The Quasigroup Completion Problem

QCP Help


MODES

A mode must be selected before a completion algorithm can be run.

Manual

To manually preplace a square, click the "manual" button to enable the manual preplacement bar. Click on the bar to select a color, then click squares on the QCP board. When you have finished, select an algorithm by clicking on either "RUN" button.

Random

Click on the "random" button to activate the random preplacement selector. Use the arrows to increment or decrement by one. Click on the +10 and -10 icons to increment or decrement by ten. When you have reached the desired percentage, click on either "RUN" button. You will see the random preplacement, then the algorithm will begin.

Patterns

The "pattern" button will display a selection of five preplacements that have interesting properties. The top row of patterns are solvable, and the bottom row are proven unsolvable. Browse the patterns by clicking on them. Each will display on the QCP board. Then run either algorithm several times. Use the stochastic algorithm to observe the heavy-tailed behavior of these patterns.


ALGORITHMS

Stochastic vs. Deterministic

Once a mode has been selected, you may use a deterministic algorithm, a stochastic algorithm, or both to attempt completion. You may also run the algorithms several times with the same preplacement or pattern. Just wait until the algorithm has finished (a comment box will appear at the bottom of the screen), then click again on either "RUN" button. Notice that the deterministic algorithm will always give the same solution (if solvable) in the same number of backtracks. However, the stochastic algorithm will tend to produce several solutions with different numbers of backtracks.


OPTIONS

You may click on the "option" button at any time to change the maximum number of backtracks or the speed of the algorithm.

Maximum Number Of Backtracks

Use the slide bar to raise or lower the maximum number of backtracks. The default setting is 500.

Speed Of Algorithm

Use the slide bar to slow down the algorithm. The displayed number will produce a x-milliseconds delay between each loop. WARNING: if you select the maximum delay, it will take quite a while for the algorithm to terminate! The default setting is 0.



PROJECT OVERVIEW

The quasigroup completion problem is a benchmark that we developed as part of our project INTEGRATION OF ARTIFICIAL INTELLIGENCE AND OPERATIONS RESEARCH FOR COMBINATORIAL PROBLEMS




If you have questions, comments, or suggestions e-mail us: gomes@ai.rl.af.mil
alguirek@rl.af.mil


Created by Tammy Bailey