# HS-4205: Multi-Objective Optimization Study Using an Excel Spreadsheet

Learn how to perform a multi-objective optimization with HyperStudy.

Before you begin, complete HS-1035: Optimization Study using an Excel Spreadsheet or import the HS-1035.hstx archive file, available in <hst.zip>/HS-4205/.

The objective of this tutorial is to find the cross-sectional dimensions (width and height) of a beam that minimize the beam volume while keeping the tip deflection below 0.53 mm.

In this tutorial, both the beam volume and tip deflection will be considered as objective functions to be minimized. The constraint in the tip deflection is not applied in an effort to understand the trade-off associated with this condition Using a Global Response Search Method (GRSM), a series of solutions (called non-dominated solutions), will be found. These solutions form a Pareto front in which users can do trade-off analysis.

## Add Approach and Run Multi-Objective Optimization Study

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 2 > Definition > Define Input Variables step.
2. For both input variables, change the lower, initial, and upper bounds to the values indicated in Figure 1.
3. Go to the Optimization 2 > Definition > Define Output Responses step.
1. Click the Objectives/Constraints - Goals tab.
3. Define Goal 1 and Goal 2 by selecting the options indicated in the image below from the Apply On and Type columns.
5. Go to the Optimization 2 > Specifications step.
6. In the work area, set the Mode to Global Response Search Method (GRSM).
Note: Only the methods that are valid for the problem formulation are enabled.
7. In the Settings tab, change the Number of Runs to 50.
8. Click Apply.
9. Go to the Optimization 2 > Evaluate step.
10. Click Evaluate Tasks to launch the Optimization.
11. Optional: HyperStudy also allows you to perform multi-objective Optimizations using a Weighted Sum approach. Add and activate multiple objectives amongst the output responses, set a weight respectively for each objective in the Weighted Sum field, and select an algorithm (SQP, MFD, GA, ARSM) in the Specifications table. Proceed with the optimization.
12. Go to the Optimization 2 > Post-Processing step.

## Post-Process Multi-Objective Optimization Results

1. Click the Optima tab.
2. Using the Channel selector, select Goal 1 for the X Axis and Goal 2 for the Y Axis.
The Optima tab plots the trade-off between competing objectives. One objective cannot improve without the other competing objective getting worse.