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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1><center>Guide Notebook for the 380CT Assignment on TSP</center></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_Kamal Bentahar_\n",
"\n",
"[https://github.coventry.ac.uk/380CT-2021/TSP-Guidance](https://github.coventry.ac.uk/380CT-2021/TSP-Guidance)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```\n",
"DISCLAIMER:\n",
"\n",
"- This is meant to help you get started.\n",
"- You can use it as a starting template, but you can also build your own from scratch. You can even use another programming language (but in Jupyter still).\n",
"- Be ware! Care is not taken into checking validity of paramters, etc. -- simplicity of code for understanding is favoured (mostly).\n",
"- There may be bugs! Please report them. Thanks.\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1) Notation and definitions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let $G$ be a [complete]( \"graph is undirected, has no self-loops, and each node is connected to all the other vertices\") [weighted]( \"the edges have a weight (a positive integer)\") graph with $n$ vertices."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Optimisation TSP**:\n",
"> Given $G$, find a cycle of minimal total cost.\n",
"\n",
"Here:\n",
"- A *cycle* is a path that visits every vertex once, and goes back to the start point.\n",
"- The *total cost of the cycle* is the sum of the edge weights of the cycle.\n",
"\n",
"This problem is **NP-Hard** because its decision version is **NP-complete** (Garey and Johnson, 1979, p. 211)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2) Testing methodology"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* **Exact method (Exhaustive search)**:\n",
" Average _time_ for instances with increasing $n$.\n",
"\n",
"* **Greedy and meta-heuristics**:\n",
" Average _time_ and _\"quality\"_ as $n$ increases.\n",
"\n",
"Instances will be generated randomly as shown in the next subsection."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2.1) Random instances sampling strategy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Four types of TSP instances will be generated by creating an **adjacency matrices** $M$ as follows:\n",
"1. **Asymmetric**: The edge weights are independent and uniformly random in an interval $[1,\\text{MAX_WEIGHT}]$, i.e the graph is assumed to be directed.\n",
"2. **Symmetric**: Like the asymmetric case but the graph is undirected, and the matrix is therefore symmetric: $M_{ij}=M_{ji}$.\n",
"3. **Euclidean**: Generate points using $(x,y)$ coordinates, then generate the adjacency matrix by calculating all the required distances. Recall that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$. The points are generated in the rectangle defined by the points $(0,0)$ and $(\\text{MAX_Y},\\text{MAX_Y})$.\n",
"4. **Graphs with obvious shortest cycle**: A graph where all the distances are 2 except for the edges on a predefined cycle, where the distance is 1. Such a graph would be useful for testing/debugging the \"nearest neighbour greedy\" search."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Implementation of the instances generation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First start by importing relevant libraries."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from random import randint, shuffle # random integers and random shuffling of a list\n",
"from itertools import permutations # iterate over all possible permutations of a list\n",
"from itertools import chain # concatenate range()'s'\n",
"from math import inf as oo # Infinity (∞) is larger than any number\n",
"from math import sqrt, log, factorial # square root, logarithm, and n!\n",
"from time import perf_counter # for measuring time. NB. 'perf_counter' is better/more accurate than 'time'\n",
"import networkx as nx # to draw sample graphs\n",
"import pandas as pd # to show the adjacency matrix in a nice format\n",
"import matplotlib.pyplot as plt # to plot graphs of time and quality vs n\n",
"import seaborn as sns # nice statistical plots -- see e.g. https://seaborn.pydata.org/tutorial/relational.html#relational-tutorial\n",
"sns.set_style(\"white\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Basics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let the set of vertices be $\\{0, 1, 2,\\ldots, n-1\\}$.\n",
"\n",
"For simplicity, we will consider $0$ to be the start and end point of cycles."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"class Graph:\n",
" ''' Random graphs '''\n",
" def __init__(self, n=0, type='asymmetric', MAX_WEIGHT=100, MAX_X=200, MAX_Y=200):\n",
" self.n = n\n",
" self.vertices = list(range(n)) # [0,1,...,n-1]\n",
" self.type = type\n",
" self.adj_matrix = [[oo for i in range(n)] for j in range(n)]\n",
" # Generate a random adjacency matrix according to the required type\n",
" if type=='symmetric': self.__random_symmetric_graph(n,MAX_WEIGHT)\n",
" elif type=='Euclidean': self.__random_euclidean_graph(n,MAX_X,MAX_Y)\n",
" elif type=='easy': self.__random_cycle_graph(n)\n",
" else: self.__random_asymmetric_graph(n,MAX_WEIGHT) # assume 'asymmetric' otherwise\n",
" \n",
" def __getitem__(self, i):\n",
" ''' Allow indexing to get the weights '''\n",
" return self.adj_matrix[i]\n",
" \n",
" def __random_asymmetric_graph(self,n, MAX_WEIGHT):\n",
" ''' Asymmetric adjacency matrix of size nxn '''\n",
" for i in range(n):\n",
" for j in range(n):\n",
" if i==j: continue # no self-loops\n",
" self.adj_matrix[i][j] = randint(1,MAX_WEIGHT)\n",
"\n",
" def __random_symmetric_graph(self,n,MAX_WEIGHT):\n",
" ''' Symmetric adjacency matrix of size nxn '''\n",
" for i in range(n):\n",
" for j in range(i+1,n):\n",
" w = randint(1,MAX_WEIGHT)\n",
" self.adj_matrix[i][j] = w\n",
" self.adj_matrix[j][i] = w\n",
"\n",
" def __random_cycle_graph(self,n):\n",
" ''' Symmetric adjacency matrix of size nxn with one reandomly chosen cycle\n",
" All the edge weights are 2 except for the cycle (weight=1) '''\n",
" self.adj_matrix = [[2 for _ in range(n)] for _ in range(n)] # All weights=2\n",
" # Select a random cycle which will have weight=1\n",
" cycle = list(range(1,n)) # don't include 0 as we want to be at the start\n",
" shuffle(cycle) # in-place random permutation\n",
" cycle = [0]+cycle+[0] # cycle starting and ending at 0\n",
" for a,b in zip(cycle, cycle[1:]): # set the cycle's weights to 1\n",
" self.adj_matrix[a][b] = 1\n",
" self.adj_matrix[b][a] = 1\n",
"\n",
" def __random_euclidean_graph(self,n,MAX_X,MAX_Y):\n",
" ''' Symmetric adjacency matrix of a Euclidean graph of size nxn '''\n",
" # (1/2) Generate random (x,y) points\n",
" points = set()\n",
" while len(points)<n: # We may get duplicate (x,y) so we try until we get enough points\n",
" x,y = randint(0,MAX_X), randint(0,MAX_Y)\n",
" points.add((x,y))\n",
" points = list(points) # Sets are not indexed, so convert into a list\n",
" # (2/2) Now compute the adjacency matrix\n",
" for i in range(n):\n",
" p1 = points[i]\n",
" for j in range(i+1,n):\n",
" p2 = points[j]\n",
" distance = sqrt((p1[0]-p2[0])**2+(p1[1]-p2[1])**2)\n",
" self.adj_matrix[i][j] = distance\n",
" self.adj_matrix[j][i] = distance\n",
" self.points=points"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def cost(G, cycle):\n",
" ''' Calculate the cost of the given cycle [0,...,0] in G '''\n",
" return sum(G[a][b] for a,b in zip(cycle, cycle[1:]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Functions to show the graphs as **adjacency matrices** or as a **drawing**:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def show(G):\n",
" ''' Show adjacency matrix. Useful for debugging.\n",
" 'type' is a string from: Euclidean, Cycle, ...\n",
" The distances are round to 1 decimal point for clarity/simplicity\n",
" '''\n",
" print(f\"{G.n}x{G.n} {G.type} graph:\")\n",
" if G.type=='Euclidean': print(\"Points:\",G.points)\n",
" r = pd.DataFrame({str(i): G[i] for i in range(G.n)})\n",
" display(r)\n",
" \n",
"def nx_graph(G):\n",
" ''' Convert G into NetworkX format '''\n",
" nxG = nx.Graph() if G.type!='asymmetric' else nx.DiGraph() # undirected/directed graph\n",
" nxG.add_nodes_from(G.vertices) # Add the vertices\n",
" # Now add the edges\n",
" for a in G.vertices:\n",
" for b in G.vertices:\n",
" if a==b: continue # no self-loops\n",
" nxG.add_edge(a, b, weight=G[a][b]) \n",
" if G.type=='Euclidean': # add (x,y) coordinates if available\n",
" pos=dict(enumerate(G.points)) # vertex:(x,y) pairs\n",
" nx.set_node_attributes(nxG, pos, 'coord')\n",
" return nxG\n",
"\n",
"def draw(G):\n",
" ''' Draw the graph G using NetworkX '''\n",
" nxG = nx_graph(G)\n",
" weights_dictionary = nx.get_edge_attributes(nxG,'weight')\n",
" edges,weights = zip(*weights_dictionary.items())\n",
" pos = nx.circular_layout(nxG) if G.type!='Euclidean' else nx.get_node_attributes(nxG,'coord')\n",
" nx.draw(nxG, pos, \\\n",
" with_labels=True, node_color='red', font_color='white', font_weight='bold', font_size=14,\\\n",
" edge_color=weights, width=1.5, connectionstyle=\"arc3,rad=0.1\", edge_cmap=plt.cm.copper)\n",
" # see https://matplotlib.org/stable/gallery/color/colormap_reference.html\n",
" nx.draw_networkx_edge_labels(nxG, pos, edge_labels=weights_dictionary, label_pos=0.5 if G.type!=\"asymmetric\" else 0.25)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Examples of the different graph types"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"8x8 easy graph:\n"
]
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G = Graph(8,'easy')\n",
"show(G)\n",
"draw(G)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5x5 symmetric graph:\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>inf</td>\n",
" <td>45.0</td>\n",
" <td>62.0</td>\n",
" <td>51.0</td>\n",
" <td>47.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>45.0</td>\n",
" <td>inf</td>\n",
" <td>7.0</td>\n",
" <td>54.0</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>62.0</td>\n",
" <td>7.0</td>\n",
" <td>inf</td>\n",
" <td>98.0</td>\n",
" <td>3.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>51.0</td>\n",
" <td>54.0</td>\n",
" <td>98.0</td>\n",
" <td>inf</td>\n",
" <td>73.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>47.0</td>\n",
" <td>1.0</td>\n",
" <td>3.0</td>\n",
" <td>73.0</td>\n",
" <td>inf</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4\n",
"0 inf 45.0 62.0 51.0 47.0\n",
"1 45.0 inf 7.0 54.0 1.0\n",
"2 62.0 7.0 inf 98.0 3.0\n",
"3 51.0 54.0 98.0 inf 73.0\n",
"4 47.0 1.0 3.0 73.0 inf"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G = Graph(5,'symmetric')\n",
"show(G)\n",
"draw(G)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3x3 Euclidean graph:\n",
"Points: [(24, 27), (33, 80), (73, 184)]\n"
]
},
{
"data": {
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" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
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" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>inf</td>\n",
" <td>53.758720</td>\n",
" <td>164.468842</td>\n",
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" <tr>\n",
" <th>1</th>\n",
" <td>53.758720</td>\n",
" <td>inf</td>\n",
" <td>111.427106</td>\n",
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" <tr>\n",
" <th>2</th>\n",
" <td>164.468842</td>\n",
" <td>111.427106</td>\n",
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"</table>\n",
"</div>"
],
"text/plain": [
" 0 1 2\n",
"0 inf 53.758720 164.468842\n",
"1 53.758720 inf 111.427106\n",
"2 164.468842 111.427106 inf"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G = Graph(3,'Euclidean')\n",
"show(G)\n",
"draw(G)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3x3 asymmetric graph:\n"
]
},
{
"data": {
"text/html": [
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" <tr style=\"text-align: right;\">\n",
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" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>inf</td>\n",
" <td>67.0</td>\n",
" <td>59.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>99.0</td>\n",
" <td>inf</td>\n",
" <td>22.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>87.0</td>\n",
" <td>25.0</td>\n",
" <td>inf</td>\n",
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],
"text/plain": [
" 0 1 2\n",
"0 inf 67.0 59.0\n",
"1 99.0 inf 22.0\n",
"2 87.0 25.0 inf"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G = Graph(3,'asymmetric')\n",
"show(G)\n",
"draw(G)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3) Solution methods"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3.1) Exact method - Exhaustive search"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Idea"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The idea is to:\n",
"- Consider vertex $0$ as the start and end point.\n",
"- Iterate over all permutations of the vertices $\\{1,2,\\ldots, n-1\\}$.\n",
" - Calculate cost of each permutation and keep track of minimum cost permutation.\n",
"- Return the cycle with minimum cost.\n",
"\n",
"More formally, the pseudo-code is as follows:\n",
"\n",
"**Input**: $G$.\n",
"\n",
"**Output**: a cycle in $G$ of shortest cost."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Pseudocode"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. $bestcycle\\gets \\emptyset$\n",
"2. $bestcost\\gets \\infty$\n",
"3. **for all** possible cycles $p$ in $G$ (starting and ending at $0$) **do**\n",
"4. $\\quad$ $c\\gets$ cost of $p$\n",
"2. $\\quad$ **if** $c<bestcost$ **then**\n",
"3. $\\qquad$ $bestcycle\\gets p$\n",
"3. $\\qquad$ $bestcost\\gets c$\n",
"4. $\\quad$ **end if**\n",
"5. **end for**\n",
"6. **return** $bestcycle, bestcost$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Running time analysis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are $(n-1)!$ possible cycles, and each computation of a cycle's cost costs $O(n)$. So this algorithm costs $$O((n-1)!\\cdot n)=O(n!).$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Implementation"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def exhaustive_search(G):\n",
" ''' Perform exhaustive search on G for the shortest TSP tour\n",
" Returns the best cycle and its cost (tuple) '''\n",
" best_cost = oo # infinity\n",
" best_cycle = []\n",
" for cycle in permutations(range(1,G.n)): # permutations of [1,2,...,n-1]\n",
" cycle=[0]+list(cycle)+[0] # add the starting city: 0\n",
" c = cost(G, cycle)\n",
" if c < best_cost:\n",
" best_cost = c\n",
" best_cycle = cycle\n",
" return (best_cycle, best_cost)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us check it works on a **cycle graph**:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"8x8 easy graph:\n"
]
},
{
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G=Graph(8,'easy')\n",
"show(G)\n",
"draw(G)\n",
"exhaustive_search(G)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Testing exhaustive search time cost"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Test completely random graphs:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5, 6, 7, 8, 9, 10, 11, "
]
}
],
"source": [
"MAX_REPETITIONS = 10\n",
"MAX_n = 12\n",
"\n",
"exhaustive_data = pd.DataFrame(columns=['n', 'time'])\n",
"\n",
"i=0\n",
"for n in range(5,MAX_n):\n",
" print(n, end=', ')\n",
" for repetitions in range(MAX_REPETITIONS):\n",
" G = Graph(n)\n",
" # Time the search\n",
" t0 = perf_counter()\n",
" exhaustive_search(G)\n",
" t1 = perf_counter()\n",
" # Record the data\n",
" exhaustive_data.loc[i] = [n, t1-t0]\n",
" i += 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us compute some statistics on the the times that we have just measured."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead tr th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe thead tr:last-of-type th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr>\n",
" <th></th>\n",
" <th colspan=\"4\" halign=\"left\">time</th>\n",
" </tr>\n",
" <tr>\n",
" <th></th>\n",
" <th>min</th>\n",
" <th>max</th>\n",
" <th>mean</th>\n",
" <th>std</th>\n",
" </tr>\n",
" <tr>\n",
" <th>n</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>5.0</th>\n",
" <td>0.000266</td>\n",
" <td>0.000336</td>\n",
" <td>0.000283</td>\n",
" <td>0.000022</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6.0</th>\n",
" <td>0.000675</td>\n",
" <td>0.001949</td>\n",
" <td>0.001266</td>\n",
" <td>0.000360</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7.0</th>\n",
" <td>0.004323</td>\n",
" <td>0.010206</td>\n",
" <td>0.006413</td>\n",
" <td>0.002125</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8.0</th>\n",
" <td>0.033611</td>\n",
" <td>0.068590</td>\n",
" <td>0.052586</td>\n",
" <td>0.010640</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9.0</th>\n",
" <td>0.298948</td>\n",
" <td>0.599419</td>\n",
" <td>0.437434</td>\n",
" <td>0.099777</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10.0</th>\n",
" <td>3.002048</td>\n",
" <td>3.735461</td>\n",
" <td>3.200750</td>\n",
" <td>0.215204</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11.0</th>\n",
" <td>34.012786</td>\n",
" <td>39.915659</td>\n",
" <td>37.147266</td>\n",
" <td>2.045363</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" time \n",
" min max mean std\n",
"n \n",
"5.0 0.000266 0.000336 0.000283 0.000022\n",
"6.0 0.000675 0.001949 0.001266 0.000360\n",
"7.0 0.004323 0.010206 0.006413 0.002125\n",
"8.0 0.033611 0.068590 0.052586 0.010640\n",
"9.0 0.298948 0.599419 0.437434 0.099777\n",
"10.0 3.002048 3.735461 3.200750 0.215204\n",
"11.0 34.012786 39.915659 37.147266 2.045363"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"exhaustive_data.groupby('n').agg(['min','max','mean','std'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us plot this data to see it visually.\n",
"We will use the following convention:\n",
"- The blue dots are the actual measurements.\n",
"- The solid red line is the mean time.\n",
"- The light red shade shows the standard deviation around the mean."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x432 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(12, 6))\n",
"sns.scatterplot(data=exhaustive_data, x='n', y='time', ax=ax)\n",
"sns.lineplot(data=exhaustive_data, x='n', y='time', ci='sd', color='red', ax=ax)\n",
"plt.title('Running time')\n",
"plt.xlabel('n')\n",
"plt.ylabel('Time (s)')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Theoretically, the ratio of \"the time taken for a graph of size $n$\" to $n!$ should approach a constant, as $n$ gets larger and larger. Let us check and estimate this constant."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>time</th>\n",
" <th>time/n!</th>\n",
" </tr>\n",
" <tr>\n",
" <th>n</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>5.0</th>\n",
" <td>0.000283</td>\n",
" <td>2.358333e-06</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6.0</th>\n",
" <td>0.001266</td>\n",
" <td>1.757944e-06</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7.0</th>\n",
" <td>0.006413</td>\n",
" <td>1.272506e-06</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8.0</th>\n",
" <td>0.052586</td>\n",
" <td>1.304217e-06</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9.0</th>\n",
" <td>0.437434</td>\n",
" <td>1.205451e-06</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10.0</th>\n",
" <td>3.200750</td>\n",
" <td>8.820410e-07</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11.0</th>\n",
" <td>37.147266</td>\n",
" <td>9.306173e-07</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" time time/n!\n",
"n \n",
"5.0 0.000283 2.358333e-06\n",
"6.0 0.001266 1.757944e-06\n",
"7.0 0.006413 1.272506e-06\n",
"8.0 0.052586 1.304217e-06\n",
"9.0 0.437434 1.205451e-06\n",
"10.0 3.200750 8.820410e-07\n",
"11.0 37.147266 9.306173e-07"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"exhaustive_data['time/n!'] = exhaustive_data['time']/exhaustive_data['n'].transform(factorial)\n",
"exhaustive_data.groupby('n').mean()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x14635760>"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ratio = plt.subplots(figsize=(16, 4))\n",
"sns.scatterplot(data=exhaustive_data, x='n', y='time/n!', alpha=0.3, ax=ratio, color='#777') # actual data\n",
"sns.lineplot (data=exhaustive_data, x='n', y='time/n!', alpha=0.3, ci='sd', ax=ratio, color='red') # mean"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us estimate the constant, and then how long it will take to solve the problem for graphs of increasing size (using this code on the current machine)."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"9.306173297959752e-07"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"exhaustive_constant = exhaustive_data[exhaustive_data.n==MAX_n-1]['time/n!'].mean() # use the largest n available\n",
"exhaustive_constant"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10\t3\n",
"11\t3\n",
"12\t7\n",
"13\t1\n",
"14\t2\n",
"15\t1\n",
"16\t7\n",
"17\t1\n",
"18\t1\n",
"19\t3\n",
"20\t7\n",
"30\t7\n",
"40\t2\n",
"50\t8\n",
"60\t2\n",
"70\t3\n",
"80\t2\n",
"90\t4\n",
"100\t2\n"
]
}
],
"source": [
"def time_in_human_units(t):\n",
" if t<60: return f'{t} seconds'\n",
" t /= 60 # now in minutes\n",
" if t<60: return f'{t} minutes'\n",
" t /= 60 # now in hours\n",
" if t<24: return f'{t} hours'\n",
" t /= 24 # now in days\n",
" if t<30: return f'{t} days'\n",
" t /= 30 # now in months\n",
" if t<12: return f'{t} months'\n",
" t = t*30/365.25 # now in years\n",
" if t<100: return f'{t} years'\n",
" return f'{t/100} centuries'\n",
"\n",
"for n in chain(range(10,21), range(30,101,10)):\n",
" estimated_running_time = exhaustive_constant*factorial(n) # O(n!)\n",
" print(f'{n}\\t{time_in_human_units(estimated_running_time):.1}') # constant_min is used"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Clearly, we cannot wait that long! We need alternatives..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Discussion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* Exhaustive search exhibits combinatorial running time $O(n!)$:\n",
"* So it is only useful/possible when $n$ is small, up to about 13 on the current machine if it needs to finish within an hour."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3.2) Approximation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3.2.1) Greedy search"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Nearest neigbours"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Idea\n",
"\n",
"Start at city 0, move to the nearest city, then from there to the next nearest city, and so on, until all cities are visited. Finally, return back to the start city."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Pseudocode\n",
"\n",
"1. $city \\gets 0$\n",
"2. $visited\\gets []$\n",
"3. **while** not all cities are visited **do**\n",
"4. $\\quad$ $nearest\\_city \\gets \\text{nearest city to $city$ that has not been visited yet}$\n",
"5. $\\quad$ Append $city$ to $visited$ $\\qquad\\qquad\\text{(i.e. mark $city$ as visited)}$\n",
"5. $\\quad$ $city\\gets nearest\\_city$\n",
"6. **end while**\n",
"8. **return** $visited$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Running time analysis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The while-loop costs $O(n)$, and searching for the nearest city on line 4 costs $O(n)$ also, while the rest can be assumed to cost $O(1)$.\n",
"So the total cost of this greedy approach is therefore $O(n)\\times O(n) = O(n^2)$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Implementation"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"def greedy_nearest_neighbour(G):\n",
" ''' Returns best found cycle and its cost '''\n",
" unvisited = G.vertices.copy()\n",
" visited = [] # solution to be built\n",
" city = 0 # Start city\n",
" while len(unvisited)>0:\n",
" # Find nearest neighbour\n",
" nearest_city = None\n",
" shortest_distance = oo\n",
" for neighbour in unvisited:\n",
" if G[city][neighbour] < shortest_distance:\n",
" shortest_distance = G[city][neighbour]\n",
" nearest_city = neighbour\n",
" # Update 'cycle' and 'cities' and G then 'city'\n",
" visited.append(city)\n",
" unvisited.remove(city)\n",
" city = nearest_city\n",
" return (visited, cost(G, visited+[0]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### Example"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5x5 easy graph:\n"
]
},
{
"data": {
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"text/plain": [
" 0 1 2 3 4\n",
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"data": {
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"([0, 1, 4, 3, 2], 5)"
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G=Graph(5,'easy')\n",
"show(G)\n",
"draw(G)\n",
"greedy_nearest_neighbour(G)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Test time and quality"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us first test the greedy approach on **cycle graphs**, as it should work perfectly all the time."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10 20 30 40 50 60 70 80 90 100 "
]
}
],
"source": [
"MAX_REPETITIONS = 500\n",
"\n",
"greedy_data = pd.DataFrame(columns=['n','time'])\n",
"\n",
"i = 0\n",
"for n in range(10,101,10):\n",
" print(n, end=' ')\n",
" for repetitions in range(MAX_REPETITIONS):\n",
" G = Graph(n,'easy') # this has shortest cycle length = n\n",
" t0 = perf_counter()\n",
" cycle, length = greedy_nearest_neighbour(G)\n",
" t1 = perf_counter()\n",
" greedy_data.loc[i] = [n, t1-t0]\n",
" i += 1"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr>\n",
" <th></th>\n",
" <th colspan=\"4\" halign=\"left\">time</th>\n",
" </tr>\n",
" <tr>\n",
" <th></th>\n",
" <th>min</th>\n",
" <th>max</th>\n",
" <th>mean</th>\n",
" <th>std</th>\n",
" </tr>\n",
" <tr>\n",
" <th>n</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>10.0</th>\n",
" <td>0.000039</td>\n",
" <td>0.000223</td>\n",
" <td>0.000056</td>\n",
" <td>0.000019</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20.0</th>\n",
" <td>0.000101</td>\n",
" <td>0.000264</td>\n",
" <td>0.000164</td>\n",
" <td>0.000051</td>\n",
" </tr>\n",
" <tr>\n",
" <th>30.0</th>\n",
" <td>0.000191</td>\n",
" <td>0.000533</td>\n",
" <td>0.000291</td>\n",
" <td>0.000093</td>\n",
" </tr>\n",
" <tr>\n",
" <th>40.0</th>\n",
" <td>0.000315</td>\n",
" <td>0.000854</td>\n",
" <td>0.000464</td>\n",
" <td>0.000152</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50.0</th>\n",
" <td>0.000466</td>\n",
" <td>0.002513</td>\n",
" <td>0.000745</td>\n",
" <td>0.000256</td>\n",
" </tr>\n",
" <tr>\n",
" <th>60.0</th>\n",
" <td>0.000652</td>\n",
" <td>0.001818</td>\n",
" <td>0.001039</td>\n",
" <td>0.000338</td>\n",
" </tr>\n",
" <tr>\n",
" <th>70.0</th>\n",
" <td>0.000866</td>\n",
" <td>0.002469</td>\n",
" <td>0.001368</td>\n",
" <td>0.000466</td>\n",
" </tr>\n",
" <tr>\n",
" <th>80.0</th>\n",
" <td>0.001026</td>\n",
" <td>0.003000</td>\n",
" <td>0.001467</td>\n",
" <td>0.000489</td>\n",
" </tr>\n",
" <tr>\n",
" <th>90.0</th>\n",
" <td>0.001268</td>\n",
" <td>0.002956</td>\n",
" <td>0.001502</td>\n",
" <td>0.000280</td>\n",
" </tr>\n",
" <tr>\n",
" <th>100.0</th>\n",
" <td>0.001563</td>\n",
" <td>0.003774</td>\n",
" <td>0.001844</td>\n",
" <td>0.000342</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" time \n",
" min max mean std\n",
"n \n",
"10.0 0.000039 0.000223 0.000056 0.000019\n",
"20.0 0.000101 0.000264 0.000164 0.000051\n",
"30.0 0.000191 0.000533 0.000291 0.000093\n",
"40.0 0.000315 0.000854 0.000464 0.000152\n",
"50.0 0.000466 0.002513 0.000745 0.000256\n",
"60.0 0.000652 0.001818 0.001039 0.000338\n",
"70.0 0.000866 0.002469 0.001368 0.000466\n",
"80.0 0.001026 0.003000 0.001467 0.000489\n",
"90.0 0.001268 0.002956 0.001502 0.000280\n",
"100.0 0.001563 0.003774 0.001844 0.000342"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"greedy_data.groupby('n').agg(['min','max','mean','std'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We estimated above that the time for this method will scale like $O(n^2)$, so if we expect a graph $y=c\\cdot x^2$. If we take logarithms of both sides then we get $\\log y = 2\\log x+\\log c$. So, wif we use a log-log plot then we should expect a straight line. Let us check this."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,5))\n",
"sns.scatterplot(data=greedy_data, x='n', y='time', alpha=0.1, color='#777') # actual data\n",
"sns.lineplot(data=greedy_data, x='n', y='time', ci='sd', color='red') # mean\n",
"plt.xscale('log')\n",
"plt.yscale('log')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us estimate the slope of the mean line."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.0533333333333332e-05"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# (......-.........)/(100-10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That is pretty close to 2!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Symmetric"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us next see what happens with **symmetric graphs**. This time we will compare it against the exhaustive search to see if it is accurate."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2..............................3..............................4..............................5..............................6..............................7..............................8..............................9..............................10..............................11.............................."
]
}
],
"source": [
"MAX_REPETITIONS = 30\n",
"\n",
"greedy_sym_data = pd.DataFrame(columns=['n','time','quality'])\n",
"\n",
"i = 0\n",
"for n in range(2,MAX_n):\n",
" print(n, end='')\n",
" for repetitions in range(MAX_REPETITIONS):\n",
" print('.', end='')\n",
" G = Graph(n,'symmetric')\n",
" # Solve exactly\n",
" actual_shortest_length = exhaustive_search(G)[1]\n",
" # Solve with Greedy\n",
" t0 = perf_counter()\n",
" cycle, greedy_length = greedy_nearest_neighbour(G)\n",
" t1 = perf_counter()\n",
" # Collect data\n",
" greedy_sym_data.loc[i] = [n, t1-t0, (greedy_length/actual_shortest_length-1)*100]\n",
" i += 1"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead tr th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe thead tr:last-of-type th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr>\n",
" <th></th>\n",
" <th colspan=\"3\" halign=\"left\">time</th>\n",
" <th colspan=\"3\" halign=\"left\">quality</th>\n",
" </tr>\n",
" <tr>\n",
" <th></th>\n",
" <th>min</th>\n",
" <th>max</th>\n",
" <th>mean</th>\n",
" <th>min</th>\n",
" <th>max</th>\n",
" <th>mean</th>\n",
" </tr>\n",
" <tr>\n",
" <th>n</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2.0</th>\n",
" <td>0.000010</td>\n",
" <td>0.000055</td>\n",
" <td>0.000015</td>\n",
" <td>0.0</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.0</th>\n",
" <td>0.000011</td>\n",
" <td>0.000014</td>\n",
" <td>0.000012</td>\n",
" <td>0.0</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4.0</th>\n",
" <td>0.000014</td>\n",
" <td>0.000021</td>\n",
" <td>0.000016</td>\n",
" <td>0.0</td>\n",
" <td>20.388350</td>\n",
" <td>2.549429</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5.0</th>\n",
" <td>0.000016</td>\n",
" <td>0.000076</td>\n",
" <td>0.000021</td>\n",
" <td>0.0</td>\n",
" <td>53.048780</td>\n",
" <td>5.557196</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6.0</th>\n",
" <td>0.000019</td>\n",
" <td>0.000028</td>\n",
" <td>0.000022</td>\n",
" <td>0.0</td>\n",
" <td>52.866242</td>\n",
" <td>8.689809</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7.0</th>\n",
" <td>0.000022</td>\n",
" <td>0.000053</td>\n",
" <td>0.000026</td>\n",
" <td>0.0</td>\n",
" <td>62.068966</td>\n",
" <td>13.958661</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8.0</th>\n",
" <td>0.000028</td>\n",
" <td>0.000042</td>\n",
" <td>0.000032</td>\n",
" <td>0.0</td>\n",
" <td>54.545455</td>\n",
" <td>20.725066</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9.0</th>\n",
" <td>0.000034</td>\n",
" <td>0.000089</td>\n",
" <td>0.000044</td>\n",
" <td>0.0</td>\n",
" <td>86.138614</td>\n",
" <td>29.763685</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10.0</th>\n",
" <td>0.000040</td>\n",
" <td>0.000101</td>\n",
" <td>0.000060</td>\n",
" <td>0.0</td>\n",
" <td>83.870968</td>\n",
" <td>25.248837</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11.0</th>\n",
" <td>0.000045</td>\n",
" <td>0.000123</td>\n",
" <td>0.000067</td>\n",
" <td>0.0</td>\n",
" <td>81.914894</td>\n",
" <td>28.099201</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" time quality \n",
" min max mean min max mean\n",
"n \n",
"2.0 0.000010 0.000055 0.000015 0.0 0.000000 0.000000\n",
"3.0 0.000011 0.000014 0.000012 0.0 0.000000 0.000000\n",
"4.0 0.000014 0.000021 0.000016 0.0 20.388350 2.549429\n",
"5.0 0.000016 0.000076 0.000021 0.0 53.048780 5.557196\n",
"6.0 0.000019 0.000028 0.000022 0.0 52.866242 8.689809\n",
"7.0 0.000022 0.000053 0.000026 0.0 62.068966 13.958661\n",
"8.0 0.000028 0.000042 0.000032 0.0 54.545455 20.725066\n",
"9.0 0.000034 0.000089 0.000044 0.0 86.138614 29.763685\n",
"10.0 0.000040 0.000101 0.000060 0.0 83.870968 25.248837\n",
"11.0 0.000045 0.000123 0.000067 0.0 81.914894 28.099201"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"greedy_sym_data.groupby('n').agg(['min','max','mean'])"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,5))\n",
"sns.scatterplot(data=greedy_sym_data, x='n', y='time', alpha=0.3, color='#777') # actual data\n",
"sns.lineplot(data=greedy_sym_data, x='n', y='time', ci='sd', color='red') # mean\n",
"plt.xscale('log')\n",
"plt.yscale('log')"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x18ab718>"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,5))\n",
"sns.scatterplot(data=greedy_sym_data, x='n', y='quality', alpha=0.3, color='#777') # actual data\n",
"sns.lineplot(data=greedy_sym_data, x='n', y='quality', ci='sd', color='green') # mean"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Euclidean graphs**"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2..............................3..............................4..............................5..............................6..............................7..............................8..............................9..............................10..............................11.............................."
]
}
],
"source": [
"MAX_REPETITIONS = 30\n",
"\n",
"greedy_euc_data = pd.DataFrame(columns=['n','time','quality'])\n",
"\n",
"i = 0\n",
"for n in range(2,MAX_n):\n",
" print(n, end='')\n",
" for repetitions in range(MAX_REPETITIONS):\n",
" print('.', end='')\n",
" G = Graph(n,'Euclidean')\n",
" # Solve exactly\n",
" actual_shortest_length = exhaustive_search(G)[1]\n",
" # Solve with Greedy\n",
" t0 = perf_counter()\n",
" cycle, greedy_length = greedy_nearest_neighbour(G)\n",
" t1 = perf_counter()\n",
" # Collect data\n",
" greedy_euc_data.loc[i] = [n, t1-t0, (greedy_length/actual_shortest_length-1)*100]\n",
" i += 1"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead tr th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe thead tr:last-of-type th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr>\n",
" <th></th>\n",
" <th colspan=\"3\" halign=\"left\">time</th>\n",
" <th colspan=\"3\" halign=\"left\">quality</th>\n",
" </tr>\n",
" <tr>\n",
" <th></th>\n",
" <th>min</th>\n",
" <th>max</th>\n",
" <th>mean</th>\n",
" <th>min</th>\n",
" <th>max</th>\n",
" <th>mean</th>\n",
" </tr>\n",
" <tr>\n",
" <th>n</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2.0</th>\n",
" <td>0.000010</td>\n",
" <td>0.000024</td>\n",
" <td>0.000013</td>\n",
" <td>0.0</td>\n",
" <td>0.000000e+00</td>\n",
" <td>0.000000e+00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.0</th>\n",
" <td>0.000012</td>\n",
" <td>0.000028</td>\n",
" <td>0.000015</td>\n",
" <td>0.0</td>\n",
" <td>2.220446e-14</td>\n",
" <td>2.960595e-15</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4.0</th>\n",
" <td>0.000013</td>\n",
" <td>0.000032</td>\n",
" <td>0.000017</td>\n",
" <td>0.0</td>\n",
" <td>9.533980e+00</td>\n",
" <td>1.429205e+00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5.0</th>\n",
" <td>0.000016</td>\n",
" <td>0.000062</td>\n",
" <td>0.000021</td>\n",
" <td>0.0</td>\n",
" <td>2.371406e+01</td>\n",
" <td>4.859237e+00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6.0</th>\n",
" <td>0.000019</td>\n",
" <td>0.000050</td>\n",
" <td>0.000024</td>\n",
" <td>0.0</td>\n",
" <td>1.340071e+01</td>\n",
" <td>3.815022e+00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7.0</th>\n",
" <td>0.000024</td>\n",
" <td>0.000077</td>\n",
" <td>0.000036</td>\n",
" <td>0.0</td>\n",
" <td>2.798089e+01</td>\n",
" <td>4.710930e+00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8.0</th>\n",
" <td>0.000028</td>\n",
" <td>0.000382</td>\n",
" <td>0.000050</td>\n",
" <td>0.0</td>\n",
" <td>2.131230e+01</td>\n",
" <td>6.958534e+00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9.0</th>\n",
" <td>0.000034</td>\n",
" <td>0.000147</td>\n",
" <td>0.000054</td>\n",
" <td>0.0</td>\n",
" <td>2.336361e+01</td>\n",
" <td>7.128207e+00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10.0</th>\n",
" <td>0.000040</td>\n",
" <td>0.000191</td>\n",
" <td>0.000065</td>\n",
" <td>0.0</td>\n",
" <td>3.345502e+01</td>\n",
" <td>1.072515e+01</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11.0</th>\n",
" <td>0.000045</td>\n",
" <td>0.000112</td>\n",
" <td>0.000072</td>\n",
" <td>0.0</td>\n",
" <td>3.106986e+01</td>\n",
" <td>9.816136e+00</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" time quality \n",
" min max mean min max mean\n",
"n \n",
"2.0 0.000010 0.000024 0.000013 0.0 0.000000e+00 0.000000e+00\n",
"3.0 0.000012 0.000028 0.000015 0.0 2.220446e-14 2.960595e-15\n",
"4.0 0.000013 0.000032 0.000017 0.0 9.533980e+00 1.429205e+00\n",
"5.0 0.000016 0.000062 0.000021 0.0 2.371406e+01 4.859237e+00\n",
"6.0 0.000019 0.000050 0.000024 0.0 1.340071e+01 3.815022e+00\n",
"7.0 0.000024 0.000077 0.000036 0.0 2.798089e+01 4.710930e+00\n",
"8.0 0.000028 0.000382 0.000050 0.0 2.131230e+01 6.958534e+00\n",
"9.0 0.000034 0.000147 0.000054 0.0 2.336361e+01 7.128207e+00\n",
"10.0 0.000040 0.000191 0.000065 0.0 3.345502e+01 1.072515e+01\n",
"11.0 0.000045 0.000112 0.000072 0.0 3.106986e+01 9.816136e+00"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"greedy_euc_data.groupby('n').agg(['min','max','mean'])"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x141fc370>"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1080x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(15,5))\n",
"sns.scatterplot(data=greedy_euc_data, x='n', y='quality', alpha=0.3, color='#777') # actual data\n",
"sns.lineplot(data=greedy_euc_data, x='n', y='quality', ci='sd', color='green') # mean"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Asymmetric"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2..............................3..............................4..............................5..............................6..............................7..............................8..............................9..............................10..............................11.............................."
]
}
],
"source": [
"MAX_REPETITIONS = 30\n",
"\n",
"greedy_asym_data = pd.DataFrame(columns=['n','time','quality'])\n",
"\n",
"i = 0\n",
"for n in range(2,MAX_n):\n",
" print(n, end='')\n",
" for repetitions in range(MAX_REPETITIONS):\n",
" print('.', end='')\n",
" G = Graph(n,'asymmetric')\n",
" # Solve exactly\n",
" actual_shortest_length = exhaustive_search(G)[1]\n",
" # Solve with Greedy\n",
" t0 = perf_counter()\n",
" cycle, greedy_length = greedy_nearest_neighbour(G)\n",
" t1 = perf_counter()\n",
" # Collect data\n",
" greedy_asym_data.loc[i] = [n, t1-t0, (greedy_length/actual_shortest_length-1)*100]\n",
" i += 1"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead tr th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe thead tr:last-of-type th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr>\n",
" <th></th>\n",
" <th colspan=\"3\" halign=\"left\">time</th>\n",
" <th colspan=\"3\" halign=\"left\">quality</th>\n",
" </tr>\n",
" <tr>\n",
" <th></th>\n",
" <th>min</th>\n",
" <th>max</th>\n",
" <th>mean</th>\n",
" <th>min</th>\n",
" <th>max</th>\n",
" <th>mean</th>\n",
" </tr>\n",
" <tr>\n",
" <th>n</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2.0</th>\n",
" <td>0.000010</td>\n",
" <td>0.000036</td>\n",
" <td>0.000017</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3.0</th>\n",
" <td>0.000012</td>\n",
" <td>0.000211</td>\n",
" <td>0.000033</td>\n",
" <td>0.000000</td>\n",
" <td>70.754717</td>\n",
" <td>5.461099</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4.0</th>\n",
" <td>0.000015</td>\n",
" <td>0.000289</td>\n",
" <td>0.000035</td>\n",
" <td>0.000000</td>\n",
" <td>146.464646</td>\n",
" <td>29.864393</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5.0</th>\n",
" <td>0.000018</td>\n",
" <td>0.000299</td>\n",
" <td>0.000040</td>\n",
" <td>0.000000</td>\n",
" <td>76.415094</td>\n",
" <td>20.022667</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6.0</th>\n",
" <td>0.000022</td>\n",
" <td>0.000146</td>\n",
" <td>0.000043</td>\n",
" <td>0.000000</td>\n",
" <td>185.333333</td>\n",
" <td>46.357535</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7.0</th>\n",
" <td>0.000031</td>\n",
" <td>0.001818</td>\n",
" <td>0.000116</td>\n",
" <td>0.000000</td>\n",
" <td>134.020619</td>\n",
" <td>42.345361</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8.0</th>\n",
" <td>0.000034</td>\n",
" <td>0.002674</td>\n",
" <td>0.000172</td>\n",
" <td>0.000000</td>\n",
" <td>133.082707</td>\n",
" <td>46.145371</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9.0</th>\n",
" <td>0.000040</td>\n",
" <td>0.000158</td>\n",
" <td>0.000066</td>\n",
" <td>0.000000</td>\n",
" <td>154.128440</td>\n",
" <td>46.089216</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10.0</th>\n",
" <td>0.000044</td>\n",
" <td>0.000113</td>\n",
" <td>0.000064</td>\n",
" <td>7.177033</td>\n",
" <td>105.960265</td>\n",
" <td>48.973570</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11.0</th>\n",
" <td>0.000048</td>\n",
" <td>0.000200</td>\n",
" <td>0.000074</td>\n",
" <td>2.222222</td>\n",
" <td>171.794872</td>\n",
" <td>62.586272</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" time quality \n",
" min max mean min max mean\n",
"n \n",
"2.0 0.000010 0.000036 0.000017 0.000000 0.000000 0.000000\n",
"3.0 0.000012 0.000211 0.000033 0.000000 70.754717 5.461099\n",
"4.0 0.000015 0.000289 0.000035 0.000000 146.464646 29.864393\n",
"5.0 0.000018 0.000299 0.000040 0.000000 76.415094 20.022667\n",
"6.0 0.000022 0.000146 0.000043 0.000000 185.333333 46.357535\n",
"7.0 0.000031 0.001818 0.000116 0.000000 134.020619 42.345361\n",
"8.0 0.000034 0.002674 0.000172 0.000000 133.082707 46.145371\n",
"9.0 0.000040 0.000158 0.000066 0.000000 154.128440 46.089216\n",
"10.0 0.000044 0.000113 0.000064 7.177033 105.960265 48.973570\n",
"11.0 0.000048 0.000200 0.000074 2.222222 171.794872 62.586272"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"greedy_asym_data.groupby('n').agg(['min','max','mean'])"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1420c7f0>"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1800x360 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (time, quality) = plt.subplots(nrows=1, ncols=2, figsize=(25, 5))\n",
"sns.scatterplot(data=greedy_asym_data, x='n', y='time', alpha=0.3, ax=time, color='#777')\n",
"sns.lineplot(data=greedy_asym_data, x='n', y='time', ci='sd', ax=time, color='red')\n",
"time.set(xscale=\"log\", yscale=\"log\")\n",
"sns.scatterplot(data=greedy_asym_data, x='n', y='quality', alpha=0.3, ax=quality, color='#777')\n",
"sns.lineplot(data=greedy_asym_data, x='n', y='quality', ci='sd', ax=quality, color='green')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## An ad-hoc heuristic method"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"def my_adhoc_heuristic(G):\n",
" ''' Works like Nearest Neighbour but looks at 2 unvisited ahead at each time.\n",
" Returns shortest found cycle and its cost '''\n",
" print(\"adhoc...\")\n",
" show(G)\n",
" unvisited = G.vertices.copy()\n",
" visited = [] # solution to be built\n",
" city0 = 0 # Start city\n",
" print('.......',unvisited,G.vertices)\n",
" while len(unvisited) > 1:\n",
" print(\"...at\", city0)\n",
" shortest = oo\n",
" city1 = city2 = None # the next 2 unvisited cities\n",
" visited.append(city0)\n",
" unvisited.remove(city0)\n",
" # Find the next 2 best unvisited cities (city1, city2)\n",
" for c1 in unvisited:\n",
" for c2 in unvisited:\n",
" if c2==c1: continue\n",
" cost_of_next_2_steps = G[city0][c1]+G[c1][c2] # cost of path: city0 -- c1 -- c2\n",
" if cost_of_next_2_steps < shortest:\n",
" shortest = cost_of_next_2_steps\n",
" city1, city2 = c1, c2\n",
" # Add 'city1' to 'visited', and set 'city2' to be the next starting point (city0)\n",
" if city1==city2: print(\"!\"*100)\n",
" visited.append(city1)\n",
" unvisited.remove(city1)\n",
" city0 = city2\n",
" if unvisited != []:\n",
" print(\"left...\", unvisited, \"city0 =\", city0)\n",
" visited.append(unvisited[0]) # append last city left\n",
" return (visited, cost(G, visited+[0]))"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"([0, 3, 5, 4, 2, 1, 6], 180)\n",
"adhoc...\n",
"7x7 asymmetric graph:\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" <th>5</th>\n",
" <th>6</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>inf</td>\n",
" <td>1.0</td>\n",
" <td>24.0</td>\n",
" <td>45.0</td>\n",
" <td>88.0</td>\n",
" <td>81.0</td>\n",
" <td>71.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>88.0</td>\n",
" <td>inf</td>\n",
" <td>29.0</td>\n",
" <td>73.0</td>\n",
" <td>54.0</td>\n",
" <td>31.0</td>\n",
" <td>92.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>39.0</td>\n",
" <td>90.0</td>\n",
" <td>inf</td>\n",
" <td>55.0</td>\n",
" <td>1.0</td>\n",
" <td>70.0</td>\n",
" <td>31.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>5.0</td>\n",
" <td>85.0</td>\n",
" <td>83.0</td>\n",
" <td>inf</td>\n",
" <td>49.0</td>\n",
" <td>11.0</td>\n",
" <td>66.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>87.0</td>\n",
" <td>18.0</td>\n",
" <td>74.0</td>\n",
" <td>10.0</td>\n",
" <td>inf</td>\n",
" <td>3.0</td>\n",
" <td>75.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>16.0</td>\n",
" <td>47.0</td>\n",
" <td>20.0</td>\n",
" <td>5.0</td>\n",
" <td>20.0</td>\n",
" <td>inf</td>\n",
" <td>87.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>78.0</td>\n",
" <td>66.0</td>\n",
" <td>39.0</td>\n",
" <td>63.0</td>\n",
" <td>79.0</td>\n",
" <td>4.0</td>\n",
" <td>inf</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" 0 1 2 3 4 5 6\n",
"0 inf 1.0 24.0 45.0 88.0 81.0 71.0\n",
"1 88.0 inf 29.0 73.0 54.0 31.0 92.0\n",
"2 39.0 90.0 inf 55.0 1.0 70.0 31.0\n",
"3 5.0 85.0 83.0 inf 49.0 11.0 66.0\n",
"4 87.0 18.0 74.0 10.0 inf 3.0 75.0\n",
"5 16.0 47.0 20.0 5.0 20.0 inf 87.0\n",
"6 78.0 66.0 39.0 63.0 79.0 4.0 inf"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"....... [0, 1, 2, 3, 4, 5, 6] [0, 1, 2, 3, 4, 5, 6]\n",
"...at 0\n",
"...at 5\n",
"...at 2\n",
"left... [6] city0 = 6\n",
"([0, 3, 5, 4, 2, 1, 6], 180)\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G=Graph(7)\n",
"draw(G)\n",
"print(greedy_nearest_neighbour(G))\n",
"print(my_adhoc_heuristic(G))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Testing time and quality."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 0\n",
"adhoc...\n",
"10x10 asymmetric graph:\n"
]
},
{
"data": {
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"text/plain": [
" 0 1 2 3 4 5 6 7 8 9\n",
"0 inf 11.0 23.0 49.0 5.0 73.0 10.0 71.0 83.0 95.0\n",
"1 27.0 inf 92.0 11.0 36.0 89.0 84.0 12.0 69.0 87.0\n",
"2 77.0 38.0 inf 91.0 75.0 34.0 37.0 15.0 73.0 91.0\n",
"3 29.0 72.0 40.0 inf 30.0 53.0 23.0 74.0 69.0 15.0\n",
"4 18.0 57.0 81.0 1.0 inf 47.0 25.0 49.0 7.0 93.0\n",
"5 7.0 1.0 29.0 67.0 30.0 inf 87.0 45.0 86.0 15.0\n",
"6 89.0 62.0 58.0 86.0 20.0 19.0 inf 22.0 26.0 24.0\n",
"7 50.0 49.0 99.0 55.0 88.0 40.0 64.0 inf 49.0 1.0\n",
"8 54.0 84.0 49.0 19.0 30.0 18.0 97.0 17.0 inf 62.0\n",
"9 79.0 60.0 17.0 66.0 53.0 20.0 16.0 20.0 15.0 inf"
]
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"name": "stdout",
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"text": [
"....... [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
"...at 0\n",
"...at 8\n",
"...at 7\n",
"...at 3\n",
"...at 1\n",
"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"
]
},
{
"ename": "ValueError",
"evalue": "list.remove(x): x not in list",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-36-da5a97cb3108>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m 22\u001b[0m \u001b[1;31m# Greedy 2\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 23\u001b[0m \u001b[0mt0\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mperf_counter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 24\u001b[1;33m \u001b[0mcycle\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlength_adhoc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmy_adhoc_heuristic\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mG\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 25\u001b[0m \u001b[0mt1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mperf_counter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[0mt_adhoc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mt1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mt0\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;32m<ipython-input-34-cf3249ff3f3b>\u001b[0m in \u001b[0;36mmy_adhoc_heuristic\u001b[1;34m(G)\u001b[0m\n\u001b[0;32m 25\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mcity1\u001b[0m\u001b[1;33m==\u001b[0m\u001b[0mcity2\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"!\"\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m100\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[0mvisited\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcity1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m \u001b[0munvisited\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mremove\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcity1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 28\u001b[0m \u001b[0mcity0\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcity2\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 29\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0munvisited\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mValueError\u001b[0m: list.remove(x): x not in list"
]
}
],
"source": [
"MAX_REPETITIONS = 100\n",
"MAX_TIME = 10 # minutes\n",
"\n",
"data = pd.DataFrame(columns=['n', 't_nearest_neighbour', 't_adhoc','quality'])\n",
"\n",
"n = i = 0\n",
"t_nearest_neighbour = t_adhoc = 0\n",
"\n",
"started_at = perf_counter()\n",
"while perf_counter()-started_at < MAX_TIME: # in seconds; if it takes too long then stop testing\n",
" print(n, t_nearest_neighbour+t_adhoc)\n",
" n += 10\n",
" t_nearest_neighbour = t_adhoc = 0\n",
" for repetitions in range(MAX_REPETITIONS):\n",
" i += 1\n",
" G = Graph(n,'asymmetric')\n",
" # Greedy 1\n",
" t0 = perf_counter()\n",
" cycle, length_nearest_neighbour = greedy_nearest_neighbour(G)\n",
" t1 = perf_counter()\n",
" t_nearest_neighbour = t1-t0\n",
" # Greedy 2\n",
" t0 = perf_counter()\n",
" cycle, length_adhoc = my_adhoc_heuristic(G)\n",
" t1 = perf_counter()\n",
" t_adhoc = t1-t0\n",
" # Save data\n",
" quality = length_adhoc/length_nearest_neighbour*100\n",
" data.loc[i] = [n, t_nearest_neighbour, t_adhoc, quality]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"data.groupby('n').agg(['min','max','mean'])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.figure(figsize=(16,6))\n",
"sns.lineplot(data=data, x='n', y='t_nearest_neighbour', ci='sd', alpha=0.2, color='#f30')\n",
"sns.scatterplot(data=data, x='n', y='t_nearest_neighbour', ci='sd', alpha=0.2, color='#f30')\n",
"sns.lineplot(data=data, x='n', y='t_adhoc', ci='sd', color='#f35')\n",
"sns.scatterplot(data=data, x='n', y='t_adhoc', ci='sd', color='#f35')\n",
"plt.xscale('log')\n",
"plt.yscale('log')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.figure(figsize=(16,6))\n",
"sns.scatterplot(data=data, x='n', y='quality', ci='sd', alpha=0.2, color='#777')\n",
"sns.lineplot(data=data, x='n', y='quality', ci='sd', color='green')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Metaheuristics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"............................................................\n",
"\n",
"............................................................\n",
"\n",
"............................................................\n",
"\n",
"............................................................\n",
"\n",
"............................................................\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# References"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* Garey, S. and Johnson, D. (1979). **Computers and Intractability: A Guide to the Theory of NP-Completeness.** Freeman.\n",
"\n",
"* Hoos, H. and Stutzler, T. (2005). **Stochastic Local Search: Foundations and Applications.** Morgan Kaufmann.\n",
"\n",
"* Sipser, M. (2013). **Introduction to the theory of computation.** (3rd international ed.). Cengage Learning."
]
}
],
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