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# Regions of preference and avoidance – Results

Regions of preference and avoidance represents a new approach to optimization and design improvement. It is a statistical approach to optimization, which defines a region for improvement and a region for avoidance. The region of preference is a new distribution for the input variable, which one wants to achieve in order to have stable statistical improvement. In other words, truncating the input distribution in a proper way, one can achieve stable improvement. Contrary, region of avoidance represents a region, which leads to low results in the final distribution. In other words, a region in the input distribution, which needs to be avoided in order to have a good design. However, these regions can overlap. The overlap is closely connected to the influence/sensitivity of the given variable. For very influential variables, these regions will not overlap and one should avoid the region of avoidance as it will almost surely lead to bad final design. On the other hand, for non-influential variables, these regions will overlap and re-design the input distribution according to the region of preference will lead to small improvement. Due to statistical nature of the optimization, setting only few variables variables to region of preference will still lead to an improvement in the final design. However, the improvement will not be as large as predicted by our code. Nevertheless, this allows to improve the final design according to criteria, which are not (or cannot) be specified.

We define the region of preference to be on the right side of the final distribution (maximization process) and the region of avoidance on the left side of the final distribution. If the minimization is needed, than the process is reversed, i.e. the regions of avoidance becomes the regions of preference. Nevertheless, all the conclusions stay the same.
In the section Region of preference/avoidance -> Inputs are showed input distributions with their regions of preference/avoidance. Under the subsection Results are showed final distributions, which are achieved with regions of preference / avoidance.

Fig. 1: Regions of preference and avoidance – Results

## How to use it: #

Table under Sets -> Options refers to the distributions, which should be visualized. Select distributions, which should be visualized. The distributions will be visualized the button apply is pushed.

### Buttons and switches: #

• Variables: Select the variable which input distributions will be displayed.
• Load XDis: Load of the original input distributions from the XDis.txt file.
• Apply: Changes on the graph will take effect after pressing the apply button.

The graph is fully adjustable with options, where:

• Plot title: Title of the graph
• Title font: Font type and size of the plot title
• Bin Count: Number of categories in histogram
• X Axis Label: Label of X axis
• Y Axis Label: Label of Y axis
• Axis Font: Font type and size of the plot axis
• X Range: Restriction of range for X axis, toggle on/off
• Y Range: Restriction of range for Y axis, toggle on/off
• Preference Color: Color of region of preference histogram, toggle on/off
• Avoidance Color: Color of region of avoidance histogram, toggle on/off
• Original Color: Color of original input distribution histogram, toggle on/off
• Normalize Plot: Normalization of histogram plot, toggle on/off
• Log. vertical Axis: Logarithmic scale of vertical axis, toggle on/off
• Legend Font: Font type and size of the legend, toggle on/off

Fig. 2: Regions of preference/avoidance – options

### Save and print: #

To store selected results in File (upper left corner) select save. It will allow you to choose the specific data that you want to save. The code automatically selects the format to store visualized results.

Fig. 3: Save Dialog Screen – Initial State

### Buttons and switches: #

• Load Input Set: Loads the InputSet.txt file. Needed to save input data.
• Avoidance: Select to save the files related to the avoidance distribution.
• Preference: Select to save the files related to the preference distribution.
• Inputs: Saves three input files for each selected distribution (avoidance and preference).
• Input Domain: Values of Input Distribution boundaries together with coordinates of the nominal solution.
• Input Set: Contains general information about each input distribution and its parameters.
• XDis: Matrix of Input Distribution values – each column for one input distribution.

These three files have the same format that the analogous generated in the pre-processor.

• Outputs: Saves the ResultVector.txt file, that contains the interpolated output value for each Input Distribution value.
• File Prefix: Selects the prefix of the saved files.
• Select Directory: Selects the Directory in which both figures and data will be saved.
• Save Graph Screen: Saves the plot displayed on the screen in the selected directory. The name of the file has the form: fileprefixgraphScreen.png.
• Save Data: Saves the chosen Data Files. It is needed to have selected at least one distribution (avoidance / preference) and also at least one kind of data (input / output).

Fig. 4: Save Dialog Screen