HS-4000: 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 HS-3000: 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, right-click 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.
Figure 1.
- 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.
Figure 2.
-
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.
Figure 3.
- 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.
Figure 4.
-
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.
Figure 7.
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).
Figure 8.
-
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.
Figure 10.
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
Figure 11.
-
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.
Figure 12.
-
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.
Figure 17.
- 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 |
Reliability-Based Design Optimization Study
In this step, run a reliability based design optimization study.
This topic will be discussed in HS-5000: Stochastic Method Comparison: Stochastic Study of the Arm Model
Multi-Objective Optimization Study
In this step, you will run a multi-objective optimization study.
This topic will be discussed in HS-4425: Multi-Objective Shape Optimization Study.