One-Click Optimization of Kursawe Functions

This tutorial demonstrates how to use One-Click Optimization. It showcases how to run a multi-objective optimization and a single-objective optimization on Kursawe functions.

 

Prerequisites

You must complete the Process Integration of Kursawe Functions tutorial before starting this one.

 

Tutorial Steps

To set up and run the tutorial, perform the following steps:

 

Opening the Kursawe Process Integration Project

  1. Start optiSLang.

  2. From the Start screen, click Open.

  3. Browse to the location of the Kursawe process integration project you used in the previous tutorial and click Open.

 

Running the Multi-Objective Optimization Wizard

  1. From the Wizards pane, drag the Optimization wizard to the head of the solver chain and let it drop.

  2. Do not adjust the values in the Parametrize Inputs table.

  3. Click Next.

  4. To define kursawe1 as a minimization objective, drag the row from the Responses table to the Objective Minimize icon and let it drop.

    The objective is added to the Criteria table.

  5. To define kursawe2 as a minimization objective, drag the row from the Responses table to the Objective Minimize icon and let it drop.

    The objective is added to the Criteria table.

  6. Click Next.

  7. The One-Click Optimization is recommended and selected by default.

  8. Since you did not conduct any Sensitivity analyses, set the Analysis status to Unaware. There is currently no information about Failed designs or Solver noise.

  9. Leave the maximum number of design evaluations as-is, and click Next.

  10. Do not change any of the additional options.

  11. Click Finish.

    The One-Click Optimization system is created.

 

Setting up the System for Multi-Objective Optimization

  1. Right-click the One-Click Optimization system and select Rename from the context menu.

  2. Type One-Click Optimization MOO and press Enter.

  3. Right-click the One-Click Optimization MOO system and select Create > Note from the context menu.

  4. In the note, enter MOO = Multi-Objective Optimization.

 

Saving and Running the Multi-Objective Optimization

  1. To save the project, click  .

  2. Browse to the location to save the project and type a project name in the File name field.

  3. Click Save.

  4. To run the project, click  .

 

Updating the Pareto 2D Postprocessing

The Postprocessing window launches automatically after the project is run. It shows in the Pareto 2D plot the Pareto front and the conflicting objectives.

  1. To select the best designs at the Pareto front, click Select best design(s).

  2. To investigate designs at the Pareto front only, click Invert selection.

  3. Right-click the Pareto 2D plot and select Deactivate from the context menu.

 

Multi-Objective Optimization Strategies

A Posteriori Preference Articulation

  • Search before making decisions.

    • Multi-objective (Pareto) optimization

    • Find Pareto optimal solutions and choose the most suitable one.

Strategies to Continue

  • Strategy A:

    • Only the most important objective function is used as optimization goal

    • Other objectives as constraints

  • Strategy B:

    • One objective as sum of single criteria

    • Scale and weight single criteria

You continue with Strategy A.

 

Adding and Configuring Clusters

  1. From the Visuals pane, drag the Parallel coordinates plot from the Data mining folder into the window.

    The Parallel coordinates plot is useful to understand a multidimensional space, set preferences and understand dependencies. Each line represents one design.

  2. From the menu bar select Edit > Cluster analysis > Clusters.

  3. In the Cluster Dialog, select obj_kurasawe1 and obj_kurasawe2.

  4. Select the K-means method for clustering

  5. Click Calculate cluster.

  6. Click OK.

    The conflict between the objectives is displayed in the Parallel coordinates plot.

 

Saving Postprocessing

  1. To save the postprocessing, click  .

  2. Select Save visual states.

  3. Click OK.

  4. To close the Postprocessing window, from the menu bar select File > Quit.

  5. In the dialog box, click Quit.

 

Running the Single-Objective Optimization Wizard

  1. From the Wizards pane, drag the Optimization wizard onto the One-Click Optimization MOO system and let it drop.

  2. Do not adjust the values in the Parametrize Inputs table.

  3. Click Next.

  4. To delete the existing objective for obj_kursawe1, right-click it and select Remove selected criteria from the context menu.

  5. In the confirmation dialog box, click OK.

  6. To define kursawe1 as a constraint, drag the row from the Responses table to the Constraint Less icon and let it drop.

    The constraint is added to the Criteria table.

  7. In the Limit field for constr_kursawe1, enter -14.5.

  8. Click Next.

  9. The One-Click Optimization is recommended and selected by default. The analysis status is automatically set.

  10. Change the maximum number of design evaluations to 500.

  11. Keep Define start design manually.

    Start designs cannot be automatically received from the One-Click Optimization MOO because you have changed the criteria.

  12. Click Next.

  13. Click Import start values from system.

    We want to use the best design, which was design 327 from the Multi-Objective Optimization, to be our start design for the Single-Objective Optimization The design has the lowest value of obj_kusawe2 where obj_kusawe1 < -14.5 is still given.

  14. In the Select system pane, click One-Click Optimization MOO.

  15. From the table, select line 327.

  16. Click OK.

  17. Click Next.

  18. Do not change any of the additional options.

  19. Click Finish.

    A new system is created.

 

Setting up the System for Single-Objective Optimization

  1. Right-click the One-Click Optimization system and select Rename from the context menu.

  2. Type One-Click Optimization SOO and press Enter.

  3. In the note, enter SOO = Single-Objective Optimization.

 

Saving and Running the Single-Objective Optimization

  1. To save the project, click  .

  2. To run the project, click  .

 

Viewing the Single-Objective Optimization Postprocessing

The Postprocessing window launches automatically after the project is run. The optimizer converges after 420 designs. The postprocessing displays the following information:

  1. The best design, Design 310, has been automatically selected.

  2. For this design, the following are shown:

    1. Parameters

    2. Responses

    3. Criteria

  3. The blue Convergence line in the History plot shows the improvement of the design during optimization.

 

Summary

  • Process Integration was conducted to automate the process.

  • With the One-Click Optimizer and without further configuration, the Pareto front is well captured.

  • The Multi-Objective Optimization showed the conflict of the optimization goals.

  • Define a strategy to find a Pareto optimal solution and choose the most suitable one.

  • Continue with a constrained, local Single-Objective Optimization.

    • Initial design :

      • Best Objective (Kursawe 2) : 0

      • Constraint (Kursawe 1) : -20.0 ≤ -14.5

      • Solver runs: 1.

    • Multi-objective optimization:

      • Objective (Kursawe 2) : -7.9

      • Objective 2 (Kursawe 1) : -14.5 ≤ -14.5

      • Solver runs: 400.

    • Single-objective optimization:

      • Best Objective (Kursawe 2) : -8.2

      • Constraint (Kursawe 1) : -14.5 ≤ -14.5

      • Solver runs: 420.