Objective Function Overview

These results are combined to scalar values using the so-called 'design responses.' Initially, one or several responses for the objective function must be defined using the command DRESP. These responses are then added to the objective, as seen in the following figure:

Weight and reference values can be applied in the combination using the command OBJ_FUNC.

OBJ_FUNC
 ID_NAME = ...
 DRESP   = id_name_1, WEIGHT, REFERENCE
 DRESP   = id_name_2, WEIGHT, REFERENCE
 DRESP   = id_name_3, WEIGHT, REFERENCE
 DRESP   = id_name_4, WEIGHT, REFERENCE
 ...
 TARGET  = MIN | MAX | MINMAX | MAXMIN
END_

• The ID_NAME of the OBJ_FUNC must be referenced in the OPTIMIZE command to activate the objective function.
• The WEIGHT and REFERENCE values are optional.
• The default weighting factor is ${\mathrm{w}}_i=1$ and the default reference value is ${\mathrm{\phi }}_i^{\text{ref}}=0$.

  Important: For controller-based shape optimization the reference value ( ${\mathrm{\phi }}_i^{\text{ref}}$ ) has a special meaning. The reference value is the value around which Tosca Structure homogenizes the stress. Thus, a value ${\mathrm{\phi }}_i^{\text{ref}}=0$ usually does not make sense and Tosca Structure calculates a default reference value if REFERENCE ( ${\mathrm{\phi }}_i^{\text{ref}}$ ) is unset. The reference calculated can be seen in TOSCA.OUT: For controller-based shape optimization the user must either set all REFERENCE-values or none at all (automatic reference value calculation).

• The user does not need to define WEIGHT and REFERENCE for the most common optimization formulations. The default values of WEIGHT=1.0 and REFERENCE=0.0 are good settings for most common cases.
• The command TARGET can be set to MIN, MAX, MINMAX, or MAXMIN, indicating if the objective function is minimized or maximized or if a min-max or a max-min formulation is used.

  Important: The reference value for the MINMAX function differs from the above definition by eigenfrequency optimization for the sensitivity-based algorithm. MAXMIN is not allowed for eigenfrequency optimization. The reference value for von Mises stresses in topology optimization differs from the above definition.

• The design responses listed in OPTIMZE are summed up taking into account the individual weighting and reference values if TARGET is set to MIN or MAX.
• A min-max / max-min formulation is applied if TARGET is set to MINMAX / MAXMIN. Then the design responses are dealt with individually in a multidisciplinary optimization taking into account the individual weighting and reference values.

In the log file TOSCA.OUT the object function value can be monitored:

In the above example, the total objective function is $\Phi =68.9636$, the DRESPs have values ${\mathrm{\phi }}_1=\text{DRESP\_MAX\_MISES1}=161.820$ and ${\mathrm{\phi }}_2=\text{DRESP\_MAX\_MISES2}=80.9101$.

Also the above example shows the weight and reference value of each term. These values can also be found in two extra log-files, optimization_report.csv and optimization_status_all.csv. The first file only lists DRESPs that are included in the optimization task as objective function or constraint. The latter lists all DRESPs defined in the parameter file.