EngineRoom

Response Optimizer Tutorial

Table of Contents

Single Output: Using a Regression or DOE Tool

Single Output: Building Your Own Equation

Multiple Outputs: Using Regression Tools

Multiple Outputs: Using DOE Tools

Multiple Outputs: Building Your Own Equation

Cost

Weights

Tutorial

Coming Soon

Click to Download Data File

When to use this tool

Use the Response Optimizer to calculate the response of an equation and determine the values of the inputs that maximize, minimize, or hit a target for the response. This tool is best paired with Regression tools that calculate an equation and then using the Optimizer to optimize the value of that response.

The Response Optimizer is also able to handle multiple equations with shared input factors. You can optimize up to three equations simultaneously* as well as a fourth Cost variable.

*All outputs have equal weight in the output. At this time, there is no method for indicating one equation is more important to hit its target than another.

Using EngineRoom

Single Output: Using a Regression or DOE tool

1. Complete a Multiple Regression tool or a DOE tool in EngineRoom.

2. Once you get to the results screen, click the "Push to Optimizer" button on the top right corner of the study and then click "Add New".

Regression analysis optimizer start up menu.

3. The Optimizer will open with your equation. The output will be set based on the minimum value of your input variables.

Sample optimizer results.

4. Manually calculate the resulting output from a series of inputs by using the text box to set a value, or sliding with the slider.

Optimizer with adjusted input variables.

5. For your response, select "Maximum", "Minimum", or "Target". If you select "Target", type in a value to attempt to hit.

Optimizer with goals dropdown menu.

6. Click "Optimize".

7. The optimal value will display in the blue box. The corresponding input variables will change to fit in those spaces.

Optimizer with "maximize" selected.

Single Output: Building Your Own Equation

1. Open a new Response Optimizer from the tools menu. A new equation screen will appear to allow you to build your equation.

Optimizer start-up menu.

2. Add each factor in your equation along with its coefficient:

  • Intercept: This is the y-intercept of your equation. If all of your factors were set to 0, what would the equation equal?
Optimizer start-up menu.
  • Continuous: A continuous numeric factor. You must set the minimum, maximum, and decimal spaces in order to set the parameter space for optimization.
Optimizer with "first factor" being added.
  • Categorical: A categorical factor that contains 2 or more levels. The first level is the reference level, the one on which every other level's coeffcient is based. There is only 1 level active at a time in the equation.
Optimizer with "second factor" being edited.

3. Building out your equation this way ensures that you will have all the information necessary for doing your optimization.

4. Click "Continue".

5. The interface now allows you to manipulate the inputs to get the related output response.

Optimizer menu.

Multiple Outputs: Using Regression Tools

A manufacturing company wants to minimize the Cure Time and maximize the Surface Quality score. The Cure Time equation includes Paint Thickness and Temperature, while the Surface Quality equation includes Temperature and Surface Prep Time. Download the data above to complete this example.

1. Complete a Multiple Regression tool in EngineRoom. For this example, use the Paint Thickness and Temperature as input variables and Cure Time as the output variable.

Sample multiple regression tool output.

2. Once you get to the results screen, look for the "Push to Optimizer" button on the top right corner of the study. Click the "Push to Optimizer" button, and select "Add New".

"Push to optimizer" button.

3. The Optimizer will open with your equation. The output will be set based on the minimum value of your input variables.

Sample optimizer output.

4. Create a second Multiple Regression tool. For this example, use the Temperature and Surface Prep Time as input variables and Surface Quality as the output variable.

Sample multiple regression tool output.

5. Once you get to the results screen, click the "Push to Optimizer" button and select the existing Optimizer.

"Push to optimizer" button.

6. The second equation will be added to the Optimizer tool allowing you to manipulate the values of both at the same time. Note: because the input factor "Temperature" has the same name in both cases, the factor is shared between the two outputs and controls the calculation of both.

Sample multiple output optimizer.

7. Manually calculate the resulting output from a series of inputs by using the text box to set a value, or sliding with the slider. The shared factors will recalculate both equations, while factors for just one equation will just recalculate the one output.

8. For each of your responses, select "Maximum", "Minimum", or "Target". If you select "Target", type in a value to attempt to hit. For our example, we'll set Cure Time to Minimum and Surface Quality to Maximum.

Optimizer set targets menu.

9. Click "Optimize".

10. The optimal values will display in the blue box. The corresponding input variables will change to fit in those spaces. Note: The equations are treated with equal weight. Therefore, it might not completely maximize or minimize a particular output but will find the best for both. See Weights at the bottom of this article.

Optimizer input values menu.

Multiple Outputs: Using DOE Tools

1. Complete a DOE tool in EngineRoom. This can be Full Factorial, Fractional Factorial, General Factorial, or Response Surface Methodology.

2. Once you get to the results screen, look for the "Push to Optimizer" button on the top right corner of the study. Click the "Push to Optimizer" button, and select "Add New".

Push to Optimizer Button with Add New dropdown

3. The Optimizer will open with your equation. The output will be set based on the minimum value of your input variables.

A Response Optimizer window with a highlighted output box, followed by two inputs with sliders to indicate which direction they should go.

4. Create a second DOE tool. Usually this will involve dragging on your existing DOE Matrix with a different Response Variable.

5. Once you get to the results screen, click the "Push to Optimizer" button and select the existing Optimizer.

A Push to Optimizer button with a dropdown with Add New and Central Composite Optimizer, which is the name of the existing optimizer.

6. The second equation will be added to the Optimizer tool allowing you to manipulate the values of both at the same time. Note: Factor with the same name is shared between the two outputs and controls the calculation of both.

An optimizer tool with two responses and two inputs.

7. Manually calculate the resulting output from a series of inputs by using the text box to set a value, or sliding with the slider. The shared factors will recalculate both equations, while factors for just one equation will just recalculate the one output.

Optimizer with two outputs and two inputs, where the sliders have been manipulated to change the values of the inputs and results.

8. For each of your responses, select "Maximum", "Minimum", or "Target". If you select "Target", type in a value to attempt to hit.

9. Click "Optimize".

Optimizer with two inputs and two outputs and the outputs set to maximize and minimize, and the results from that.

10. The optimal values will display in the blue box. The corresponding input variables will change to fit in those spaces. Note: The equations are treated with equal weight. Therefore, it might not completely maximize or minimize a particular output but will find the best for both. See Weights at the bottom of this article.

Multiple Outputs: Building Your Own Equation

1. Open a new Response Optimizer from the tools menu. A new equation screen will appear to allow you to build your equation.

Optimizer start-up menu.

2. Add each factor in your equation along with its coefficient. (Go to Factor Types to understand what they mean). Building out your equation this way ensures that you will have all the information necessary for doing your optimization.

Sample equation set up in optimizer menu.

3. Click "Add Output". Now you can build a second equation. You can have a total of 3 equations.

Sample multiple output optimizer.

4. Build your second equation by add each factor in your equation along with its coefficient. (Go to Factor Types to understand what they mean). When you click "Add Factor", you now have the option of adding factors that are shared between the equations.

  • For Continuous Factors, the Maximum and Minimum will be shared between the two factors, but you can set unique coefficients for each equation.
  • For Categorical Factors, the Levels will be consistent between the shared factors, but the coefficients for each level can change between the factors. If a level is not relevant to a function, just set its coefficient to 0.
Optimizer with "add parameter" modal open.

5. When you are finished with your equations, click "Continue".

6. The interface now allows you to manipulate the inputs to get the related output responses.

Sample multiple output optimizer.

Cost

1. Create an Optimizer. For this example, we completed the tutorial for Multiple Outputs: Using Regression Tools.

2. Click on the "Add Cost" button on the bottom left (you may need to scroll).

Sample optimizer output.

3. The Cost row will appear at the bottom and the Cost output will appear at the top.

Optimizer cost output.

4. Input your costs for each input factor.

  • per unit: this option will multiply the number in the input field by the cost number. As you adjust the value of the input factor, the cost will be recalculated. For example, if the cost goes up $100 for each square foot, then you would put 100 in the cost, and as you adjust the square footage by 1, the cost will recalculate and add 100.
  • fixed: this option will set a standard value to the cost that is not affected by the value of the input factor. For example, if it costs $300 because your car is painted regardless of the thickness of the paint, you can add 300 for fixed under Paint Thickness.
  • Categorical Variables Only: by level: Each value under a categorical variable is able to have its own cost. For example, if you have a categorical Parking variable with levels No Parking, Covered Parking, or Individual Garage, you can set the price for each level. For example, select No Parking and set the price to $0, then select Covered Parking and set the price to $25, then select the Individual Garage Parking and set the price to $100. These prices will persist as you set the input factor level.
Optimizer output cost row.

5. The cost will be calculated automatically at the top.

Weights

This tool can be used to optimize up to three responses simultaneously. To do this, the optimizer assigns each individual response a desirability function, ‘d’, which takes values ranging from 0 (least desirable) to 1 (most desirable) corresponding to the possible values of the response variable. The individual desirabilities are then combined using a composite desirability, D, which is basically the geometric mean of the individual desirabilities:

D = (d1* d2*…..*dk)1/k where di = the desirability of the ith response variable k = the number of responses being optimized.

Using the geometric mean ensures that the outcome is zero if any one response fails to achieve at least some measure of desirability.

When optimizing multiple equations at once:

  1. The optimizer treats each individual response as equally important. In other words, the importance score is equal for both responses. In the future, we would like to offer the ability to manipulate this score, setting a value ranging from 1 (least important) to 5 (most important).
  2. The optimizer places equal emphasis on the target and the bounds. In other words, the optimizer assigns all individual desirabilities a weight = 1. In the future, we would like to offer the ability to manipulate this weight assigned to the desirability function, which affects the shape of the desirability function.

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