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LDEE - Low-Dimensional Euclidean Embedding for Visualization of Search Spaces in Combinatorial Optimization



This web page contains additional information for the paper entitled "Low-Dimensional Euclidean Embedding for Visualization of Search Spaces in Combinatorial Optimization".

If you have any suggestions or questions concerning this website feel free to contact me at krzysztof.michalak@ue.wroc.pl


Figure 1. An overview of the LDEE workflow (click to enlarge).


Tools

Tools are available which allow using the LDEE method on your own data set.
Note: To prevent automatic opening of the contents the files have their extensions changed. Rename these files to *.zip



A step-by-step example

You can follow an example which shows step by step how to use the LDEE tools on an exemplary data set.



Examples

Videos showing the method at work on the Knapsack Problem (KP) and a visualization of an evolutionary algorithm solving the Four Peaks Problem (4PP). Also, a detailed example is available, showing how to use the tools to obtain visualizations for the The Multiobjective Firefighter Problem (MOFFP).

The Four Peaks Problem (4PP)
A video showing the population in the EA solving the Four Peaks Problem. This video corresponds to Fig. 5 in the paper.

Note: Solutions shown in this video include all solutions produced by genetic operators before some of them were removed by the selection process. This way the entire searching process is presented including bad solutions produced by the operators.

Click on the thumbnail to play the video in an HTML5-capable browser or click here to download.
A 3-D version of the Four Peaks Problem video.

Click on the thumbnail to play the video in an HTML5-capable browser or click here to download.

The Knapsack Problem (KP)
A video showing the t-SNE method embedding solutions of the Knapsack Problem from the space of binary vectors {0, 1}500 to Euclidean space R2. The video starts at iteration 300 of the t-SNE run, because earlier the entire data set looks as if placed at one point.

Click on the thumbnail to play the video in an HTML5-capable browser or click here to download.
A video showing the Vacuum Embedding method processing points obtained in the previous video using t-SNE. The result of the processing shown in this video is presented in Fig. 7 in the paper (top-right).

Note: The first frame of this video shows the same points as the last frame in the previous video. They seem different because of different scaling and resulting relative size of the plotted points.

Click on the thumbnail to play the video in an HTML5-capable browser or click here to download.

The Multiobjective Firefighter Problem (MOFFP)
A detailed example how to use the tools to obtain visualizations for the The Multiobjective Firefighter Problem (MOFFP).
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