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# a3-algorithmique-avancée # Projet de Mobilité Multimodale Intelligente - Optimisation des tournées de livraison
## Getting started
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## Add your files
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```
cd existing_repo
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git branch -M main
git push -uf origin main
```
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## Test and Deploy
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***
# Editing this README
When you're ready to make this README your own, just edit this file and use the handy template below (or feel free to structure it however you want - this is just a starting point!). Thank you to [makeareadme.com](https://www.makeareadme.com/) for this template.
## Suggestions for a good README
Every project is different, so consider which of these sections apply to yours. The sections used in the template are suggestions for most open source projects. Also keep in mind that while a README can be too long and detailed, too long is better than too short. If you think your README is too long, consider utilizing another form of documentation rather than cutting out information.
## Name
Choose a self-explaining name for your project.
## Description ## Description
Let people know what your project can do specifically. Provide context and add a link to any reference visitors might be unfamiliar with. A list of Features or a Background subsection can also be added here. If there are alternatives to your project, this is a good place to list differentiating factors.
## Badges Dans le cadre de l'appel à manifestation d'intérêt lancé par l'ADEME (Agence de l’Environnement et de la Maîtrise de l’Energie) visant à promouvoir la réalisation de démonstrateurs et d'expérimentations de nouvelles solutions de mobilité pour les personnes et les marchandises adaptées à différents types de territoires, notre structure CesiCDP, en collaboration avec plusieurs partenaires, a décidé de concentrer ses efforts sur l'optimisation de la gestion des tournées de livraison.
On some READMEs, you may see small images that convey metadata, such as whether or not all the tests are passing for the project. You can use Shields to add some to your README. Many services also have instructions for adding a badge.
## Visuals Notre problème algorithmique consiste à déterminer, sur un réseau routier, une tournée qui permet de relier entre elles un sous-ensemble de villes, puis de revenir à son point de départ de manière à minimiser la durée totale de la tournée. Cette optimisation tient compte du trafic prévu sur chaque axe pour les différentes tranches horaires.
Depending on what you are making, it can be a good idea to include screenshots or even a video (you'll frequently see GIFs rather than actual videos). Tools like ttygif can help, but check out Asciinema for a more sophisticated method.
## Installation Dans un souci de réalisme et pour capturer toute l’attention de l’ADEME, nous avons décidé d'ajouter la contrainte du nombre de camions disponibles simultanément pour effectuer les livraisons, en implémentant l'algorithme VRP (Vehicle Routing Problem).
Within a particular ecosystem, there may be a common way of installing things, such as using Yarn, NuGet, or Homebrew. However, consider the possibility that whoever is reading your README is a novice and would like more guidance. Listing specific steps helps remove ambiguity and gets people to using your project as quickly as possible. If it only runs in a specific context like a particular programming language version or operating system or has dependencies that have to be installed manually, also add a Requirements subsection.
## Usage ## Membres
Use examples liberally, and show the expected output if you can. It's helpful to have inline the smallest example of usage that you can demonstrate, while providing links to more sophisticated examples if they are too long to reasonably include in the README.
## Support - Louis DUMONT
Tell people where they can go to for help. It can be any combination of an issue tracker, a chat room, an email address, etc. - Romain HUNTZINGER
- Nathan KISS
## Roadmap - Léandre FERNANDEZ
If you have ideas for releases in the future, it is a good idea to list them in the README.
## Contributing
State if you are open to contributions and what your requirements are for accepting them.
For people who want to make changes to your project, it's helpful to have some documentation on how to get started. Perhaps there is a script that they should run or some environment variables that they need to set. Make these steps explicit. These instructions could also be useful to your future self.
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## Authors and acknowledgment
Show your appreciation to those who have contributed to the project.
## License
For open source projects, say how it is licensed.
## Project status
If you have run out of energy or time for your project, put a note at the top of the README saying that development has slowed down or stopped completely. Someone may choose to fork your project or volunteer to step in as a maintainer or owner, allowing your project to keep going. You can also make an explicit request for maintainers.

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from sklearn.cluster import KMeans
import matplotlib.pyplot as plt
import numpy as np
import random, time
from clustering import split_tour_across_clusters
def generate_cities(nb, max_coords=1000):
return [random.sample(range(max_coords), 2) for _ in range(nb)]
def plot_clusters(cities, clusters):
# Création d'une liste de couleurs pour les différents clusters
colors = ['b', 'g', 'r', 'c', 'm', 'y', 'k']
# Création d'un nouveau graphique
plt.figure()
# Pour chaque cluster
for i, cluster in clusters.items():
# Sélection d'une couleur pour le cluster
color = colors[i % len(colors)]
# Pour chaque ville dans le cluster
for city_index in cluster:
# Récupération des coordonnées de la ville
city = cities[city_index]
# Ajout de la ville au graphique
plt.scatter(city[0], city[1], c=color, s=20)
# show first city in black and twice bigger
plt.scatter(cities[0][0], cities[0][1], c='k', s=200)
# Affichage du graphique
plt.show()
nb_ville = 100
max_coords = 1000
nb_truck = 4
# Define the coordinates of the cities
# And set depot at the first city in the middle of the map
start_time_generate = time.time()
cities = generate_cities(nb_ville, max_coords)
cities[0] = [max_coords/2, max_coords/2]
stop_time_generate = time.time()
# Split the tour across clusters with nb_truck trucks
start_time_split = time.time()
clusters = split_tour_across_clusters(cities, nb_truck)
stop_time_split = time.time()
# show the number of cities in each cluster
for cluster in clusters.values():
print(len(cluster))
# show the time
print("\n---- TIME ----")
print("generate cities time: ", stop_time_generate - start_time_generate)
print("split cities time: ", stop_time_split - start_time_split)
# show the clusters
plot_clusters(cities, clusters)

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from sklearn.cluster import KMeans
import matplotlib.pyplot as plt
import numpy as np
import random, time, math
from clustering import split_tour_across_clusters
random.seed(1)
def generate_cities(nb, max_coords=1000):
return [random.sample(range(max_coords), 2) for _ in range(nb)]
def distance(city1, city2):
return math.sqrt((city1[0] - city2[0]) ** 2 + (city1[1] - city2[1]) ** 2)
def total_distance(cities):
return sum([distance(cities[i - 1], cities[i]) for i in range(len(cities))])
previous_route = None
def draw_cities(cities, previous_route, color='b', title=' '):
plt.title(title)
# If there's a previous route, we remove it.
if previous_route is not None:
previous_route.remove()
x = [city[0] for city in cities]
y = [city[1] for city in cities]
x.append(x[0])
y.append(y[0])
# We plot the route with the specified color and keep a reference to the Line2D object.
previous_route, = plt.plot(x, y, color=color, marker='x', linestyle='-')
plt.draw()
plt.pause(0.005)
# We return the reference so we can remove this route when a new one is found.
return previous_route
def simulated_annealing(cities, color='b', temperature=100000, cooling_rate=0.9999, temperature_ok=0.001):
interration = 0
plt.ion()
current_solution = cities.copy()
best_solution = cities.copy()
previous_route = draw_cities(best_solution, None, color, 'Initial solution')
while temperature > temperature_ok:
new_solution = current_solution.copy()
# Swap two cities in the route
i = random.randint(0, len(new_solution) - 1)
j = random.randint(0, len(new_solution) - 1)
new_solution[i], new_solution[j] = new_solution[j], new_solution[i]
# Calculate the acceptance probability
current_energy = total_distance(current_solution)
new_energy = total_distance(new_solution)
delta = new_energy - current_energy
if delta < 0 or random.random() < math.exp(-delta / temperature):
current_solution = new_solution
if total_distance(current_solution) < total_distance(best_solution):
best_solution = current_solution
previous_route = draw_cities(best_solution, previous_route, color, 'Current best solution, total distance = ' + str(total_distance(best_solution)) + ', iteration = ' + str(interration))
# Cool down
temperature *= cooling_rate
interration += 1
plt.ioff()
return best_solution
nb_ville = 100
max_coords = 1000
nb_truck = 4
temperature = 10000
cooling_rate = 0.999
temperature_ok = 0.000001
start_time_generate = time.time()
cities = generate_cities(nb_ville, max_coords) # generate 100 cities
cities[0] = [max_coords/2, max_coords/2] # placing depot at the center
stop_time_generate = time.time()
start_time_split = time.time()
clusters = split_tour_across_clusters(cities, nb_truck)
stop_time_split = time.time()
for cluster in clusters.values():
print(len(cluster))
print("\n---- TIME ----")
print("generate cities time: ", stop_time_generate - start_time_generate)
print("split cities time: ", stop_time_split - start_time_split)
# create new figure for annealing paths
plt.figure()
colors = ['b', 'g', 'r', 'c', 'm', 'y', 'k']
for i, cluster_indices in enumerate(clusters.values()):
# Sélection d'une couleur pour le cluster
color = colors[i % len(colors)]
# Récupération des coordonnées de la ville
cluster_cities = [cities[index] for index in cluster_indices]
# Appel de la fonction simulated_annealing avec la couleur choisie
best_route = simulated_annealing(cluster_cities, color, temperature, cooling_rate, temperature_ok)
print("Final solution for cluster ", i, ":", best_route)
print("Total distance: ", total_distance(best_route))
plt.show()

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from sklearn.cluster import KMeans
import matplotlib.pyplot as plt
import numpy as np
import random, time, math
from clustering import split_tour_across_clusters
def generate_cities(nb, max_coords=1000):
return [random.sample(range(max_coords), 2) for _ in range(nb)]
def distance(city1, city2):
return math.sqrt((city1[0] - city2[0]) ** 2 + (city1[1] - city2[1]) ** 2)
def total_distance(cities):
return sum([distance(cities[i - 1], cities[i]) for i in range(len(cities))])
previous_route = None
def simulated_annealing(cities, temperature=10000, cooling_rate=0.9999, temperature_ok=0.001, cluster_index=0):
interration = 0
current_solution = cities.copy()
best_solution = cities.copy()
while temperature > temperature_ok:
new_solution = current_solution.copy()
# Swap two cities in the route
i = random.randint(0, len(new_solution) - 1)
j = random.randint(0, len(new_solution) - 1)
new_solution[i], new_solution[j] = new_solution[j], new_solution[i]
# Calculate the acceptance probability
current_energy = total_distance(current_solution)
new_energy = total_distance(new_solution)
delta = new_energy - current_energy
if delta < 0 or random.random() < math.exp(-delta / temperature):
current_solution = new_solution
if total_distance(current_solution) < total_distance(best_solution):
best_solution = current_solution
# Cool down
temperature *= cooling_rate
interration += 1
# Print every 1000 iterations
if interration % 1000 == 0:
print("Cluster", cluster_index, ": iteration", interration, "with current total distance", total_distance(current_solution))
return best_solution
nb_ville = 20
max_coords = 1000
nb_truck = 4
temperature = 10000
cooling_rate = 0.999
temperature_ok = 0.001
start_time_generate = time.time()
cities = generate_cities(nb_ville, max_coords)
cities[0] = [max_coords/2, max_coords/2]
stop_time_generate = time.time()
start_time_split = time.time()
clusters = split_tour_across_clusters(cities, nb_truck)
stop_time_split = time.time()
for cluster in clusters.values():
print(len(cluster))
print("\n---- TIME ----")
print("generate cities time: ", stop_time_generate - start_time_generate)
print("split cities time: ", stop_time_split - start_time_split)
# create new figure for annealing paths
plt.figure()
colors = [
'#1f77b4', # Bleu moyen
'#ff7f0e', # Orange
'#2ca02c', # Vert
'#d62728', # Rouge
'#9467bd', # Violet
'#8c564b', # Marron
'#e377c2', # Rose
'#7f7f7f', # Gris
'#bcbd22', # Vert olive
'#17becf', # Turquoise
'#1b9e77', # Vert Teal
'#d95f02', # Orange foncé
'#7570b3', # Violet moyen
'#e7298a', # Fuchsia
'#66a61e', # Vert pomme
'#e6ab02', # Jaune or
'#a6761d', # Bronze
'#666666', # Gris foncé
'#f781bf', # Rose clair
'#999999', # Gris moyen
]
best_routes = []
for i, cluster_indices in enumerate(clusters.values()):
# Sélection d'une couleur pour le cluster
color = colors[i % len(colors)]
# Récupération des coordonnées de la ville
cluster_cities = [cities[index] for index in cluster_indices]
# Appel de la fonction simulated_annealing
best_route = simulated_annealing(cluster_cities, temperature, cooling_rate, temperature_ok)
best_routes.append((best_route, color))
print("Final solution for cluster ", i, ":", best_route)
print("Total distance: ", total_distance(best_route))
for i, (route, color) in enumerate(best_routes):
x = [city[0] for city in route]
y = [city[1] for city in route]
x.append(x[0])
y.append(y[0])
plt.plot(x, y, color=color, marker='x', linestyle='-', label=f"Cluster {i}")
plt.legend(loc="best")
plt.show()

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from sklearn.cluster import KMeans
import matplotlib.pyplot as plt
import numpy as np
import random, time, math
from clustering import split_tour_across_clusters
random.seed(2)
def generate_cities(nb, max_coords=1000):
return [random.sample(range(max_coords), 2) for _ in range(nb)]
def distance(city1, city2):
return math.sqrt((city1[0] - city2[0]) ** 2 + (city1[1] - city2[1]) ** 2) + 1e-10
def total_distance(cities):
return sum([distance(cities[i - 1], cities[i]) for i in range(len(cities))])
class AntColony:
def __init__(self, cities, n_ants, alpha=1, beta=2, evaporation=0.5, intensification=2, max_time=0.1):
self.cities = cities
self.n = len(cities)
self.n_ants = n_ants
self.alpha = alpha
self.beta = beta
self.evaporation = evaporation
self.intensification = intensification
self.max_time = max_time
self.pheromones = [[1 / self.n for _ in range(self.n)] for __ in range(self.n)]
def choose_next_city(self, ant):
unvisited_cities = [i for i in range(self.n) if i not in ant]
probabilities = [self.pheromones[ant[-1]][i] ** self.alpha * ((1 / distance(self.cities[ant[-1]], self.cities[i])) ** self.beta) for i in unvisited_cities]
total = sum(probabilities)
if total == 0:
probabilities = [1 / len(unvisited_cities) for _ in unvisited_cities]
else:
probabilities = [p / total for p in probabilities]
return np.random.choice(unvisited_cities, p=probabilities)
def update_pheromones(self, ant):
pheromones_delta = self.intensification / total_distance([self.cities[i] for i in ant])
for i in range(len(ant) - 1):
self.pheromones[ant[i]][ant[i+1]] += pheromones_delta
def run(self):
best_ant = []
best_distance = float('inf')
start_time = time.time()
while time.time() - start_time < self.max_time:
ants = [[random.randint(0, self.n - 1)] for _ in range(self.n_ants)]
for ant in ants:
for _ in range(self.n - 1):
ant.append(self.choose_next_city(ant))
ant_distance = total_distance([self.cities[i] for i in ant])
if ant_distance < best_distance:
best_distance = ant_distance
best_ant = ant.copy()
self.update_pheromones(ant)
self.pheromones = [[(1 - self.evaporation) * p for p in row] for row in self.pheromones]
return [self.cities[i] for i in best_ant]
nb_ville = 200
max_coords = 1000
nb_truck = 4
max_time = 5
start_time_generate = time.time()
cities = generate_cities(nb_ville, max_coords)
cities[0] = [max_coords/2, max_coords/2]
stop_time_generate = time.time()
start_time_split = time.time()
clusters = split_tour_across_clusters(cities, nb_truck)
stop_time_split = time.time()
for cluster in clusters.values():
print(len(cluster))
print("\n---- TIME ----")
print("generate cities time: ", stop_time_generate - start_time_generate)
print("split cities time: ", stop_time_split - start_time_split)
# create new figure for annealing paths
plt.figure()
colors = [
'#1f77b4', # Bleu moyen
'#ff7f0e', # Orange
'#2ca02c', # Vert
'#d62728', # Rouge
'#9467bd', # Violet
'#8c564b', # Marron
'#e377c2', # Rose
'#7f7f7f', # Gris
'#bcbd22', # Vert olive
'#17becf', # Turquoise
'#1b9e77', # Vert Teal
'#d95f02', # Orange foncé
'#7570b3', # Violet moyen
'#e7298a', # Fuchsia
'#66a61e', # Vert pomme
'#e6ab02', # Jaune or
'#a6761d', # Bronze
'#666666', # Gris foncé
'#f781bf', # Rose clair
'#999999', # Gris moyen
]
best_routes = []
for i, cluster_indices in enumerate(clusters.values()):
# Sélection d'une couleur pour le cluster
color = colors[i % len(colors)]
# Récupération des coordonnées de la ville
cluster_cities = [cities[index] for index in cluster_indices]
# Appel de la fonction AntColony.run
ant_colony = AntColony(cluster_cities, n_ants=10, max_time=max_time)
best_route = ant_colony.run()
best_routes.append((best_route, color))
print("Final solution for cluster ", i, ":", best_route)
print("Total distance: ", total_distance(best_route))
for i, (route, color) in enumerate(best_routes):
x = [city[0] for city in route]
y = [city[1] for city in route]
x.append(x[0])
y.append(y[0])
plt.plot(x, y, color=color, marker='x', linestyle='-', label=f"Cluster {i}")
# add title with nb_ville, nb_truck and max_time
plt.title(f"nb_ville = {nb_ville}, nb_truck = {nb_truck}, max_time = {max_time}")
plt.show()

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from sklearn.cluster import KMeans
import numpy as np
def split_tour_across_clusters(cities, nb_truck):
if nb_truck == 1:
return {0: list(range(len(cities)))}
# clustering initial
kmeans = KMeans(n_clusters=nb_truck, random_state=0).fit(cities)
clusters = {i:[] for i in range(nb_truck)}
# assignation des indices des villes aux clusters
for i, label in enumerate(kmeans.labels_):
clusters[label].append(i)
max_iterations = len(cities)**2
iteration = 0
while True:
iteration += 1
if iteration > max_iterations:
print("Le nombre maximum d'itérations a été atteint. La boucle a été interrompue.")
break
# calcul des tailles de clusters
cluster_sizes = {i:len(clusters[i]) for i in range(nb_truck)}
# identification du cluster le plus grand et du plus petit
max_cluster = max(cluster_sizes, key=cluster_sizes.get)
min_cluster = min(cluster_sizes, key=cluster_sizes.get)
# s'il n'y a pas de grande disparité, on arrête la boucle
if cluster_sizes[max_cluster] - cluster_sizes[min_cluster] <= 1:
break
# calcul du centre de chaque cluster
cluster_centers = {i:np.mean([cities[index] for index in clusters[i]], axis=0) for i in range(nb_truck)}
# calcul des distances entre le centre du cluster le plus grand et les autres
distances = {i:np.linalg.norm(cluster_centers[max_cluster]-cluster_centers[i]) for i in range(nb_truck)}
del distances[max_cluster] # on supprime la distance vers lui-même
if nb_truck >= 3:
# on identifie les 2 clusters les plus proches
closest_clusters = sorted(distances, key=distances.get)[:2]
# parmi les deux clusters les plus proches, on choisit le plus petit
if cluster_sizes[closest_clusters[0]] <= cluster_sizes[closest_clusters[1]]:
target_cluster = closest_clusters[0]
else:
target_cluster = closest_clusters[1]
else:
closest_clusters = sorted(distances, key=distances.get)[:1]
target_cluster = closest_clusters[0]
# si le transfert va créer une plus grande disparité, on arrête la boucle
if cluster_sizes[target_cluster] >= cluster_sizes[max_cluster]:
break
# calcul des distances entre le centre du cluster cible et les villes du cluster le plus grand
distances_to_target = {index:np.linalg.norm(cluster_centers[target_cluster]-cities[index])
for index in clusters[max_cluster]}
# on identifie la ville la plus proche du centre du cluster cible
closest_city_index = min(distances_to_target, key=distances_to_target.get)
# on transfère la ville du cluster le plus grand au cluster cible
clusters[target_cluster].append(closest_city_index)
clusters[max_cluster].remove(closest_city_index)
# Ajout du point de départ et d'arrivée pour chaque cluster
depot_index = 0
for cluster in clusters.values():
if cluster[0] != depot_index:
cluster.insert(0, depot_index)
if cluster[-1] != depot_index:
cluster.append(depot_index)
return clusters

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tests/data_sample/15_cities_minimum_293.txt Normal file
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[[-0.0, 0.0], [-21.5, -7.3], [-28.9, -0.0], [-43.1, -14.6], [-50.5, -7.4], [-64.7, -21.9], [-72.1, -0.2], [-79.3, 21.4], [-65.1, 36.1], [-57.6, 43.3], [-50.6, 21.6], [-36.0, 21.6], [-29.1, 43.2], [-14.7, 43.4], [-0.1, 28.7], [-0.0, 0.0]]

3
tests/data_sample/48_cities_minimum_33523.txt Normal file
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[[6734.0, 1453.0], [2233.0, 10.0], [5530.0, 1424.0], [401.0, 841.0], [3082.0, 1644.0], [7608.0, 4458.0], [7573.0, 3716.0], [7265.0, 1268.0], [6898.0, 1885.0], [1112.0, 2049.0], [5468.0, 2606.0], [5989.0, 2873.0], [4706.0, 2674.0], [4612.0, 2035.0], [6347.0, 2683.0], [6107.0, 669.0], [7611.0, 5184.0], [7462.0, 3590.0],
[7732.0, 4723.0], [5900.0, 3561.0], [4483.0, 3369.0], [6101.0, 1110.0], [5199.0, 2182.0], [1633.0, 2809.0], [4307.0, 2322.0], [675.0, 1006.0], [7555.0, 4819.0], [7541.0, 3981.0], [3177.0, 756.0], [7352.0, 4506.0], [7545.0, 2801.0], [3245.0, 3305.0], [6426.0, 3173.0], [4608.0, 1198.0], [23.0, 2216.0], [7248.0, 3779.0],
[7762.0, 4595.0], [7392.0, 2244.0], [3484.0, 2829.0], [6271.0, 2135.0], [4985.0, 140.0], [1916.0, 1569.0], [7280.0, 4899.0], [7509.0, 3239.0], [10.0, 2676.0], [6807.0, 2993.0], [5185.0, 3258.0], [3023.0, 1942.0]]