraint.
The user-defined optimizer must provide design point information in a format readable by HyperStudy, in a file named extrnopt.des.
The format of the extrnopt.des file is:
```
keyword
Variable_number,value
Variable_number,value
...
```
where:

Keyword

One of design, intermediate and stop. These stand for design point, intermediate point, and converged result, respectively. Intermediate points are design points that are not stored in the iteration history (points which may be required for finite difference calculations).

Variable_number

An integer value corresponding to the value assigned in the extrnopt.des file. This identifies the input variables.

value

Value of the input variable for the next solver run.
Note: The format of the extrnopt.des file can be repeated to handle multiple run points.
The user-defined optimizer must be able to read results output by HyperStudy to the extrnopt.rsp file.
The format of the extrnopt.rsp file is:
```
Number_of_constraints
Constraint_number,value
Constraint_number,value
...
Objective_value
```
where:

Number_of_constraints

Total number of constraints. There must be a "Constraint_number,value" line for each constraint.

Constraint_number

An integer value corresponding to the value assigned in the extrnopt.dat file. This identifies the constraint.

value

Value of the constraint from the latest solver run.

Objective_value

Value of the objective function from the latest solver run.
Remember: The optimization is to minimize this value.
Note: The format of the extrnopt.rsp file can be repeated to handle multiple run points.
The user-defined optimizer must always try to minimize the objective value given in the extrnopt.rsp file.

Minimize

If Minimize is chosen from the HyperStudy interface, the objective is written out as the value of the objective output response.

Maximize

If Maximize is chosen from the HyperStudy interface, the objective is written out with the opposite sign. (i.e, an objective output response value of 100.0 would be written to the extrnopt.rsp file as -100.0, and an objective output response of -45.0 would be written to the extrnopt.rsp file as 45.0).

System Identification

If System Identification is chosen from the HyperStudy interface, the objective is calculated as:

Objective=((value-target)/target)²

An optimizer will only appear in the user-defined pull-down menu if it is registered in the current preference file.

An example of a user-defined optimizer is provided with HyperStudy. This optimizer is called Xopt.