Nearly finished

Author: di

CS612/a2/written/a2.tex

@@ -25,10 +25,63 @@ \section*{Written}
 
 \item{} % 1
 
+I would equip the robots with simple sensors to detect radioactivity at a
+specific location (such as a digital Geiger counter). I will assume that the
+robots have no other means of control or inter-communication. The large number
+of robots will go into the plant with a small number of pellets, drop them at
+some location, and return for more pellets. When the robots enter the plant for
+the first time, they will travel randomly within it. This is for two reasons:
+one, because it is initially unknown where the highly radioactive areas are, and
+two, because it is unknown how radioactive the most radioactive areas are. The
+robots travels randomly for a set period of time to determine an average
+radioactivity for the area. It then proceeds to continue moving randomly until
+it finds an area which is more radioactive than the average it has found. When
+it has found such a location, it will drop the pellets, thus reducing the
+overall average radioactivity for the area it has seen, and leave for more
+pellets. The entire time the robot is moving, it will be continually updating
+it's running average, to have a better knowledge of the true radioactivity of
+the space. As each robot places their pellets, the total actual average
+radioactivity of the plant will decrease. Once the robots find no place within
+the plant whose maximum radioactivity exceeds the allowable radioactivity within
+a given amount of time, it will leave and the plant will be considered safe.
+
 \item{} % 2
 
+The key concepts from actual ant behavior that are used in most ant colony
+optimization algorithms are:
+
+\begin{itemize}
+    \item Random initial search - Without any initial pheromone trails, scout
+    ants will randomly (or quasi-randomly) move about their environment in
+    search of food. This ensures eventually finding a food source and returning
+    to the nest;
+    \item Pheroemone laying - Actual ants, once they have found a food source,
+    will leave a trail of pheromones from the food to the nest. This serves as a
+    path for other ants to follow, to strengthen the path to the food;
+    \item Collective pheromones - In actual ant systems, ants to not have unique
+    pheremones, so multiple ants laying pheromones in the same location will
+    simply multiply the ``signal'' for that location, allowing a good path to be
+    strengthened;
+    \item Pheromone decay - In the real world, pheromones decay and dissipate
+    over time. While this may degrade a path to a good solution, it also ensures
+    that longer or less frequently traveled paths to the same location are less
+    desirable for any given ant than a more optimal path.
+    \item Path following - Actual ants have the ability to detect a pheromone
+    trail, and to follow it from it's source to it's destination. This allows
+    ants to intelligently follow a path laid by their predecessors.
+    \item Deviations - Actual ants aren't perfect at following the trail,
+    though, and may deviate from it. This helps ants find a possibly shorter
+    path than the one they should be following.
+\end{itemize}
+
 \item{} % 3
 
+To adapt a particle swarm optimization problem to a dynamic or ``online''
+solution, my main focus would be to allow the system to determine when there has
+been a change in the system, and tell the particles to discard or re-determine
+their best positions and velocities accordingly. By being able to discard this
+outdated memory of the optimal solution, the particles will be able to
+re-optimize to find a new solution every time the problem changes.
 
 \end{enumerate}
 
@@ -40,15 +93,34 @@ \section*{Programming}
 The control parameters for my implementation are as follows:
 
 \begin{align*}
-    $\alpha &= 1.0$
+    \alpha &= 1.0\\
+    \beta &= 10.0\\
+    \rho &= 0.1\\
+    Q &= 1.0\\
+    n_{ants} &= 5
 \end{align*}
 
+I arrived at these parameters after trying a few values and seeing which ones
+solved the Djibouti case the fastest. If I had more time, I would likely specify
+a range and a step for each of these, and attempt to see which combination of
+each (out of possibly hundreds) actually performed the best.
+
 \begin{enumerate}
 
 \item{} % 1
 
+For the Djibouti case, my implementation is able to converge, on average, within
+0.2\% of the optimal solution. The best run of my implementation was able to
+converge on the optimal solution. To generate this statistic, I ran my
+implementation 30 times, giving it 5 seconds to complete.
+
 \item{} % 2
 
+For the Luxembourg case, my implementation is able to converge, on average,
+within 28\% of the optimal solution. The best run of my implementation was
+a length of 14353. To generate this statistic, I ran my implementation 10 times,
+giving it 120 seconds to complete.
+
 \item{} % 3
 
 \item{} % 4