HS-4425: Multi-Objective Shape Optimization Study

Perform a multi-objective Optimization study, and search for the Pareto front that minimizes both volume and maximum displacement.

Before you begin, complete HS-4000: Optimization Method Comparison: Arm Model Shape Optimization or import the HS-4000.hstx archive file, available in <hst.zip>/HS-4425/.
In this tutorial you will be using MOGA with a Fit to save time.
Note: If a Fit was not available, GRSM would be the suggested method to use in order to solve a MOO problem. MOO problems require many evaluations, therefore GRSM is more efficient than MOGA.

Run Multi-Objective Shape Optimization

  1. Add an Optimization.
    1. In the Explorer, right-click and select Add from the context menu.
    2. In the Add dialog, select Optimization.
    3. For Definition from, select Setup and click OK.
  2. Modify input variables.
    1. Go to the Optimization 7 > Definition > Define Input Variables step.
    2. In the work area, Active column, clear the radius_1, radius_2 and radius_3 checkboxes.
  3. Go to the Optimization 7 > Definition > Define Output Responses step.
  4. Click the Objectives/Constraints - Goals tab.
  5. Apply an objective on the Volume and Max_Disp output responses.
    1. Click Add Goal twice.
    2. In the Apply On column, select the following:
      • Goal 1: Volume
      • Goal 2: Max_Disp
    3. In the Type column, select Minimize.
    Figure 1.

  6. Click the Define Output Responses step, and change the Evaluate From column to Fit - RBF (fit_4) for Volume, Max_Stress, and Max_Disp.
    Figure 2.

  7. Go to the Optimization 7 > Specifications step.
  8. In the work area, set the Mode to Multi_Objective Genetic Algorithm (MOGA).
  9. Click Apply.
  10. Go to the Optimization 7 > Evaluate step.
  11. Click Evaluate Tasks.
    HyperStudy stops MOGA after 50 iterations, and performs a total of 13317 analyses. The Pareto front of the last iteration contains 408 points.
  12. Go to the Optimization > Post-Processing step.
  13. Click the Optima tab.

    The Pareto front of Objective 2 versus Objective 1 is displayed in the plot.

    The goal of this study was to minimize both Volume (Objective 1) and Max_Disp (Objective 2). The Pareto plot shows all of the non-dominated solutions. A non-dominated solution is a solution which can no longer improve one objective without deteriorating another. You can see that minimizing Objective 1 will increase Objective 2, and minimizing Objective 2 will increase Objective 1. According to these results, you must decide what would be the optimal solution. For instance, the Pareto plot may allow a compromise solution to be selected somewhere in the middle.

    Figure 3.