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https://github.com/sejas/muia-multiagent-systems-tsp-aco
TSP problem solution implementing ACO for MultiAgent Systems subject of Master in Artificial Intelligence @UPM
https://github.com/sejas/muia-multiagent-systems-tsp-aco
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TSP problem solution implementing ACO for MultiAgent Systems subject of Master in Artificial Intelligence @UPM
- Host: GitHub
- URL: https://github.com/sejas/muia-multiagent-systems-tsp-aco
- Owner: sejas
- Created: 2020-07-07T00:44:25.000Z (over 4 years ago)
- Default Branch: master
- Last Pushed: 2020-07-07T21:54:00.000Z (over 4 years ago)
- Last Synced: 2025-01-01T15:42:14.747Z (2 days ago)
- Language: Jupyter Notebook
- Size: 6.11 MB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Multiagent systems - TSP Problem
- Author: Antonio Sejas
- Sistemas Multiagente
- MUIA - UPM
- Julio 2020
In this jupyter notebook I've coded the Ant System, and ACO algorithm to resolve two TSP maps. It's interesting play with the parameters to fully understand the algorithm.
```python
import tsplib95
from random import randrange, random, shuffle
from bisect import bisect
import pandas as pd
import matplotlib.pyplot as plt
# import pixiedust
import numpy as np
```
```python
#!pip install ipython-autotime
%load_ext autotime
```
## Load TSP Problem
```python
# Data Source : http://www.math.uwaterloo.ca/tsp/world/countries.html
#TSP_FILE = 'uy734.tsp' # 🇺🇾 Uruguay
TSP_FILE = 'wi29.tsp' # 🇪🇭 Western Sahara
```
time: 314 µs
```python
# LOAD TSP FILE
PROBLEM = tsplib95.load(TSP_FILE)
print(type(PROBLEM))
```
time: 2.45 ms
```python
PROBLEM.type
```
'TSP'
time: 2.03 ms
```python
N = len(list(PROBLEM.get_nodes())) # N is total cities
print("%s Cities"%N)
```
29 Cities
time: 579 µs
```python
# Example city coordinates
PROBLEM.node_coords[3]
```
[21300.0, 13016.6667]
time: 1.34 ms
```python
# Distance between first and last cities
edge = {'start':1,'end':N}
PROBLEM.get_weight(**edge)
```
7799
time: 1.68 ms
## Basic Ant
```python
HALF_MATRIX = True
class Ant:
tour = None
tsp = PROBLEM
def __init__(self, city_i=0):
self.tour = []
if city_i>0:
self.visit(city_i)
@property
def current_city(self):
return self.tour[-1]
@property
def tour_weight(self):
return self.tsp.trace_tours([self.tour])[0]
def visit(self, i:int):
if i in self.tour and i != self.tour[0]:
raise Exception("The city i: %s is already visited. Imposible to visit again"%i)
if i < 1 or i > N:
raise Exception("The city i (%s) is out of range: -> [1, %s]"%(i, N))
self.tour.append(i)
def distance_to(self, city_j:int):
return self.tsp.get_weight(self.current_city, city_j)
def _not_visited_cities(self):
return [i for i in range(1,N+1) if i not in self.tour]
def _raw_probability(self, city_j:int, pheromones_matrix):
## ASSUMPTION: We consider the edge has two ways. Phromones to go and to go back. In other words. I->J != J->I
# careful, we must substract one from the cities index
if HALF_MATRIX:
a = min([self.current_city-1, city_j-1])
b = max([self.current_city-1, city_j-1])
else:
a = self.current_city-1
b = city_j-1
return (pheromones_matrix[a][b]**ALPHA) * ((1/self.distance_to(city_j))**BETA)
def normalized_probabilities(self, pheromones_matrix):
""" Returns a tuple
First element: List of neighbors, cities not visited
Second element: List of probabilities calculated with the formular of tau_ij^A* h_ij^B
"""
neighbors = self._not_visited_cities()
neighbors_pheromone_list = [self._raw_probability(neighbor_j, pheromones_matrix) for neighbor_j in neighbors]
total = sum(neighbors_pheromone_list)
normalized_probabilities = [pheromone_ij/total for pheromone_ij in neighbors_pheromone_list]
#print(normalized_probabilities)
return neighbors, normalized_probabilities
def pick_next_city(self, cities, probabilities):
roulette_x = random()
idx = 0
roulette_sum = 0
for p in probabilities:
roulette_sum += p
if roulette_sum >= roulette_x :
return cities[idx]
idx += 1
def finished_tour(self):
return len(self.tour) == N
```
time: 4.46 ms
```python
a = Ant(1)
print(a.tour)
a.visit(29)
print(a.tour)
print("Total weight of this ant tour is: %s"%a.tour_weight)
```
[1]
[1, 29]
Total weight of this ant tour is: 15598
time: 1 ms
```python
def plot_pheromones(df, step, show=True, title=''):
print(title)
if show:
plt.imshow(df, cmap='hot', interpolation='nearest')
plt.savefig("pheromones-%03d.png"%step)
plt.show()
#plt.imsave("pheromones-%03d.png"%step, df, cmap='hot')
```
time: 736 µs
## BASE LINE
```python
# Solution joining all the cities in sequence
ant = Ant(1)
for i in range(2,N+1):
ant.visit(i)
print(ant.tour)
print(ant.tour_weight)
```
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]
52284
time: 994 µs
```python
# Random Solution
ant = Ant(1)
random_cities = list(range(2,N+1))
shuffle(random_cities)
for i in random_cities:
ant.visit(i)
print(ant.tour)
print(ant.tour_weight)
```
[1, 22, 17, 10, 16, 19, 29, 27, 15, 25, 18, 4, 23, 11, 13, 28, 14, 2, 8, 24, 26, 12, 21, 20, 7, 3, 9, 5, 6]
99557
time: 1.21 ms
```python
# Solution using the heuristic
ant = Ant(1)
while not ant.finished_tour():
neighbors = ant._not_visited_cities()
distances = []
for city_j in range(1, len(neighbors)+1):
distances.append(ant.distance_to(city_j))
pos_min_distance = distances.index(min(distances))
next_closest_city = neighbors[pos_min_distance]
ant.visit(next_closest_city)
print(ant.tour)
print(ant.tour_weight)
```
[1, 2, 4, 7, 11, 16, 22, 29, 28, 27, 23, 26, 25, 24, 20, 21, 19, 18, 17, 14, 15, 13, 12, 8, 9, 6, 5, 10, 3]
56645
time: 3.67 ms
## ANT SYSTEM
```python
def ant_system(show=True):
# INIT MATRIX for each CITY IJ with TAU INITIAL (t_0)
_pheromones_row = [TAU_INITIAL for i in range(N)]
pheromones_matrix = [_pheromones_row for j in range(N)]
history_list = []
for step in range(STEPS):
ants_list = []
for ant_i in range(M_ANTS):
# pick a starting point
first_random_city = randrange(N)+1
ant = Ant(first_random_city)
ants_list.append(ant)
while not ant.finished_tour():
# calculate probability P_j for all unvisited neightbors J
# ANT SYSTEM (AS): Probability of each edge in the neighborhood
# p_ij_k = (t_ij^a * (1/d_ij)^b ) / SUM(all feasible g edges) # It's like edge normalized
neighbors, probabilities = ant.normalized_probabilities(pheromones_matrix) # sum(probabilities) == 1
# pick the next node using the probabilities
next_city = ant.pick_next_city(neighbors, probabilities)
ant.visit(next_city)
ant.visit(first_random_city) # Close cycle??
history_list.append(ants_list.copy()) # save results
# update pheromone values based upon the quality of each solution
# ANT SYSTEM (AS): All ants contribute updating the pheromone as follows
# TAU_I_J = (1-RO)*TAU_I_J + SUM(Q/(Lk or 0)) # Attention! In TSP Lk will be always the same == N Total cities
# Probably in TSP the length means the distance
pheromones_to_add = [[0 for i in range(N)] for j in range(N)]
for ant in ants_list:
tau_delta = Q/ant.tour_weight
for tour_i in range(1, len(ant.tour)):
i = ant.tour[tour_i-1]-1 # city
j = ant.tour[tour_i]-1 # next city
if HALF_MATRIX:
a = min([i,j])
b = max([i,j])
else:
a = i
b = j
pheromones_to_add[a][b] += tau_delta
# update fermonones
df = pd.DataFrame(pheromones_matrix)*(1-RO)+pd.DataFrame(pheromones_to_add)
pheromones_matrix = df.values
# PLOT every 10th of steps
if step % int(STEPS/10) == 0:
plot_pheromones(df,step=step+1, title="Step %s from %s."%(step+1,STEPS), show=show)
# Plot last result
plot_pheromones(df,step=step+1, title="Step %s from %s."%(step+1,STEPS), show=True)
return history_list, ants_list
```
time: 4 ms
```python
M_ANTS = int(N) # Number of ants ~ to number of nodes (N)
for m in N:
M_ANTS
ALPHA = 1 # History coefficietn ~ 1
BETA = 3 # 0,1,2,3,4,5,6 # Heuristic Coefficient [2,5]
RO = 0.2# Evaporation rate # It's like cooling. A high value is similar to very decrease the temparature drastically and get stucked in a local optimum
Q = 1*30000 # Pheromone change factor
TAU_INITIAL = 1/70000 # Initial pheromone ~ 1/RO*C^nn ; C^nn is the length of the tour generated by the nearest neighbor heuristic
STEPS = 100
history_list, ants_list = ant_system(show=False)
```
time: 9.19 s
```python
for m in range(1,N+1):
M_ANTS = 2*m # Number of ants ~ to number of nodes (N)
print("STARTING WITH %d ANTS:"%M_ANTS)
ALPHA = 1 # History coefficietn ~ 1
BETA = 3 # 0,1,2,3,4,5,6 # Heuristic Coefficient [2,5]
RO = 0.2# Evaporation rate # It's like cooling. A high value is similar to very decrease the temparature drastically and get stucked in a local optimum
Q = 1*30000 # Pheromone change factor
TAU_INITIAL = 1/70000 # Initial pheromone ~ 1/RO*C^nn ; C^nn is the length of the tour generated by the nearest neighbor heuristic
STEPS = 100
history_list, ants_list = ant_system(show=False)
#Results
all_ants_list = [ant for ants_step_list in history_list for ant in ants_step_list]
all_tours_weight_list = [a.tour_weight for a in all_ants_list]
pos_min = all_tours_weight_list.index(min(all_tours_weight_list))
print("Min weigth: %s"%all_tours_weight_list[pos_min])
best_ant = all_ants_list[pos_min]
best_tour = best_ant.tour
print("Best Tour: %s"%best_tour)
```
STARTING WITH 2 ANTS:
Min weigth: 34342
Best Tour: [21, 23, 22, 18, 19, 15, 10, 11, 12, 13, 9, 7, 3, 4, 5, 6, 1, 2, 8, 17, 16, 24, 27, 25, 26, 20, 14, 29, 28, 21]
STARTING WITH 4 ANTS:
Min weigth: 29835
Best Tour: [17, 18, 19, 15, 11, 10, 12, 8, 4, 5, 1, 2, 6, 3, 7, 9, 13, 14, 16, 25, 27, 24, 20, 26, 28, 29, 21, 23, 22, 17]
STARTING WITH 6 ANTS:
Min weigth: 29033
Best Tour: [22, 23, 21, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 12, 10, 11, 6, 1, 2, 5, 4, 3, 7, 9, 8, 15, 19, 18, 17, 22]
STARTING WITH 8 ANTS:
Min weigth: 28453
Best Tour: [15, 19, 18, 22, 23, 21, 29, 28, 26, 20, 16, 24, 27, 25, 17, 14, 13, 9, 7, 3, 4, 8, 5, 6, 2, 1, 11, 10, 12, 15]
STARTING WITH 10 ANTS:
Min weigth: 27811
Best Tour: [9, 7, 3, 4, 8, 5, 6, 2, 1, 11, 10, 12, 15, 19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 9]
STARTING WITH 12 ANTS:
Min weigth: 27935
Best Tour: [15, 19, 18, 17, 22, 23, 21, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 9, 7, 3, 4, 8, 5, 6, 1, 2, 10, 11, 12, 15]
STARTING WITH 14 ANTS:
Min weigth: 28453
Best Tour: [19, 18, 22, 23, 21, 29, 28, 26, 20, 16, 24, 27, 25, 17, 14, 13, 9, 7, 3, 4, 8, 5, 6, 2, 1, 11, 10, 12, 15, 19]
STARTING WITH 16 ANTS:
Min weigth: 28253
Best Tour: [10, 11, 15, 19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 12, 8, 9, 7, 3, 4, 5, 6, 2, 1, 10]
STARTING WITH 18 ANTS:
Min weigth: 28763
Best Tour: [15, 19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 16, 25, 27, 24, 14, 13, 9, 7, 3, 4, 8, 5, 6, 1, 2, 11, 10, 12, 15]
STARTING WITH 20 ANTS:
Min weigth: 28377
Best Tour: [22, 23, 21, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 12, 8, 9, 7, 3, 4, 5, 6, 2, 1, 10, 11, 15, 19, 18, 17, 22]
STARTING WITH 22 ANTS:
Min weigth: 28181
Best Tour: [17, 18, 19, 15, 11, 10, 6, 2, 1, 5, 4, 3, 7, 9, 8, 12, 13, 14, 16, 24, 27, 25, 20, 26, 28, 29, 21, 23, 22, 17]
STARTING WITH 24 ANTS:
Min weigth: 27749
Best Tour: [17, 18, 19, 15, 12, 10, 11, 6, 2, 1, 5, 8, 4, 3, 7, 9, 13, 14, 16, 24, 27, 25, 20, 26, 28, 29, 21, 23, 22, 17]
STARTING WITH 26 ANTS:
Min weigth: 28424
Best Tour: [15, 19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 12, 8, 7, 9, 3, 4, 5, 6, 2, 1, 10, 11, 15]
STARTING WITH 28 ANTS:
Min weigth: 28670
Best Tour: [24, 27, 25, 16, 20, 26, 28, 29, 21, 23, 22, 18, 19, 15, 12, 10, 11, 6, 2, 1, 5, 8, 4, 3, 7, 9, 13, 14, 17, 24]
STARTING WITH 30 ANTS:
Min weigth: 28252
Best Tour: [26, 20, 25, 27, 24, 16, 14, 13, 12, 8, 9, 7, 3, 4, 5, 6, 1, 2, 10, 11, 15, 19, 18, 17, 21, 23, 22, 29, 28, 26]
STARTING WITH 32 ANTS:
Min weigth: 28042
Best Tour: [19, 18, 17, 23, 22, 21, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 9, 7, 3, 4, 8, 5, 6, 2, 1, 11, 10, 12, 15, 19]
STARTING WITH 34 ANTS:
Min weigth: 27811
Best Tour: [13, 9, 7, 3, 4, 8, 5, 6, 2, 1, 11, 10, 12, 15, 19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13]
STARTING WITH 36 ANTS:
Min weigth: 28454
Best Tour: [14, 13, 9, 7, 3, 4, 8, 5, 6, 2, 1, 10, 11, 12, 15, 19, 18, 22, 23, 21, 29, 28, 26, 20, 16, 24, 27, 25, 17, 14]
STARTING WITH 38 ANTS:
Min weigth: 27612
Best Tour: [16, 24, 27, 25, 20, 26, 28, 29, 23, 22, 21, 17, 18, 19, 15, 12, 10, 11, 6, 2, 1, 5, 8, 4, 3, 7, 9, 13, 14, 16]
STARTING WITH 40 ANTS:
Min weigth: 28252
Best Tour: [15, 19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 12, 8, 9, 7, 3, 4, 5, 6, 1, 2, 10, 11, 15]
STARTING WITH 42 ANTS:
Min weigth: 28226
Best Tour: [14, 13, 9, 7, 3, 4, 8, 5, 6, 2, 1, 11, 10, 12, 15, 19, 18, 22, 23, 21, 29, 28, 26, 20, 25, 27, 24, 16, 17, 14]
STARTING WITH 44 ANTS:
Min weigth: 28257
Best Tour: [29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 9, 7, 3, 4, 8, 5, 2, 1, 6, 10, 11, 12, 15, 19, 18, 22, 23, 21, 17, 29]
STARTING WITH 46 ANTS:
Min weigth: 28406
Best Tour: [19, 18, 22, 23, 21, 29, 28, 26, 24, 27, 25, 16, 20, 17, 14, 13, 9, 7, 3, 4, 8, 5, 6, 1, 2, 11, 10, 12, 15, 19]
STARTING WITH 48 ANTS:
Min weigth: 27946
Best Tour: [19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 27, 25, 24, 16, 14, 13, 9, 7, 3, 4, 8, 5, 6, 2, 1, 11, 10, 12, 15, 19]
STARTING WITH 50 ANTS:
Min weigth: 27811
Best Tour: [14, 13, 9, 7, 3, 4, 8, 5, 6, 2, 1, 11, 10, 12, 15, 19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 25, 27, 24, 16, 14]
STARTING WITH 52 ANTS:
Min weigth: 27811
Best Tour: [14, 13, 9, 7, 3, 4, 8, 5, 6, 1, 2, 10, 11, 12, 15, 19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 25, 27, 24, 16, 14]
STARTING WITH 54 ANTS:
Min weigth: 28228
Best Tour: [15, 19, 18, 17, 21, 23, 22, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 12, 8, 7, 9, 3, 4, 5, 1, 2, 6, 10, 11, 15]
STARTING WITH 56 ANTS:
Min weigth: 28203
Best Tour: [17, 18, 19, 15, 12, 10, 11, 6, 2, 1, 5, 4, 8, 7, 3, 9, 13, 14, 16, 24, 27, 25, 20, 26, 28, 29, 21, 23, 22, 17]
STARTING WITH 58 ANTS:
Min weigth: 27749
Best Tour: [23, 21, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 9, 7, 3, 4, 8, 5, 1, 2, 6, 11, 10, 12, 15, 19, 18, 17, 22, 23]
time: 7min 33s
```python
tours_weight_list = [a.tour_weight for a in ants_list]
print(tours_weight_list)
```
[41452, 34264, 31520, 31167, 32841, 30794, 33718, 35413, 34299, 35205, 35409, 36502, 32727, 35078, 32767, 31543, 31218, 37909, 40431, 30039, 32038, 38803, 39163, 31978, 36819, 37753, 31793, 33751, 36302, 42885, 31795, 35961, 31886, 40050, 30739, 28512, 34902, 34616, 35421, 41793, 39343, 36512, 33163, 40943, 39181, 36074, 32207, 35010, 29991, 29966, 39768, 36854, 37645, 38673, 41095, 32418, 39090, 34212]
time: 9.53 ms
```python
#pos_min = tours_weight_list.index(min(tours_weight_list))
all_ants_list = [ant for ants_step_list in history_list for ant in ants_step_list]
all_tours_weight_list = [a.tour_weight for a in all_ants_list]
pos_min = all_tours_weight_list.index(min(all_tours_weight_list))
print("Min weigth: %s"%all_tours_weight_list[pos_min])
best_ant = all_ants_list[pos_min]
best_tour = best_ant.tour
print("Best Tour: %s"%best_tour)
```
Min weigth: 27749
Best Tour: [23, 21, 29, 28, 26, 20, 25, 27, 24, 16, 14, 13, 9, 7, 3, 4, 8, 5, 1, 2, 6, 11, 10, 12, 15, 19, 18, 17, 22, 23]
time: 872 ms
```python
pd.DataFrame(all_tours_weight_list).plot(figsize=(15,10))
```
time: 417 ms
```python
pd.DataFrame([min([a.tour_weight for a in ants_step_list]) for ants_step_list in history_list]).plot()
```
time: 1.01 s
```python
pd.DataFrame([max([a.tour_weight for a in ants_step_list]) for ants_step_list in history_list]).plot()
```
time: 1 s
```python
pd.DataFrame([np.mean([a.tour_weight for a in ants_step_list]) for ants_step_list in history_list]).plot()
```
time: 1 s
```python
map_df_lat = pd.DataFrame([PROBLEM.node_coords[i][0] for i in best_tour], columns=['lat'])
map_df_long = pd.DataFrame([PROBLEM.node_coords[i][1] for i in best_tour], columns=['long'])*-1
print(len(map_df_lat))
plt.figure(figsize=(15,10))
plt.plot(map_df_long,
map_df_lat,
c='DarkBlue',
#style=['o', 'rx'],
#s=2,
#figsize=(15,8),
marker="o",
markerfacecolor="r")
```
30
[]
time: 210 ms
```python
```
```python
best_ant.tour_weight
```
27749
time: 1.83 ms
```python
```
```python
```