DATA ANALYSIS
In order to complete comparative analysis between
the algorithms, RandomMotion and Dominance, two
algorithm applets were created. Both applets allowed the programmer to
control three parameters: size of robot, number of robots, and size of the
applet. Along with controlling parameters, the engine running the applet
indicates that total time and number of collisions allotted to complete
simulation. A fail-safe mechanism was then added to limit the amount of run
time for a simulation, at which if run time met the limit, the time would
then be coded as being an infinite loop. But in order to accurately compare the two algorithms, multiple
simulations were required, thus a Data Analysis program was written to run
the applet a specified amount of times with varying parameters and would
simultaneously record the data into text files.
After completing
approximately three hundred simulations for both algorithms, the following
data was recorded.
Time
- The randomness
involved in RandomMotion makes an observer
inclined to believe this algorithm may not come to end (infinite) or may
take extensive amount of time to complete. But rather than being
infinite, this algorithm when tested completed almost 248 out of 300
simulations with varying sizes ranging from 10-50 units (increments by
10) and ranging from 1- 30 robots. RandomMotion averaged 5.7 seconds per simulation for robots of size 20. The diagram
below demonstrates the Time (secs) vs. Number
of Robots of Random Motion.
*Colors correspond to incremental size of
the robots blue
beginning at 10 and green at 50.*
- The diminished random
quality of Dominance makes an observer inclined to believe it will be a
more efficient algorithm. But the increase efficiency proved only to
occur in the time domain. On average it took robots of size 20 ranging
from 1 to 30 robots to complete simulation in 5.3 seconds. The diagram
below demonstrates the Time (secs) vs. Number
of Robots of Dominance.
*Colors correspond to incremental size of
the robots blue
beginning at 10 and green at 50.*
Comparison:
As expected, entropy increased as the size
increased due to a higher number of collisions. The randomness became more
and more of a problem, causing the steepness of the trend lines to increase
exponentially as time increased. Thus there will be a breakdown point which
occurs when the multitude of robots size encompasses more than ¼ of the size
of the applet. But on average with respect to time, Dominance holds to be
more effective by a margin of a couple of seconds, which can be quantified by
the reasoning: Dominance required fewer robots to be in a random phase unlike
the constant randomness involved in RandomMotion.
The graph below shows the
results. Pay close attention to the purple lines (RandomMotion)
above the green lines (Dominance), which proves that RandomMotion on average requires more time to complete than Dominance.
*The purple lines correspond to RandomMotion and green line
corresponds to weights*
Collisions
- The randomness
involved in RandomMotion makes an observer
inclined to believe that this algorithm may accumulate an excessive
amount of collisions. The diagram below demonstrates the Number of
Collisions vs. Number of Robots of RandomMotion.
*Colors correspond to incremental size of
the robots blue
beginning at 10 and green at 50.*
- The diminished random
quality of Dominance proved to hold a negative effect on the total
number of collisions, which is in contrast to the effect held in the
time domain. Rather than having both robots moving away from collision,
the higher ranking robot insists on staying on its path. Theoretically
in effect, the probability of the higher ranking robot colliding with
the same lower ranking robot (attempting to move away from collision)
increases. This makes the amount of collisions rise significantly. The
diagram below demonstrates the Number of Collisions vs. Number of Robots
of Dominance.
*Colors correspond to incremental size of
the robots blue
beginning at 10 and green at 50.*
Comparison:
As expected as the size of the robot increased the
probability of secondary collision for Dominance. The build of second
collisions became more and more of a problem causing the steepness of the
exponential trend lines to increase. On average with respect to collisions, RandomMotion holds to be more effective by a ratio of 2
to 1. The ratio can be quantified again by the reasoning that Dominance tends
be more aggressive thus more careless with respect to collisions but more
efficient in time.
*The purple lines correspond to RandomMotion and green line
corresponds to weights*
