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implementation-and-comparison-of-navigation-algorithms.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
},
"gpuClass": "standard"
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/nicholsonjf/7025174c68a028b48beb27d9eeb5d593/implementation-and-comparison-of-navigation-algorithms.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"source": [
"# Dependencies"
],
"metadata": {
"id": "wCMf3DNJacxr"
}
},
{
"cell_type": "code",
"source": [
"%matplotlib inline \n",
"\n",
"import numpy as np\n",
"from heapdict import heapdict\n",
"from math import floor, sqrt\n",
"\n",
"# for running experiments\n",
"import itertools\n",
"from multiprocessing import Pool\n",
"import pandas as pd\n",
"from google.colab import files\n",
"\n",
"# for plotting\n",
"from matplotlib import pyplot as plt\n",
"from matplotlib import colors\n",
"import networkx as nx"
],
"metadata": {
"id": "wFXeyLy3PWIt"
},
"execution_count": 1,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"# Source Code"
],
"metadata": {
"id": "GyyLCsZUXwr3"
}
},
{
"cell_type": "code",
"source": [
"# TYPE_MAPPING is used to colour the tile according to the type\n",
"# e.g. all obstacles are in black colour. these tiles will be inaccessible\n",
"TYPE_MAPPING = {\n",
" 'obstacle' : 'black',\n",
" 'source' : 'royalblue',\n",
" 'target' : 'green',\n",
" 'path' : 'peachpuff',\n",
" 'others' : 'white',\n",
" 'visited' : 'yellow'\n",
"}\n",
"\n",
"# COLOUR_MAPPING is used to assign a value in numpy array so that matplotlib knows which value will be mapped to which colour\n",
"# e.g. if coordinate (1,2) has value 0, the tile will be of black colour\n",
"COLOUR_MAPPING = {\n",
" 'black' : 0,\n",
" 'royalblue' : 1,\n",
" 'green' : 2,\n",
" 'peachpuff' : 3,\n",
" 'white' : 4,\n",
" 'yellow' : 5\n",
"}"
],
"metadata": {
"id": "GAEBLmFrthFB"
},
"execution_count": 2,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"**Graph Implementation**"
],
"metadata": {
"id": "shOaPfcU8uCt"
}
},
{
"cell_type": "code",
"source": [
"class Graph:\n",
" \"\"\"\n",
" The graph implementation that all the algorithms in our project are designed\n",
" to search (with the exception of RRT). The graph is 2d. The height, width\n",
" and obstacle density can be set by the caller. The graph can be searched by\n",
" using its adjacency list, and easily plotted by calling the plot method.\n",
" \"\"\"\n",
"\n",
" def __init__(self, w, h, seed=0):\n",
" \"\"\"\n",
" Args:\n",
" w: The width of the graph (number of nodes)\n",
" h: The height of the graph (number of nodes)\n",
" seed: Using a seed value allows the same random number sequence to \n",
" be recalled, i.e. so the same obstacle layout can be used in\n",
" different trials.\n",
" \"\"\"\n",
" self.COLOUR_MAPPING = COLOUR_MAPPING\n",
" self.TYPE_MAPPING = TYPE_MAPPING\n",
"\n",
" # set the colour based on values in graph array (self.g). the mapping is determined by COLOUR_MAPPING\n",
" self.cmap = colors.ListedColormap( list( self.COLOUR_MAPPING.keys() ) )\n",
" self.bounds = list( self.COLOUR_MAPPING.values() ) + [ max(self.COLOUR_MAPPING.values()) +1 ]\n",
" self.norm = colors.BoundaryNorm(self.bounds, self.cmap.N)\n",
"\n",
" self.w = w\n",
" self.h = h\n",
" # initialise with others type of tiles\n",
" self.g = np.full(\n",
" (h, w),\n",
" self.COLOUR_MAPPING[self.TYPE_MAPPING['others']],\n",
" dtype=np.uint8\n",
" )\n",
" self.seed = seed\n",
"\n",
" self.adjacency_list = {}\n",
" self.source = None\n",
" self.target = None\n",
" self.obstacles = []\n",
" \n",
" def add_obstacle(self, x, y):\n",
" \"\"\"\n",
" args:\n",
" x: The x coordinate for where to add the obstacle.\n",
" y: The y coordinate for where to add the obstacle.\n",
" \"\"\"\n",
" self.g[y,x] = self.COLOUR_MAPPING[ self.TYPE_MAPPING['obstacle'] ]\n",
" self.obstacles += [(x,y)]\n",
" \n",
" def add_source(self, x, y):\n",
" \"\"\"\n",
" args:\n",
" x: The x coordinate for where to add the obstacle.\n",
" y: The y coordinate for where to add the obstacle.\n",
" \"\"\"\n",
" # reset previous source to ensure that there is only one source\n",
" if self.source is not None:\n",
" self.g[self.source[1],self.source[0]] = self.COLOUR_MAPPING[ self.TYPE_MAPPING['others'] ]\n",
"\n",
" # update new source\n",
" self.g[y,x] = self.COLOUR_MAPPING[ self.TYPE_MAPPING['source'] ]\n",
" self.source = (x,y)\n",
" \n",
" def add_target(self, x, y):\n",
" \"\"\"\n",
" args:\n",
" x: The x coordinate for where to add the obstacle.\n",
" y: The y coordinate for where to add the obstacle.\n",
" \"\"\"\n",
" # reset previous target to ensure that there is only one target\n",
" if self.target is not None:\n",
" self.g[self.target[1],self.target[0]] = self.COLOUR_MAPPING[ self.TYPE_MAPPING['others'] ]\n",
" \n",
" # update new target\n",
" self.g[y,x] = self.COLOUR_MAPPING[ self.TYPE_MAPPING['target'] ]\n",
" self.target = (x,y)\n",
"\n",
" def generate_random_graph(self, probability_obstacle=0.2):\n",
" \"\"\"\n",
" args:\n",
" probability_obstacle: The probability that any given node in the grid\n",
" will be an obstacle.\n",
" \"\"\"\n",
" np.random.seed(self.seed)\n",
"\n",
" # generate list of all nodes\n",
" nodes = [ (x,y) for x in range(self.w) for y in range(self.h) ]\n",
" nodes_idx = list( range(self.w * self.h) )\n",
" # print(f\"nodes : {nodes}\")\n",
" \n",
" # pick one node as the source and remove node from the list\n",
" source_idx = np.random.choice(nodes_idx)\n",
" nodes_idx.remove(source_idx)\n",
" # print(f\"source : {source_idx}\\n nodes : {nodes_idx}\")\n",
" self.add_source(nodes[source_idx][0], nodes[source_idx][1])\n",
" \n",
" # pick one node as the target and remove node from the list\n",
" target_idx = np.random.choice(nodes_idx)\n",
" nodes_idx.remove(target_idx)\n",
" # print(f\"target : {target_idx}\\n nodes : {nodes_idx}\")\n",
" self.add_target(nodes[target_idx][0], nodes[target_idx][1])\n",
"\n",
" # pick a few nodes as obstacles\n",
" number_obstacles = floor(probability_obstacle * self.w * self.h)\n",
" obstacles_idx = np.random.choice(nodes_idx, size=number_obstacles, replace=False)\n",
" # print(f\"obstacles : {obstacles_idx}\")\n",
" for obstacles_idx in obstacles_idx:\n",
" self.add_obstacle(nodes[obstacles_idx][0], nodes[obstacles_idx][1])\n",
" \n",
" def add_path(self, x, y):\n",
" \"\"\"\n",
" args:\n",
" x: The x coordinate for where to add the obstacle.\n",
" y: The y coordinate for where to add the obstacle.\n",
" \"\"\"\n",
" # only add path if target or source is not (x,y)\n",
" if (x,y) != self.target and (x,y) != self.source:\n",
" self.g[y,x] = self.COLOUR_MAPPING[ self.TYPE_MAPPING['path'] ]\n",
"\n",
" def add_paths(self, paths):\n",
" \"\"\"\n",
" args:\n",
" paths: A list of nodes to add to the found path.\n",
" \"\"\"\n",
" for x,y in paths:\n",
" self.add_path(x,y)\n",
"\n",
" # Add a single visited node to the list of visited nodes.\n",
" def add_visited_node(self, x, y):\n",
" \"\"\"\n",
" args:\n",
" x: The x coordinate for where to add the obstacle.\n",
" y: The y coordinate for where to add the obstacle.\n",
" \"\"\"\n",
" if (x,y) != self.target and (x,y) != self.source:\n",
" self.g[y,x] = self.COLOUR_MAPPING[ self.TYPE_MAPPING['visited'] ]\n",
" \n",
" # Add a list of visited nodes to the list of visited nodes.\n",
" def add_visited(self, paths):\n",
" \"\"\"\n",
" args:\n",
" paths: A list of nodes to add to the visited nodes list.\n",
" \"\"\"\n",
" for x,y in paths:\n",
" self.add_visited_node(x,y)\n",
"\n",
" def plot(self, plot_type, distance_fn=None):\n",
" \"\"\"\n",
" args:\n",
" plot_type: The type of matplotlib.pyplot to use to plot the graph.\n",
" distance_fn: A functiom which can be used to calculate distances\n",
" between vertices in the plot.\n",
" \n",
" \"\"\"\n",
" if plot_type == 'grid':\n",
" plt.figure( figsize=(self.w, self.h) )\n",
"\n",
" plt.imshow(\n",
" self.g,\n",
" interpolation = 'none',\n",
" cmap = self.cmap,\n",
" norm = self.norm,\n",
" extent=[0, self.w, self.h, 0] # to ensure that the coordinate plot is adjusted\n",
" )\n",
" plt.ylim((0, self.h))\n",
" plt.xlim((0, self.w))\n",
" plt.xticks(np.arange(0., self.w + 1., 1.))\n",
" plt.yticks(np.arange(0., self.h + 1., 1.))\n",
" plt.grid(which='major', axis='both', linestyle='-', color='k', linewidth=2)\n",
" plt.show()\n",
"\n",
" elif plot_type == 'graph' and distance_fn is not None:\n",
" # source : https://stackoverflow.com/questions/28372127/add-edge-weights-to-plot-output-in-networkx\n",
" plt.figure( figsize=(self.w, self.h) )\n",
" \n",
" self.g_nx = nx.Graph()\n",
" self.adjacency_list = self.get_adjacency_list(distance_fn)\n",
"\n",
" nodes = [ (x,y) for x in range(self.w) for y in range(self.h) ]\n",
"\n",
" for node in nodes:\n",
" self.g_nx.add_node(node, pos=node)\n",
"\n",
" for node in self.adjacency_list.keys():\n",
" for neighbour, distance in self.adjacency_list[node].items():\n",
" self.g_nx.add_edge(node, neighbour, weight=distance)\n",
"\n",
" pos = nx.get_node_attributes(self.g_nx, 'pos')\n",
" nx.draw(self.g_nx, pos)\n",
" labels = nx.get_edge_attributes(self.g_nx, 'weight')\n",
" nx.draw_networkx_edge_labels(self.g_nx, pos, edge_labels=labels)\n",
"\n",
"\n",
" def is_valid_coordinate(self, x, y):\n",
" \"\"\"\n",
" args:\n",
" x: The x coordinate to check if the coordinate is valid.\n",
" y: The y coordinate to check if the coordinate is valid.\n",
" \"\"\"\n",
" return (x >= 0) and (x < self.w) and (y >= 0) and (y < self.h)\n",
"\n",
" def add_neighbour(self, current, neighbour, distance_fn):\n",
" \"\"\"\n",
" args:\n",
" current: The node currently being expanded.\n",
" neighbor: The neighbor of the current node to be added to the adjacency list.\n",
" distance_fn : the distance fn to be used to calculate the distance between the current and neighbouring node\n",
" \"\"\"\n",
" x, y = neighbour\n",
" if self.is_valid_coordinate(x, y):\n",
" if self.g[y, x] != self.COLOUR_MAPPING[ self.TYPE_MAPPING['obstacle'] ]:\n",
" self.adjacency_list[current][neighbour] = distance_fn(current, neighbour)\n",
" \n",
" def get_adjacency_list(self, distance_fn):\n",
" '''\n",
" distance_fn needs to be a function that expects 2 inputs and returns float / int\n",
" return adjacency list with the following format\n",
" { (x_source, y_source) :\n",
" { \n",
" (x_neighbour, y_neighbour) : distance_to_neighbour,\n",
" (x_neighbour, y_neighbour) : distance_to_neighbour\n",
" }\n",
" }\n",
" '''\n",
"\n",
" self.adjacency_list = {}\n",
" np.random.seed(self.seed)\n",
" for x in range(self.w):\n",
" for y in range(self.h):\n",
" # obstacle node is not added in the adjacency list\n",
" if self.g[y,x] != self.COLOUR_MAPPING[ self.TYPE_MAPPING['obstacle'] ]:\n",
" self.adjacency_list[ (x,y) ] = {}\n",
"\n",
" self.add_neighbour((x,y), (x-1, y-1), distance_fn) # add bottom left\n",
" self.add_neighbour((x,y), (x, y-1), distance_fn) # add bottom\n",
" self.add_neighbour((x,y), (x+1, y-1), distance_fn) # add bottom right\n",
" self.add_neighbour((x,y), (x+1, y), distance_fn) # add right\n",
" self.add_neighbour((x,y), (x+1, y+1), distance_fn) # add top right\n",
" self.add_neighbour((x,y), (x, y+1), distance_fn) # add top\n",
" self.add_neighbour((x,y), (x-1, y+1), distance_fn) # add top left\n",
" self.add_neighbour((x,y), (x-1, y), distance_fn) # add left\n",
" return self.adjacency_list"
],
"metadata": {
"id": "Lq8tnx5UPD9k"
},
"execution_count": 3,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"**Distance Functions**"
],
"metadata": {
"id": "IPm-LUxH81rs"
}
},
{
"cell_type": "code",
"source": [
"def manhattan_distance(current, target):\n",
" \"\"\"\n",
" args:\n",
" current: The node currently being expanded.\n",
" target: The neighboring node to calculate the distance to. \n",
" \"\"\"\n",
" return abs(current[0] - target[0]) + abs(current[1] - target[1])\n",
"\n",
"def diagonal_distance(current, target, lateral_cost=1, diag_cost=sqrt(2)):\n",
" \"\"\"\n",
" args:\n",
" current: The node currently being expanded.\n",
" target: The neighboring node to calculate the distance to.\n",
" lateral_cost: The cost to travel laterally in a 2d grid.\n",
" diag_cost: The cost to travel diagonally in a 2d grid.\n",
" \"\"\"\n",
" # heuristic function for euclidean distance\n",
" dx = abs(current[0] - target[0])\n",
" dy = abs(current[1] - target[1])\n",
" h = lateral_cost*(dx+dy) + (diag_cost-2*lateral_cost)*min(dx,dy)\n",
" return h\n",
"\n",
"def euclidian_distance(current, target):\n",
" \"\"\"\n",
" args:\n",
" current: The node currently being expanded.\n",
" target: The neighboring node to calculate the distance to. \n",
" \"\"\"\n",
" return sqrt( (current[0]-target[0])**2 + (current[1]-target[1])**2 )\n",
"\n",
"def random_distance(current, target, upper_bound=10):\n",
" \"\"\"\n",
" args:\n",
" current: The node currently being expanded.\n",
" target: The neighboring node to calculate the distance to.\n",
" upper_bound: The exclusive upper bound of the random number that will be\n",
" used as the distance.\n",
" \"\"\"\n",
" return np.random.randint(upper_bound)"
],
"metadata": {
"id": "VEjOKcgRyzH0"
},
"execution_count": 4,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"**A* Algorithm**"
],
"metadata": {
"id": "0Isj-Ssf85UY"
}
},
{
"cell_type": "code",
"source": [
"class Astar:\n",
"\n",
" def __init__(self, adjacency_list):\n",
" \"\"\"\n",
" args:\n",
" adjacency_list: A nested dict of all nodes, their neighbors, and\n",
" the distances to each neighbor.\n",
" \"\"\"\n",
" self.adjacency_list = adjacency_list\n",
" self.visited = None\n",
" self.path_len = None\n",
"\n",
" def initialize_scores(self, init_value=float('inf')):\n",
" \"\"\"\n",
" args:\n",
" init_value: the starting g value for all nodes in the adjacency list.\n",
" \"\"\"\n",
" # initialize scores for all nodes as inf\n",
" scores = {}\n",
" for node in self.adjacency_list.keys():\n",
" scores[node] = init_value\n",
" return scores\n",
"\n",
" def reconstruct_path_and_cost(self, closed_set, current):\n",
" \"\"\"\n",
" args:\n",
" closed_set: The list of nodes that have already been explored.\n",
" current: A dict that maps nodes to their immediate predecessors on\n",
" the optimal path from start to goal.\n",
" \"\"\"\n",
" # to reconstruct shortest path and calculate cost of shortest path\n",
" path = [current]\n",
" cost = 0\n",
" while current in closed_set.keys():\n",
" cost += self.adjacency_list[current][ closed_set[current] ]\n",
" current = closed_set[current]\n",
" path = [current] + path\n",
" self.path_len = len(path)\n",
" return path, cost, len(self.visited)\n",
"\n",
" def search(self, source, target, heuristic_func):\n",
" \"\"\"\n",
" args:\n",
" source: The starting node of the search.\n",
" target: The goal of the search.\n",
" heuristic_func: The function used to calculate h(n) in the f function.\n",
" \"\"\"\n",
" self.visited = []\n",
"\n",
" # return source if source is target\n",
" if source == target:\n",
" return [target], 0\n",
"\n",
" open_set = heapdict()\n",
" open_set[source] = 0\n",
" closed_set = {}\n",
"\n",
" gscores = self.initialize_scores()\n",
" gscores[source] = 0\n",
" fscores = self.initialize_scores()\n",
" fscores[source] = heuristic_func(source, target)\n",
" \n",
" while len(open_set) != 0:\n",
"\n",
" current, f_score = open_set.popitem()\n",
" if current == target:\n",
" return self.reconstruct_path_and_cost(closed_set, current)\n",
" # Add current to visited nodes list.\n",
" if current not in self.visited:\n",
" self.visited.append(current)\n",
" for neighbour, distance in self.adjacency_list[current].items():\n",
" # Add neighbour to visited nodes list\n",
" if neighbour not in self.visited:\n",
" self.visited.append(neighbour)\n",
" neighbour_gscore = gscores[current] + distance\n",
" # print(f'Neighbour : {neighbour}, gscore : {neighbour_gscore}')\n",
" if neighbour_gscore < gscores[neighbour]:\n",
" closed_set[neighbour] = current\n",
" gscores[neighbour] = neighbour_gscore\n",
" fscores[neighbour] = neighbour_gscore + heuristic_func(neighbour, target)\n",
" if neighbour not in open_set.keys():\n",
" open_set[neighbour] = fscores[neighbour]\n",
" return [], float('Inf')"
],
"metadata": {
"id": "iG2lWBE0JkDt"
},
"execution_count": 5,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"**Variations of A\\***"
],
"metadata": {
"id": "5tbiBOnf5fLa"
}
},
{
"cell_type": "code",
"source": [
"class Weighted_Astar(Astar):\n",
" \"\"\"\n",
" Traditional A* will find the optimal solution to a graph search problem. Often\n",
" though, it's too expensive to find the optimal solution and a sub-optimal\n",
" solution is good enough.\n",
" Weighted A* is a variation of traditional A* that uses a constant scalar to\n",
" \"weight\" the importance of the heuristic value. The f-value is computed\n",
" as follows:\n",
"\n",
" f(n) = g(n) + epsilon * h(n)\n",
"\n",
" where epsilon >= 1\n",
" \"\"\"\n",
"\n",
" def __init__(self, adjacency_list, epsilon=2):\n",
" \"\"\"\n",
" args:\n",
" adjacency_list: A nested dict of all nodes, their neighbors, and\n",
" the distances to each neighbor.\n",
" epsilon: An integer that will be used to multiply the heuristic value\n",
" in the f function.\n",
" \"\"\"\n",
" self.epsilon = epsilon\n",
" super().__init__(adjacency_list)\n",
"\n",
" def search(self, source, target, heuristic_func):\n",
" \"\"\"\n",
" args:\n",
" source: The starting node of the search.\n",
" target: The goal of the search.\n",
" heuristic_func: The function used to calculate h(n) in the f function.\n",
" \"\"\"\n",
" self.visited = []\n",
" if source == target:\n",
" return [target], 0\n",
"\n",
" open_set = heapdict()\n",
" open_set[source] = 0\n",
" closed_set = {}\n",
"\n",
" gscores = self.initialize_scores()\n",
" gscores[source] = 0\n",
" fscores = self.initialize_scores()\n",
" fscores[source] = heuristic_func(source, target)\n",
" \n",
" while len(open_set) != 0:\n",
" current, f_score = open_set.popitem()\n",
" if current == target:\n",
" return self.reconstruct_path_and_cost(closed_set, current)\n",
" # Add current to visited nodes list.\n",
" if current not in self.visited:\n",
" self.visited.append(current)\n",
" for neighbour, distance in self.adjacency_list[current].items():\n",
" # Add neighbour to visited nodes list\n",
" if neighbour not in self.visited:\n",
" self.visited.append(neighbour)\n",
" neighbour_gscore = gscores[current] + distance\n",
" if neighbour_gscore < gscores[neighbour]:\n",
" closed_set[neighbour] = current\n",
" gscores[neighbour] = neighbour_gscore\n",
" fscores[neighbour] = neighbour_gscore + (self.epsilon * heuristic_func(neighbour, target))\n",
" if neighbour not in open_set.keys():\n",
" open_set[neighbour] = fscores[neighbour]\n",
" return [], float('Inf')\n",
"\n",
"\n",
"class Beam_Search(Astar):\n",
" \"\"\"\n",
" With traditional A*, the open set can grow unbounded as the grid is searched\n",
" for the lowest cost path from the source node to the goal node. With beam\n",
" search, at every iteration of the main loop, the open set is redefined to be\n",
" only the highest priority beam_size nodes in the open set. This is particularly\n",
" useful for search problems where storing the entire search tree in memory\n",
" is prohibitive, like in some machine language translation applications.\n",
" \"\"\"\n",
"\n",
" def __init__(self, adjacency_list, beam_size=3):\n",
" \"\"\"\n",
" args:\n",
" adjacency_list: A nested dict of all nodes, their neighbors, and\n",
" the distances to each neighbor.\n",
" beam_size: An integer that defines the maximum number of nodes that\n",
" will be explored at each iteration of the search.\n",
" \"\"\"\n",
" self.beam_size = beam_size\n",
" super().__init__(adjacency_list)\n",
"\n",
" def search(self, source, target, heuristic_func):\n",
" \"\"\"\n",
" args:\n",
" source: The starting node of the search.\n",
" target: The goal of the search.\n",
" heuristic_func: The function used to calculate h(n) in the f function.\n",
" \"\"\"\n",
" self.visited = []\n",
" if source == target:\n",
" return [target], 0\n",
"\n",
" open_set = heapdict()\n",
" open_set[source] = 0\n",
" closed_set = {}\n",
"\n",
" gscores = self.initialize_scores()\n",
" gscores[source] = 0\n",
" fscores = self.initialize_scores()\n",
" fscores[source] = heuristic_func(source, target)\n",
" \n",
" while len(open_set) != 0:\n",
" current, f_score = open_set.popitem()\n",
" if current == target:\n",
" return self.reconstruct_path_and_cost(closed_set, current)\n",
" # Add current to visited nodes list.\n",
" if current not in self.visited:\n",
" self.visited.append(current)\n",
" for neighbour, distance in self.adjacency_list[current].items():\n",
" # Add neighbour to visited nodes list\n",
" if neighbour not in self.visited:\n",
" self.visited.append(neighbour)\n",
" neighbour_gscore = gscores[current] + distance\n",
" if neighbour_gscore < gscores[neighbour]:\n",
" closed_set[neighbour] = current\n",
" gscores[neighbour] = neighbour_gscore\n",
" fscores[neighbour] = neighbour_gscore + heuristic_func(neighbour, target)\n",
" if neighbour not in open_set.keys():\n",
" open_set[neighbour] = fscores[neighbour]\n",
" # Enforce beam size.\n",
" if len(open_set) > self.beam_size:\n",
" new_hd = heapdict()\n",
" for i in range(self.beam_size):\n",
" item, priority = open_set.popitem()\n",
" new_hd[item] = priority\n",
" open_set = new_hd\n",
" return [], float('Inf')\n",
"\n"
],
"metadata": {
"id": "CGBBBthj5wLW"
},
"execution_count": 6,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"**Best First Search**"
],
"metadata": {
"id": "GjkMwrf9gNVa"
}
},
{
"cell_type": "code",
"source": [
"class BFS:\n",
" '''\n",
" This is the class for Best First Search (BFS). \n",
" BFS visits next state based on heuristics function f(n) = h with lowest heuristic value. \n",
" It doesn't take cost of the path into consideration for that specific state. \n",
" It only evaluates which next state from the current state has lowest heuristics. \n",
" Thus it is expected to be least efficient algorithm across our choices and serve as a base to others.\n",
" '''\n",
" # initialize the BFS object with adjacency_list property\n",
" def __init__(self, adjacency_list):\n",
" \"\"\"\n",
" args:\n",
" adjacency_list: A nested dict of all nodes, their neighbors, and\n",
" the distances to each neighbor.\n",
" \"\"\"\n",
" self.adjacency_list = adjacency_list\n",
" \n",
" # this is to keep scores and return them eventually\n",
" def initialize_scores(self, init_value=float('inf')):\n",
" \"\"\"\n",
" args:\n",
" init_value: the starting g value for all nodes in the adjacency list.\n",
" \"\"\"\n",
" scores = {}\n",
" for node in self.adjacency_list.keys():\n",
" scores[node] = init_value\n",
" return scores\n",
"\n",
" # since we are using a custom graph this method is related with it and nothing to do with actual algorithm\n",
" def reconstruct_path_and_cost(self, closed_set, current):\n",
" \"\"\"\n",
" args:\n",
" closed_set: The list of nodes that have already been explored.\n",
" current: A dict that maps nodes to their immediate predecessors on\n",
" the optimal path from start to goal.\n",
" \"\"\"\n",
" path = [current]\n",
" cost = 0\n",
" while current in closed_set.keys():\n",
" cost += self.adjacency_list[current][ closed_set[current] ]\n",
" current = closed_set[current]\n",
" path = [current] + path\n",
" self.path_len = len(path)\n",
" return path, cost, len(self.visited)\n",
"\n",
" # this is the actual search method where we visit the nodes and return the result if we find the target\n",
" def search(self, source, target, heuristic_func):\n",
" \"\"\"\n",
" args:\n",
" source: The starting node of the search.\n",
" target: The goal of the search.\n",
" heuristic_func: The function used to calculate h(n) in the f function.\n",
" \"\"\"\n",
" self.visited = []\n",
"\n",
" if source == target:\n",
" return [target], 0\n",
"\n",
" open_set = heapdict()\n",
" open_set[source] = 0\n",
" closed_set = {}\n",
" #this is different from the A* in a way it ignores the gscores and take only fscores into considerati\n",
" fscores = self.initialize_scores()\n",
" fscores[source] = heuristic_func(source, target)\n",
" \n",
" while len(open_set) != 0:\n",
"\n",
" current, f_score = open_set.popitem()\n",
" if current == target:\n",
" return self.reconstruct_path_and_cost(closed_set, current)\n",
" if current not in self.visited:\n",
" # Add current to visited nodes list.\n",
" self.visited.append(current)\n",
" for neighbour, distance in self.adjacency_list[current].items():\n",
" if neighbour not in self.visited:\n",
" # Add neighbour to visited nodes list.\n",
" self.visited.append(neighbour)\n",
" neighbour_fscore = fscores[current] \n",
" if neighbour_fscore < fscores[neighbour]:\n",
" closed_set[neighbour] = current\n",
" fscores[neighbour] = neighbour_fscore + heuristic_func(neighbour, target)\n",
" if neighbour not in open_set.keys():\n",
" open_set[neighbour] = fscores[neighbour] \n",
" return [], float('Inf')"
],
"metadata": {
"id": "rbatiQWcm9aj"
},
"execution_count": 7,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"# Experiment #1\n",
"\n",
"In the experiment below, each algorithm (Astar, BFS, Weighted_Astar, Beam_Search) is used to search each grid size (10, 20, 50) at each obstacle density (.1, .2, .4). This results in 36 separate trials, as can be seen in the table of results below.\n",
"\n",
"The RRT algorthm is run in a separate environment and source code and demos will be submitted separately."
],
"metadata": {
"id": "f-ty9fEnYVUn"
}
},
{
"cell_type": "code",
"source": [
"size_list = [10, 20, 50]\n",
"probability_obstacle_list = [0.1, 0.2, 0.4]\n",
"distance_fn_list = [euclidian_distance]\n",
"heuristic_func_list = [euclidian_distance]\n",
"search_algo_list = [Astar, BFS, Weighted_Astar, Beam_Search]\n",
"# generate all permutations based on the above parameters\n",
"all_exps = itertools.product(\n",
" size_list,\n",
" probability_obstacle_list,\n",
" distance_fn_list,\n",
" heuristic_func_list,\n",
" search_algo_list\n",
")\n",
"\n",
"def run_exp(parameters):\n",
" \"\"\"\n",
" args:\n",
" parameters: Values for the following parameters neededed to conduct a\n",
" search: graph sizes, probability densities, distance functions,\n",
" heuristic functions, search algorithms.\n",
" \"\"\"\n",
" # generate graph and run search algorithm based on the parameters\n",
" size, probability_obstacle, distance_fn, heuristic_func, search_algo = parameters\n",
" g = Graph(w=size, h=size)\n",
" g.generate_random_graph(probability_obstacle=probability_obstacle)\n",
" algo = search_algo( g.get_adjacency_list(distance_fn) )\n",
" search_result = algo.search(g.source, g.target, heuristic_func)\n",
" # record the approximate_shortest distance, paths, minimum cost, number of visited nodes\n",
" approx_shortest_distance = heuristic_func(g.source, g.target)\n",
" paths = search_result[0]\n",
" cost = search_result[1]\n",
" visited = search_result[2] if len(search_result) > 2 else None\n",
" return (size, probability_obstacle, distance_fn.__name__, heuristic_func.__name__, search_algo.__name__), approx_shortest_distance, paths, cost, visited\n",
"\n",
"def run_all_exps(all_exps, pool_size):\n",
" \"\"\"\n",
" args:\n",
" all_exps: A cross product of the following values for each trial: graph sizes, \n",
" probability densities, distance functions, heuristic functions,\n",
" search algorithms.\n",
" pool_size: The number of concurrent processes to use to run the experiment.\n",
" \"\"\"\n",
" # run exp in parallel based on the pool_size\n",
" with Pool(pool_size) as p:\n",
" return p.map(run_exp, all_exps)\n",
"\n",
"def process_exps_results(results):\n",
" \"\"\"\n",
" args:\n",
" results: A list of the return values from each trial.\n",
" \"\"\"\n",
" # convert results from list of tuples to list of dictionaries\n",
" # list of dictionaries can then be converted to pandas dataframe\n",
" output = []\n",
" for result in results:\n",
" parameters, approx_shortest_distance, paths, cost, visited = result\n",
" size, probability_obstacle, distance_fn, heuristic_func, search_algo = parameters\n",
" output += [{\n",
" 'size' : size,\n",
" 'probability_obstacle' : probability_obstacle,\n",
" 'distance_fn' : distance_fn,\n",
" 'heuristic_fn' : heuristic_func,\n",
" 'search_algo' : search_algo,\n",
" 'approx_shortest_distance' : approx_shortest_distance,\n",
" 'paths_length' : len(paths),\n",
" 'cost' : cost,\n",
" 'nodes_visited' : visited \n",
" }]\n",
" return output\n",
"\n",
"# run all experiments in parallel based on the defined parameters\n",
"results = run_all_exps(all_exps, 8)\n",
"results = process_exps_results(results)\n",
"results = pd.DataFrame.from_records(results)\n",
"# save results as csv file and download it\n",
"results.to_csv('experiment1_results.csv')\n",
"files.download('experiment1_results.csv')\n",
"# display results in pivot table\n",
"results[\"env\"] = list(zip(\n",
" results['size'],\n",
" results['probability_obstacle'],\n",
" results['distance_fn'],\n",
" results['heuristic_fn'],\n",
" results['approx_shortest_distance'] ))\n",
"results.pivot(index=['env', 'search_algo'],\n",
" columns=[],\n",
" values=['paths_length', 'cost', 'nodes_visited'])"
],
"metadata": {
"id": "NygiSOH-YZGU",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"outputId": "f2b29939-08dd-4a2c-85dd-a45737bed109"
},
"execution_count": 8,
"outputs": [
{
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"\n",
" const channel = await google.colab.kernel.comms.open(id);\n",
" // Send a message to notify the kernel that we're ready.\n",
" channel.send({})\n",
"\n",
" for await (const message of channel.messages) {\n",
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" div.remove();\n",
" }\n",
" "
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"data": {
"text/plain": [
" paths_length \\\n",
"env search_algo \n",
"(10, 0.1, euclidian_distance, euclidian_distanc... Astar 5.0 \n",
" BFS 5.0 \n",
" Weighted_Astar 5.0 \n",
" Beam_Search 5.0 \n",
"(10, 0.2, euclidian_distance, euclidian_distanc... Astar 5.0 \n",
" BFS 5.0 \n",
" Weighted_Astar 5.0 \n",
" Beam_Search 5.0 \n",
"(10, 0.4, euclidian_distance, euclidian_distanc... Astar 5.0 \n",
" BFS 5.0 \n",
" Weighted_Astar 5.0 \n",
" Beam_Search 5.0 \n",
"(20, 0.1, euclidian_distance, euclidian_distanc... Astar 7.0 \n",
" BFS 7.0 \n",
" Weighted_Astar 7.0 \n",
" Beam_Search 7.0 \n",
"(20, 0.2, euclidian_distance, euclidian_distanc... Astar 7.0 \n",
" BFS 7.0 \n",
" Weighted_Astar 7.0 \n",
" Beam_Search 7.0 \n",
"(20, 0.4, euclidian_distance, euclidian_distanc... Astar 7.0 \n",
" BFS 7.0 \n",
" Weighted_Astar 7.0 \n",
" Beam_Search 7.0 \n",
"(50, 0.1, euclidian_distance, euclidian_distanc... Astar 33.0 \n",
" BFS 33.0 \n",
" Weighted_Astar 33.0 \n",
" Beam_Search 33.0 \n",
"(50, 0.2, euclidian_distance, euclidian_distanc... Astar 33.0 \n",
" BFS 33.0 \n",
" Weighted_Astar 33.0 \n",
" Beam_Search 33.0 \n",
"(50, 0.4, euclidian_distance, euclidian_distanc... Astar 33.0 \n",
" BFS 33.0 \n",
" Weighted_Astar 35.0 \n",
" Beam_Search 38.0 \n",
"\n",
" cost \\\n",
"env search_algo \n",
"(10, 0.1, euclidian_distance, euclidian_distanc... Astar 4.000000 \n",
" BFS 4.000000 \n",
" Weighted_Astar 4.000000 \n",
" Beam_Search 4.000000 \n",
"(10, 0.2, euclidian_distance, euclidian_distanc... Astar 4.000000 \n",
" BFS 4.000000 \n",
" Weighted_Astar 4.000000 \n",
" Beam_Search 4.000000 \n",
"(10, 0.4, euclidian_distance, euclidian_distanc... Astar 4.828427 \n",
" BFS 4.828427 \n",
" Weighted_Astar 4.828427 \n",
" Beam_Search 4.828427 \n",
"(20, 0.1, euclidian_distance, euclidian_distanc... Astar 8.071068 \n",
" BFS 8.071068 \n",
" Weighted_Astar 8.071068 \n",
" Beam_Search 8.071068 \n",
"(20, 0.2, euclidian_distance, euclidian_distanc... Astar 8.071068 \n",
" BFS 8.071068 \n",
" Weighted_Astar 8.071068 \n",
" Beam_Search 8.071068 \n",
"(20, 0.4, euclidian_distance, euclidian_distanc... Astar 8.071068 \n",
" BFS 8.071068 \n",
" Weighted_Astar 8.071068 \n",
" Beam_Search 8.071068 \n",
"(50, 0.1, euclidian_distance, euclidian_distanc... Astar 39.041631 \n",
" BFS 42.355339 \n",
" Weighted_Astar 39.870058 \n",
" Beam_Search 39.041631 \n",
"(50, 0.2, euclidian_distance, euclidian_distanc... Astar 39.041631 \n",
" BFS 40.698485 \n",
" Weighted_Astar 40.698485 \n",
" Beam_Search 39.041631 \n",
"(50, 0.4, euclidian_distance, euclidian_distanc... Astar 39.870058 \n",
" BFS 41.526912 \n",
" Weighted_Astar 41.870058 \n",
" Beam_Search 42.798990 \n",
"\n",
" nodes_visited \n",
"env search_algo \n",
"(10, 0.1, euclidian_distance, euclidian_distanc... Astar 16.0 \n",
" BFS 29.0 \n",
" Weighted_Astar 16.0 \n",
" Beam_Search 16.0 \n",
"(10, 0.2, euclidian_distance, euclidian_distanc... Astar 14.0 \n",
" BFS 24.0 \n",
" Weighted_Astar 14.0 \n",
" Beam_Search 14.0 \n",
"(10, 0.4, euclidian_distance, euclidian_distanc... Astar 11.0 \n",
" BFS 12.0 \n",
" Weighted_Astar 10.0 \n",
" Beam_Search 11.0 \n",
"(20, 0.1, euclidian_distance, euclidian_distanc... Astar 31.0 \n",
" BFS 58.0 \n",
" Weighted_Astar 32.0 \n",
" Beam_Search 32.0 \n",
"(20, 0.2, euclidian_distance, euclidian_distanc... Astar 27.0 \n",
" BFS 50.0 \n",
" Weighted_Astar 28.0 \n",
" Beam_Search 28.0 \n",
"(20, 0.4, euclidian_distance, euclidian_distanc... Astar 21.0 \n",
" BFS 39.0 \n",
" Weighted_Astar 21.0 \n",
" Beam_Search 21.0 \n",
"(50, 0.1, euclidian_distance, euclidian_distanc... Astar 350.0 \n",
" BFS 834.0 \n",
" Weighted_Astar 124.0 \n",
" Beam_Search 161.0 \n",
"(50, 0.2, euclidian_distance, euclidian_distanc... Astar 309.0 \n",
" BFS 695.0 \n",
" Weighted_Astar 109.0 \n",
" Beam_Search 149.0 \n",
"(50, 0.4, euclidian_distance, euclidian_distanc... Astar 231.0 \n",
" BFS 448.0 \n",
" Weighted_Astar 92.0 \n",
" Beam_Search 126.0 "
],
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"\n",
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" <th></th>\n",
" <th></th>\n",
" <th>paths_length</th>\n",
" <th>cost</th>\n",
" <th>nodes_visited</th>\n",
" </tr>\n",
" <tr>\n",
" <th>env</th>\n",
" <th>search_algo</th>\n",
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" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th rowspan=\"4\" valign=\"top\">(10, 0.1, euclidian_distance, euclidian_distance, 4.0)</th>\n",
" <th>Astar</th>\n",
" <td>5.0</td>\n",
" <td>4.000000</td>\n",
" <td>16.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>BFS</th>\n",
" <td>5.0</td>\n",
" <td>4.000000</td>\n",
" <td>29.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Weighted_Astar</th>\n",
" <td>5.0</td>\n",
" <td>4.000000</td>\n",
" <td>16.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Beam_Search</th>\n",
" <td>5.0</td>\n",
" <td>4.000000</td>\n",
" <td>16.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th rowspan=\"4\" valign=\"top\">(10, 0.2, euclidian_distance, euclidian_distance, 4.0)</th>\n",
" <th>Astar</th>\n",
" <td>5.0</td>\n",
" <td>4.000000</td>\n",
" <td>14.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>BFS</th>\n",
" <td>5.0</td>\n",
" <td>4.000000</td>\n",
" <td>24.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Weighted_Astar</th>\n",
" <td>5.0</td>\n",
" <td>4.000000</td>\n",
" <td>14.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Beam_Search</th>\n",
" <td>5.0</td>\n",
" <td>4.000000</td>\n",
" <td>14.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th rowspan=\"4\" valign=\"top\">(10, 0.4, euclidian_distance, euclidian_distance, 4.0)</th>\n",
" <th>Astar</th>\n",
" <td>5.0</td>\n",
" <td>4.828427</td>\n",
" <td>11.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>BFS</th>\n",
" <td>5.0</td>\n",
" <td>4.828427</td>\n",
" <td>12.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Weighted_Astar</th>\n",
" <td>5.0</td>\n",
" <td>4.828427</td>\n",
" <td>10.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Beam_Search</th>\n",
" <td>5.0</td>\n",
" <td>4.828427</td>\n",
" <td>11.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th rowspan=\"4\" valign=\"top\">(20, 0.1, euclidian_distance, euclidian_distance, 7.810249675906654)</th>\n",
" <th>Astar</th>\n",
" <td>7.0</td>\n",
" <td>8.071068</td>\n",
" <td>31.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>BFS</th>\n",
" <td>7.0</td>\n",
" <td>8.071068</td>\n",
" <td>58.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Weighted_Astar</th>\n",
" <td>7.0</td>\n",
" <td>8.071068</td>\n",
" <td>32.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Beam_Search</th>\n",
" <td>7.0</td>\n",
" <td>8.071068</td>\n",
" <td>32.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th rowspan=\"4\" valign=\"top\">(20, 0.2, euclidian_distance, euclidian_distance, 7.810249675906654)</th>\n",
" <th>Astar</th>\n",
" <td>7.0</td>\n",
" <td>8.071068</td>\n",
" <td>27.0</td>\n",
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" <tr>\n",
" <th>BFS</th>\n",
" <td>7.0</td>\n",
" <td>8.071068</td>\n",
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" <th>Weighted_Astar</th>\n",
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" <td>8.071068</td>\n",
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" <tr>\n",
" <th>Beam_Search</th>\n",
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" <td>8.071068</td>\n",
" <td>28.0</td>\n",
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" <tr>\n",
" <th rowspan=\"4\" valign=\"top\">(20, 0.4, euclidian_distance, euclidian_distance, 7.810249675906654)</th>\n",
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" <td>8.071068</td>\n",
" <td>21.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>BFS</th>\n",
" <td>7.0</td>\n",
" <td>8.071068</td>\n",
" <td>39.0</td>\n",
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" <tr>\n",
" <th>Weighted_Astar</th>\n",
" <td>7.0</td>\n",
" <td>8.071068</td>\n",
" <td>21.0</td>\n",
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" <tr>\n",
" <th>Beam_Search</th>\n",
" <td>7.0</td>\n",
" <td>8.071068</td>\n",
" <td>21.0</td>\n",
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" <tr>\n",
" <th rowspan=\"4\" valign=\"top\">(50, 0.1, euclidian_distance, euclidian_distance, 36.235341863986875)</th>\n",
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" <td>39.041631</td>\n",
" <td>350.0</td>\n",
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" <th>BFS</th>\n",
" <td>33.0</td>\n",
" <td>42.355339</td>\n",
" <td>834.0</td>\n",
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" <tr>\n",
" <th>Weighted_Astar</th>\n",
" <td>33.0</td>\n",
" <td>39.870058</td>\n",
" <td>124.0</td>\n",
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" <th>Beam_Search</th>\n",
" <td>33.0</td>\n",
" <td>39.041631</td>\n",
" <td>161.0</td>\n",
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" <tr>\n",
" <th rowspan=\"4\" valign=\"top\">(50, 0.2, euclidian_distance, euclidian_distance, 36.235341863986875)</th>\n",
" <th>Astar</th>\n",
" <td>33.0</td>\n",
" <td>39.041631</td>\n",
" <td>309.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>BFS</th>\n",
" <td>33.0</td>\n",
" <td>40.698485</td>\n",
" <td>695.0</td>\n",
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" <tr>\n",
" <th>Weighted_Astar</th>\n",
" <td>33.0</td>\n",
" <td>40.698485</td>\n",
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{
"cell_type": "markdown",
"source": [
"# Experiment #2\n",
"\n",
"For this experiment, we wanted to see how the results differ when the grid sizes are larger and the obstacle density is smaller (compared to experiment #1).\n",
"\n",
"The RRT algorthm is run in a separate environment and source code and demos will be submitted separately."
],
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"id": "Y4LAroVPp4v0"
}
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{
"cell_type": "code",
"source": [
"size_list = [75, 100, 125]\n",
"probability_obstacle_list = [0.05]\n",
"distance_fn_list = [euclidian_distance]\n",
"heuristic_func_list = [euclidian_distance]\n",
"search_algo_list = [Astar, BFS, Weighted_Astar, Beam_Search]\n",
"# generate all permutations based on the above parameters\n",
"all_exps = itertools.product(\n",
" size_list,\n",
" probability_obstacle_list,\n",
" distance_fn_list,\n",
" heuristic_func_list,\n",
" search_algo_list\n",
")\n",
"\n",
"def run_exp(parameters):\n",
" \"\"\"\n",
" args:\n",
" parameters: Values for the following parameters neededed to conduct a\n",
" search: graph sizes, probability densities, distance functions,\n",
" heuristic functions, search algorithms.\n",
" \"\"\"\n",
" # generate graph and run search algorithm based on the parameters\n",
" size, probability_obstacle, distance_fn, heuristic_func, search_algo = parameters\n",
" g = Graph(w=size, h=size)\n",
" g.generate_random_graph(probability_obstacle=probability_obstacle)\n",
" algo = search_algo( g.get_adjacency_list(distance_fn) )\n",
" search_result = algo.search(g.source, g.target, heuristic_func)\n",
" # record the approximate_shortest distance, paths, minimum cost, number of visited nodes\n",
" approx_shortest_distance = heuristic_func(g.source, g.target)\n",
" paths = search_result[0]\n",
" cost = search_result[1]\n",
" visited = search_result[2] if len(search_result) > 2 else None\n",
" return (size, probability_obstacle, distance_fn.__name__, heuristic_func.__name__, search_algo.__name__), approx_shortest_distance, paths, cost, visited\n",
"\n",
"def run_all_exps(all_exps, pool_size):\n",
" \"\"\"\n",
" args:\n",
" all_exps: A cross product of the following values for each trial: graph sizes, \n",
" probability densities, distance functions, heuristic functions,\n",
" search algorithms.\n",
" pool_size: The number of concurrent processes to use to run the experiment.\n",
" \"\"\"\n",
" # run exp in parallel based on the pool_size\n",
" with Pool(pool_size) as p:\n",
" return p.map(run_exp, all_exps)\n",
"\n",
"def process_exps_results(results):\n",
" \"\"\"\n",
" args:\n",
" results: A list of the return values from each trial.\n",
" \"\"\"\n",
" # convert results from list of tuples to list of dictionaries\n",
" # list of dictionaries can then be converted to pandas dataframe\n",
" output = []\n",
" for result in results:\n",
" parameters, approx_shortest_distance, paths, cost, visited = result\n",
" size, probability_obstacle, distance_fn, heuristic_func, search_algo = parameters\n",
" output += [{\n",
" 'size' : size,\n",
" 'probability_obstacle' : probability_obstacle,\n",
" 'distance_fn' : distance_fn,\n",
" 'heuristic_fn' : heuristic_func,\n",
" 'search_algo' : search_algo,\n",
" 'approx_shortest_distance' : approx_shortest_distance,\n",
" 'paths_length' : len(paths),\n",
" 'cost' : cost,\n",
" 'nodes_visited' : visited \n",
" }]\n",
" # number of visited nodes\n",
" # approximate shortest distance\n",
" return output\n",
"\n",
"# run all experiments in parallel based on the defined parameters\n",
"results = run_all_exps(all_exps, 8)\n",
"results = process_exps_results(results)\n",
"results = pd.DataFrame.from_records(results)\n",
"# save results as csv file and download it\n",
"results.to_csv('experiment2_results.csv')\n",
"files.download('experiment2_results.csv')\n",
"# display results in pivot table\n",
"results[\"env\"] = list(zip(\n",
" results['size'],\n",
" results['probability_obstacle'],\n",
" results['distance_fn'],\n",
" results['heuristic_fn'],\n",
" results['approx_shortest_distance'] ))\n",
"results.pivot(index=['env', 'search_algo'],\n",
" columns=[],\n",
" values=['paths_length', 'cost', 'nodes_visited'])"
],
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" paths_length \\\n",
"env search_algo \n",
"(75, 0.05, euclidian_distance, euclidian_distan... Astar 26.0 \n",
" BFS 26.0 \n",
" Weighted_Astar 26.0 \n",
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" Beam_Search 72.0 \n",
"(125, 0.05, euclidian_distance, euclidian_dista... Astar 66.0 \n",
" BFS 66.0 \n",
" Weighted_Astar 66.0 \n",
" Beam_Search 66.0 \n",
"\n",
" cost \\\n",
"env search_algo \n",
"(75, 0.05, euclidian_distance, euclidian_distan... Astar 25.828427 \n",
" BFS 31.627417 \n",
" Weighted_Astar 25.828427 \n",
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" Weighted_Astar 76.798990 \n",
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"(125, 0.05, euclidian_distance, euclidian_dista... Astar 88.610173 \n",
" BFS 89.438600 \n",
" Weighted_Astar 88.610173 \n",
" Beam_Search 88.610173 \n",
"\n",
" nodes_visited \n",
"env search_algo \n",
"(75, 0.05, euclidian_distance, euclidian_distan... Astar 135.0 \n",
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" Weighted_Astar 82.0 \n",
" Beam_Search 95.0 \n",
"(100, 0.05, euclidian_distance, euclidian_dista... Astar 1108.0 \n",
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" Beam_Search 336.0 \n",
"(125, 0.05, euclidian_distance, euclidian_dista... Astar 785.0 \n",
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" <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
" </svg>\n",
" </button>\n",
" \n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" flex-wrap:wrap;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-0a953794-fe0f-463b-8db2-cbe287502081 button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-0a953794-fe0f-463b-8db2-cbe287502081');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
" </div>\n",
" "
]
},
"metadata": {},
"execution_count": 9
}
]
},
{
"cell_type": "markdown",
"source": [
"# Quickstart"
],
"metadata": {
"id": "Hw8R_vRTX1_S"
}
},
{
"cell_type": "markdown",
"source": [
"**Manual Graph Creation**"
],
"metadata": {
"id": "2EYyMJhCO0kh"
}
},
{
"cell_type": "code",
"source": [
"# initialize grid with width=4 and height=2\n",
"# note that x can range from 0 (inclusive) to 3 (inclusive)\n",
"# note that y can range from 0 (inclusive) to 1 (inclusive)\n",
"g = Graph(4,2)\n",
"\n",
"# add obstacle at coordinate x=1, y=1\n",
"g.add_obstacle(1,1)\n",
"\n",
"# add obstacle at coordinate x=0, y=1\n",
"g.add_obstacle(0,1)\n",
"\n",
"# add source at coordinate x=0, y=0\n",
"g.add_source(0,0)\n",
"\n",
"# add target at coordinate x=3, y=1\n",
"g.add_target(3,1)\n",
"\n",
"# one of the shortest path\n",
"g.add_path(1,0)\n",
"g.add_path(2,0)\n",
"\n",
"# source : blue, obstacle : black, path : cream, target : green\n",
"g.plot('grid')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 161
},
"id": "WTBDMU2gZJn3",
"outputId": "aed2a665-5293-4d3f-86cd-93d65128e637"
},
"execution_count": 10,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 288x144 with 1 Axes>"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAACQCAYAAAAldqY8AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAAsTAAALEwEAmpwYAAAF1klEQVR4nO3b0YtcdxmH8edrErHQghd6sSah8aINhIItkbaQKwPStIp6acFeFRZEIQVB9K7+A6U3Ulja0AulItQLCYVQcEGEUu3GKE1WpYhibCGISCtCJfb1YqYQIfScZs/s2X19PjAwk/xm8h6yD2fOzG9TVUjq6SNzDyBpdQxcaszApcYMXGrMwKXGDFxqbDDwJEeTbCa5kuRykrO7MZikncvQ9+BJ1oC1qrqY5A5gC/hKVV3ZjQEl3brBM3hVvVVVF5f33wG2gcOrHkzSzn2oa/Akx4D7gFdXMo2kSR0cuzDJ7cCLwBNV9fZN/n4dWF8+PDnNeJJu6jaof1WGlg1egwMkOQScBy5U1VMj1rvBfZ/p+DsJyfLn/8lZx5jek8Aa1JvDgY/5FD3Ac8D2mLgl7R1jrsFPAY8Bp5NcWt4eWfFckiYweA1eVb8ABt8KSNp73MkmNWbgUmMGLjVm4FJjBi41ZuBSYwYuNWbgUmMGLjVm4FJjBi41ZuBSYwYuNWbgUmMGLjVm4FJjBi41ZuBSYwYuNWbgUmMGLjVm4FJjBi41ZuBSYwYuNWbgUmMGLjVm4FJjBi41ZuBSYwYuNWbgUmMGLjVm4FJjBi41ZuBSYwYuNWbgUmMGLjVm4FJjBi41ZuBSYwYuNWbgUmMGLjVm4FJjg4EnOZfkWpLXd2MgSdMZcwZ/Hjiz4jkkrUCqanhRcgw4X1X3jHrRZPhFJd26Nag3K0PLDk717yVZB9anej1JOzdZ4FW1AWzA4gz+ua//eaqX3hM2n7kTgPrDhZknmVbufgjod1xww7GNeJe6nyTh5KdOjlrrp+hSYwYuNTbma7IXgFeA40muJnl89WNJmsLgNXhVPbobg0ianm/RpcYMXGrMwKXGDFxqzMClxgxcaszApcYMXGrMwKXGDFxqzMClxgxcaszApcYMXGrMwKXGDFxqzMClxgxcaszApcYMXGrMwKXGDFxqzMClxgxcaszApcYMXGrMwKXGDFxqzMClxgxcaszApcYMXGrMwKXGDFxqzMClxgxcaszApcYMXGrMwKXGDFxqzMClxgxcaszApcYMXGrMwKXGRgWe5EyS3yd5I8l3Vj2UpGkMBp7kAPB94GHgBPBokhOrHkzSzo05g98PvFFVf6yqfwM/Ar682rEkTeHgiDWHgb/c8Pgq8MDQkzafufNWZ9rTcvdDc4+wEl2PCyDJ3CPMZkzgoyRZB9aXD98FXp/qtfeQTwB/m3uIFeh6XND02La2to6PWTcm8L8CR294fGT5Z/+jqjaADYAkr1XVZ8cMsJ94XPtP12NL8tqYdWOuwX8F3JXk00k+CnwV+OlOhpO0OwbP4FV1Pck3gQvAAeBcVV1e+WSSdmzUNXhVvQS89CFed+PWxtnzPK79p+uxjTquVNWqB5E0E7eqSo1NGnjXLa1JziW5lqTVV39JjibZTHIlyeUkZ+eeaQpJPpbkl0l+szyu780905SSHEjy6yTnh9ZOFnjzLa3PA2fmHmIFrgPfqqoTwIPAN5r8n70LnK6qzwD3AmeSPDjvSJM6C2yPWTjlGbztltaq+jnw97nnmFpVvVVVF5f332HxQ3N43ql2rhb+uXx4aHlr8WFTkiPAF4Bnx6yfMvCbbWnd9z8s/y+SHAPuA16deZRJLN/GXgKuAS9XVYvjAp4Gvg28N2axH7KJJLcDLwJPVNXbc88zhar6T1Xdy2Ln5f1J7pl5pB1L8kXgWlVtjX3OlIGP2tKqvSXJIRZx/7CqfjL3PFOrqn8Am/T4DOUU8KUkf2JxCXw6yQ8+6AlTBu6W1n0mi1+zeg7Yrqqn5p5nKkk+meTjy/u3AZ8HfjfrUBOoqu9W1ZGqOsair59V1dc+6DmTBV5V14H3t7RuAz/usqU1yQvAK8DxJFeTPD73TBM5BTzG4kxwaXl7ZO6hJrAGbCb5LYsTz8tVNfiVUkfuZJMa80M2qTEDlxozcKkxA5caM3CpMQOXGjNwqTEDlxr7L7zgUOCO+Z4JAAAAAElFTkSuQmCC\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"from pprint import pprint\n",
"# generate adjacency list of the graph\n",
"# note that obstacles coordinates are excluded (0,1) and (1,1)\n",
"'''\n",
"input :\n",
"distance_fn needs to be a function that expects 2 inputs and returns float / int\n",
" for constant distance : lambda current, neighbour : 3\n",
" for linear distance : lambda current, neighbour : abs(current[0] - neighbour[0]) + abs(current[1] - neighbour[1])\n",
" for random distance : lambda current, neighbour : np.random.randint(10)\n",
"\n",
"output format\n",
"{ (x_source, y_source) : [ \n",
" (distance_to_neighbour, (x_neighbour, y_neighbour)),\n",
" (distance_to_neighbour, (x_neighbour, y_neighbour))\n",
"] }\n",
"'''\n",
"\n",
"distance_fn = lambda current, neighbour : abs(current[0] - neighbour[0]) + abs(current[1] - neighbour[1])\n",
"\n",
"pprint( g.get_adjacency_list(distance_fn = distance_fn) )\n",
"\n",
"# to visualize adjacency list as a graph\n",
"g.plot(\n",
" plot_type = 'graph',\n",
" distance_fn = distance_fn\n",
")"
],
"metadata": {
"id": "m_fBxpRbhWzb",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 282
},
"outputId": "7ffedc3f-f6c6-4df4-a97c-bcc19c09fcdf"
},
"execution_count": 11,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"{(0, 0): {(1, 0): 1},\n",
" (1, 0): {(0, 0): 1, (2, 0): 1, (2, 1): 2},\n",
" (2, 0): {(1, 0): 1, (2, 1): 1, (3, 0): 1, (3, 1): 2},\n",
" (2, 1): {(1, 0): 2, (2, 0): 1, (3, 0): 2, (3, 1): 1},\n",
" (3, 0): {(2, 0): 1, (2, 1): 2, (3, 1): 1},\n",
" (3, 1): {(2, 0): 2, (2, 1): 1, (3, 0): 1}}\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 288x144 with 1 Axes>"
],
"image/png": "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},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"# Qucickstart Example: Weighted A*, epsilon=2\n",
"Performance Note:\n",
"\n",
"Compared to regular Astar, using weighted Astar with an epsilon of 2 delivers\n",
"a 79% decrease in nodes visited for only a 5% increase in path length. See how regular Astar performed on the same grid below."
],
"metadata": {
"id": "oPm16p2eolhJ"
}
},
{
"cell_type": "code",
"source": [
"zxi = Graph(50,50)\n",
"# generate graph with probability of obstacle = 0.3\n",
"zxi.generate_random_graph(0.3)\n",
"\n",
"distance_fn = lambda current, neighbour : abs(current[0] - neighbour[0]) + abs(current[1] - neighbour[1])\n",
"a = Weighted_Astar(zxi.get_adjacency_list(distance_fn), epsilon=2)\n",
"\n",
"paths, cost, visited = a.search(zxi.source, zxi.target, diagonal_distance)\n",
"zxi.add_visited(a.visited)\n",
"zxi.add_paths(paths)\n",
"# source : blue, obstacle : black, path : cream, target : green\n",
"# visualize sample problem\n",
"print(\"Visited: \", len(a.visited))\n",
"print(\"Path length: \", a.path_len)\n",
"print(\"Cost :\", cost)\n",
"zxi.plot('grid')"
],
"metadata": {
"id": "Rg7Lei6gom0e",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"outputId": "0aea3433-5909-4237-dcef-7d7737b55f09"
},
"execution_count": 12,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Visited: 107\n",
"Path length: 41\n",
"Cost : 49\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 3600x3600 with 1 Axes>"
],
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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"# Qucickstart Example: A*"
],
"metadata": {
"id": "ZzAqolvv9YEA"
}
},
{
"cell_type": "code",
"source": [
"zxi = Graph(50,50)\n",
"# generate graph with probability of obstacle = 0.3\n",
"zxi.generate_random_graph(0.3)\n",
"\n",
"distance_fn = lambda current, neighbour : abs(current[0] - neighbour[0]) + abs(current[1] - neighbour[1])\n",
"a = Astar(zxi.get_adjacency_list(distance_fn))\n",
"\n",
"paths, cost, visited = a.search(zxi.source, zxi.target, diagonal_distance)\n",
"zxi.add_visited(a.visited)\n",
"zxi.add_paths(paths)\n",
"# source : blue, obstacle : black, path : cream, target : green\n",
"# visualize sample problem\n",
"print(\"Visited: \", len(a.visited))\n",
"print(\"Path length: \", a.path_len)\n",
"print(\"Cost :\", cost)\n",
"zxi.plot('grid')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "i2SgAGp67p53",
"outputId": "051ef122-1ed7-4a7e-b2cb-6fa07133943e"
},
"execution_count": 13,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Visited: 530\n",
"Path length: 39\n",
"Cost : 49\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 3600x3600 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
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}
}
]
}
]
}
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