Convergence Criteria

Default is that both criteria should be fulfilled before the optimization algorithm stops. To specify that just one of the criteria has to be fulfilled set STOP_CRITERION_LEVEL equal to SINGLE. The default value for STOP_CRITERION_LEVEL is BOTH.

E.g. the optimization algorithm should stop when just one of the criteria is fulfilled

OPT_PARAM
 ID_NAME = opt_params
 OPTIMIZE = id_of_optimize

 STOP_CRITERION_LEVEL = SINGLE
END_

Convergence Criteria are defined in the SETTINGS window of Tosca ANSA® environment and the OPT_PARAM command in Tosca Structure.gui respectively.

Stop Criterion: Change in Objective Function

A second stop criterion is a measurement based upon the change in the objective function from one optimization iteration to the next optimization iteration. This stop criterion is defined by

$\frac{| Θ_{n} - Θ_{n - 1} |}{| Θ_{n} |} \leq S T O P_C R I T E R I O N_O B J$

where the index n is representing the present optimization iteration and is n-1 is the previous iteration. When the criterion is lower than STOP_CRITERION_OBJ the stop criterion is fulfilled. The default for STOP_CRITERION_OBJ is 0.001. The value can be changed by the user, e.g.

OPT_PARAM
 ID_NAME = opt_params
 OPTIMIZE = id_of_optimize

 STOP_CRITERION_OBJ =  0.01
END_

This could be desirable when the number of optimization should be reduced.

Stop Criterion: Change in Element Densities

The third stop criterion is based upon the change in the densities (design variables) in each element from one optimization iteration to the next optimization iteration and is defined by

$\frac{{\sum_{1}}^{N u m b e r o f e l e m e n t s} | ρ_{n} - ρ_{n - 1} |}{N u m b e r o f e l e m e n t s} \leq S T O P_C R I T E R I O N_D E N S I T Y$

where the index n is representing the present optimization iteration and is n-1 is the previous iteration. When the criterion is lower than STOP_CRITERION_DENSITY the stop criterion is fulfilled. The default for STOP_CRITERION_DENSITY is 0.005. The value can be changed by the user, e.g.

OPT_PARAM
 ID_NAME = opt_params
 OPTIMIZE = id_of_optimize

 STOP_CRITERION_DENSITY = 0.0001
END_

Start Iteration for Convergence Check

The two above convergence criteria are not checked before a specified number of optimization iterations have been executed. Meaning that the optimization will always be executed until STOP_CRITERION_ITER is reached. The number is set by the number of STOP_CRITERION_ITER. If STOP_CRITERION_ITER is changed to e.g. 2.

OPT_PARAM
 ID_NAME = opt_params
 OPTIMIZE = id_of_optimize

 STOP_CRITERION_ITER = 2
END_

The default value for STOP_CRITERION_ITER is 4.