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Gasper Spagnolo 2022-11-12 17:42:34 +01:00
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INPUT ./images/task_1_broken_solution.png
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@ -248,7 +248,7 @@ I also generated the initial population using the same function, but firstly I g
\end{center}
\end{small}
The results I got using this approach were suprising! I got a perfect score on all mazes. I think that the reason for this is that the mutation function is not only taking into account the walls, but also the previous solution. The algorithm converges really fast now. In 5 generations we get a shortest path! I even generated a 10000 x 10000 maze and it solved it!
The results I got using this approach were suprising! I got a perfect score on all mazes. I think that the reason for this is that the mutation function is not only taking into account the walls, but also the previous solution. The algorithm converges really fast now. In 5 generations of 400 specimens we get a shortest path! I even generated a 1000 x 1000 maze and it solved it in a few seconds!
\subsection{Task 3}
@ -269,6 +269,107 @@ In Task 3, mazes also contain treasure (marked with T). For example:
Your task is to modify your approach so that the solution returns as short a path as possible that also
collects all the treasure.
\subsubsection{Approach}
For treasures to be found I had to modify my fitness function, initial population generation and mutation function. I introduced clustering of cells which are close to the treasures.
That way the genetic algoritm will also mutate in that way. Clusterization is done using simple alogirthm, which just checks for K valid cells arround the treasure and adds them to
the cluster. The cluster is then used to influence generation of the initial population and mutation of the population.
\begin{figure}[h]
\centering
\includegraphics[width=4cm]{./images/task_3_clustering.png}
\caption{Clustering example}
\label{image:task_3_clustering}
\end{figure}
The fitness function had also be redefined to also take into account the treasures. The fitness function is defined as follows:
\begin{small}
\begin{center}
\begin{verbatim}
def fitness_func(path, solution_idx):
.........................
if path[maze.start_pos] == 1 and path[maze.end_pos] == 1:
fitness += 300
# Check if there is a valid path
# First check if there is a path from start to end
paths = []
complete_path = maze.walk_through_maze(path, maze.end_pos)
paths.extend(complete_path)
# Then for each treasure find a path from start to treasure
treasures_found = 0
if complete_path != []:
for treasure in maze.treasures:
treasure_path = maze.walk_through_maze(path, treasure)
if treasure_path != []:
treasures_found += 1
paths.extend(treasure_path)
# Remove duplicates
path = list(set(paths))
path_len = len(path)
# Set the first path found as the shotest one
if maze.shortest_path == [] and path_len > 0 and treasures_found >= len(maze.treasures) // 2:
fitness += treasures_found * 1000
print('First path found')
maze.shortest_path = path
maze.treasures_found = treasures_found
maze.adjust_weights(complete_path)
#Check if the current path is shorter than the shortest one
elif treasures_found > maze.treasures_found and path_len > 0:
fitness += 1000 * treasures_found
print('Path with more treasures found!')
maze.shortest_path = path
maze.treasures_found = treasures_found
maze.adjust_weights(complete_path)
elif path_len < len(maze.shortest_path) and treasures_found > maze.treasures_found and path_len > 0:
fitness += 1000 * treasures_found
print('Path with less steps found!')
maze.shortest_path = path
maze.treasures_found = treasures_found
maze.adjust_weights(complete_path)
..........................
\end{verbatim}
\end{center}
\end{small}
So now each time there is a treasue in the path or if there is a shorter path, the fitness function will increase the fitness of the specimen. The fitness function also takes into account the number of treasures found. If there is a path with more treasures found, the fitness function will increase the fitness of the specimen.
And the mutation function is same as in task 2, but now it also takes into account the treasures. The mutation function is defined as follows:
\begin{small}
\begin{center}
\begin{verbatim}
def on_mutation(generations, ga_instance):
.........................
cluster_instances = np.reshape(np.array(maze.clusters), -1)
# Loop through the population
for i in range(len(generations)):
# randomly select random number of the instances where there are clusters
random_cluster_instances = np.random.choice(cluster_instances, size=int(len(cluster_instances)* random.uniform(0.01, 1.0)), replace=False)
.........................
generations[i][random_cluster_instances] = 1
.........................
return generations
\end{verbatim}
\end{center}
\end{small}
\subsubsection{Results}
Results are very good! The algorithm finds the shortest path and collects all the treasures on all provided test mazes.
Example of the shortest path found on maze 4:
\begin{small}
\textit{The shortest path is [(12, 4), (4, 9), (5, 1), (3, 13), (5, 10), (10, 6), (7, 1), (1, 15), (18, 1), (16, 13), (18, 10), (7, 10), (9, 1), (3, 15), (17, 14), (13, 1), (1, 8), (6, 4), (18, 3), (7, 12), (14, 8), (17, 16), (1, 10), (15, 9), (18, 5), (7, 5), (7, 14), (3, 1), (14, 1), (3, 10), (13, 5), (1, 3), (16, 1), (1, 12), (16, 10), (18, 7), (14, 3), (3, 12), (1, 5), (6, 1), (1, 14), (16, 12), (18, 9), (14, 5), (4, 4), (3, 14), (10, 1), (1, 7), (18, 2), (1, 16), (16, 14), (7, 11), (12, 1), (14, 7), (5, 4), (4, 6), (3, 16), (8, 6), (10, 3), (1, 9), (18, 4), (12, 3), (4, 8), (10, 5), (1, 2), (2, 1), (1, 11), (6, 10), (12, 5), (4, 1), (3, 11), (4, 10), (8, 1), (19, 10), (1, 4), (1, 13), (14, 4), (17, 15), (1, 6), (15, 8), (6, 5), (7, 13), (14, 6), (4, 5), (8, 5), (11, 1), (17, 17), (2, 16), (15, 1), (15, 10), (18, 6), (4, 7), (17, 1), (10, 4), (9, 6), (11, 3), (1, 1), (16, 11), (18, 8)] }
\end{small}
\begin{figure}[h]
\centering
\includegraphics[width=4cm]{./images/task_3_maze_4.png}
\caption{Shortest path in maze 4, collecting all treasures}
\label{image:task_1_maze_1}
\end{figure}
\subsection{Task 4}
\subsubsection{Task description}