HS4000: Optimization Method Comparison: Arm Model Shape Optimization
Learn how to perform an Optimization and compare different methods for efficiency and effectiveness.
 Volume = 1.77E+06 mm3
 Max_Disp = 1.41 mm
 Max_Stress = 195.29 MPa
In this tutorial, the Optimization objective is to reduce Volume, while respecting a constraint on Max_Disp that should be less than 1.5 mm.
In HS3000: Fit Method Comparison  Approximation on the Arm Model, you learned that it was difficult to accurately capture the Max_Stress function using a Fit approximation. In the DOE analysis, you learned that most of the tested design configurations for Max_Stress were below 300 MPa. For these reasons, you will not consider a constraint on the Max_Stress function. Max_Stress values can be collected throughout the Optimization when running the exact solver.
ARSM, Six Input Variables, Exact Solver

Add an Optimization.
 In the Explorer, rightclick and select Add from the context menu.
 In the Add dialog, select Optimization.
 For Definition from, select Setup and click OK.
 Go to the step.

In the Active column of the work area, clear the
radius_1, radius_2 and
radius_3 checkboxes.
 Go to the step.
 Click the Objectives/Constraints  Goals tab.

Add an objective.
 Click Add Goal.
 In the Apply On column, select Volume.
 In the Type column, select Minimize.

Add a constraint.
 Click Add Goal.
 In the Apply On column, select Max_Disp.
 In the Type column, select Constraint.
 In column 1, select <= (less than or equal to).
 In column 2, enter 1.5.
 Go to the step.

In the work area, set the Mode to Adaptive
Response Surface Method (ARSM).
Note: Only the methods that are valid for the problem formulation are enabled.
 Click Apply.
 Go to the step.
 Click Evaluate Tasks.

Click the Iteration History tab to view the optimum
solution, which is highlighted green in the table.
Note: The optimal design for Max_Stress is equal to 215, which is lower than 300.

Click the Iteration Plot tab to review the results of
the optimization in an iteration plot.
ARSM, Nine Input Variables, Exact Solver
 Run a single objective, deterministic Optimization study by repeating ARSM, Six Input Variables, Exact Solver, except in the step, activate all input variables.
 Click the Iteration History and Iteration Plot tabs to review the results of the Optimization.

Select the Objective (Volume) and
Constraint (Max_Disp) functions to see their
variations during the Optimization process.
GRSM, Six Input Variables, Exact Solver
 Run a single objective, deterministic Optimization study by repeating ARSM, Six Input Variables, Exact Solver, except in the step, set the Mode to Global Response Search Method (GRSM).

Click the Iteration history tab to review the results of
the Optimization in a table.
Note: The optimal solution is found at the 19th evaluation (from 50).

Review the results of the Optimization in an iteration plot.
SQP, Six Input Variables, Exact Solver
 Run a single objective, deterministic Optimization study by repeating ARSM, Six Input Variables, Exact Solver, except in the step, set the Mode to Sequential Quadratic Programming (SQP).
 Click the Iteration Plot tab to review the results of the Optimization in an iteration plot.

Select the Objective (Volume) and
Constraint (Max_Disp) functions to see their
variations during the Optimization process.
SQP, Six Input Variables, RBF_MELS

Run a single objective, deterministic Optimization study by repeating ARSM, Six Input Variables, Exact Solver, except
change the following:
 Go to Fit, RBF (fit_4) for Max_Disp and Volume. step, set Evaluate From to
 In the Active column, clear the checkbox for Max_Stress.
 In the Sequential Quadratic Programming (SQP). step, set the Mode to

Review the results of the Optimization in an iteration plot.
 Click the Iteration Plot tab.
 Select the Objective (Volume) and Constraint (Max_Disp) functions to see their variations during the Optimization process.

For Optimizations using a Fit, it is recommended that you perform a validation
run of the optimal solution.
GA, Six Input Variables, RBF_MELS

Run a single objective, deterministic Optimization study by repeating ARSM, Six Input Variables, Exact Solver, except
change the following:
 Go to Fit, RBF (fit_4) for Max_Disp and Volume. step, set Evaluate From to
 In the Active column, clear the checkbox for Max_Stress.
 In the Genetic Algorithm (GA). step, set the Mode to

Review the results of the Optimization in an iteration plot.
 Click the Iteration Plot tab.
 Select the Objective (Volume) and Constraint (Max_Disp) functions to see their variations during the Optimization process.
 As you did in the previous Optimization (SQP, 6 IV, RBF_MELS), it is suggested that you perform a validation run to compare the values provided by the Fit and by the solver.
Optimization Methods Comparison
Optimization Method  # of Evaluations  Volume Objective 

ARSM, 9 IVs, Exact Solver  14  1702450.0 
ARSM, 6 IVs, Exact Solver  11  1703330.0 
GRSM, 6 IVs, Exact Solver  50 (22nd is the optimum)  1652830.0 
SQP, 6 IVs, Exact Solver  179  1659730.0 
SQP, 6 IVs, Fit    1666990.6 
GA, 6 IVs, Fit    1665387.3 
ReliabilityBased Design Optimization Study
In this step, run a reliability based design optimization study.
This topic will be discussed in HS5000: Stochastic Method Comparison: Stochastic Study of the Arm Model
MultiObjective Optimization Study
In this step, you will run a multiobjective optimization study.
This topic will be discussed in HS4425: MultiObjective Shape Optimization Study.