Regions of preference and avoidance – Inputs

Regions of preference and avoidance represent 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, the 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 the statistical nature of the optimization, setting only a few variables to the 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 for improving 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, then the process is reversed, i.e. the regions of avoidance become 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 – Inputs

How to use it: #

Table under Sets -> Options refers to the variables, which should be visualized. First, it is necessary to load file XDis.txt, which contains data for the original input distributions. Once the file is loaded, the regions can be visualized. To display regions of a variable, a button with variable’s name needs to be pressed. For each variable, user can select in Options which histograms should be displayed.

Buttons: #

  • 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

Print: #

To store selected results in File (upper left corner) select Save. It will allow you to browse in folders starting in the project folder. The code automatically selects the format to store visualized results.