#### Ant Colony Optimization Algorithms

I
```"""
Use an ant colony optimization algorithm to solve the travelling salesman problem (TSP)
"Given a list of cities and the distances between each pair of cities, what is the
shortest possible route that visits each city exactly once and returns to the origin
city?"

https://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms
https://en.wikipedia.org/wiki/Travelling_salesman_problem

Author: Clark
"""

import copy
import random

cities = {
0: [0, 0],
1: [0, 5],
2: [3, 8],
3: [8, 10],
4: [12, 8],
5: [12, 4],
6: [8, 0],
7: [6, 2],
}

def main(
cities: dict[int, list[int]],
ants_num: int,
iterations_num: int,
pheromone_evaporation: float,
alpha: float,
beta: float,
q: float,  # Pheromone system parameters Q, which is a constant
) -> tuple[list[int], float]:
"""
Ant colony algorithm main function
>>> main(cities=cities, ants_num=10, iterations_num=20,
...      pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
([0, 1, 2, 3, 4, 5, 6, 7, 0], 37.909778143828696)
>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=5, iterations_num=5,
...      pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
([0, 1, 0], 5.656854249492381)
>>> main(cities={0: [0, 0], 1: [2, 2], 4: [4, 4]}, ants_num=5, iterations_num=5,
...      pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
Traceback (most recent call last):
...
IndexError: list index out of range
>>> main(cities={}, ants_num=5, iterations_num=5,
...      pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
Traceback (most recent call last):
...
StopIteration
>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=0, iterations_num=5,
...      pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
([], inf)
>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=5, iterations_num=0,
...      pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
([], inf)
>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=5, iterations_num=5,
...      pheromone_evaporation=1, alpha=1.0, beta=5.0, q=10)
([0, 1, 0], 5.656854249492381)
>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=5, iterations_num=5,
...      pheromone_evaporation=0, alpha=1.0, beta=5.0, q=10)
([0, 1, 0], 5.656854249492381)
"""
# Initialize the pheromone matrix
cities_num = len(cities)
pheromone = [[1.0] * cities_num] * cities_num

best_path: list[int] = []
best_distance = float("inf")
for _ in range(iterations_num):
ants_route = []
for _ in range(ants_num):
unvisited_cities = copy.deepcopy(cities)
current_city = {next(iter(cities.keys())): next(iter(cities.values()))}
del unvisited_cities[next(iter(current_city.keys()))]
ant_route = [next(iter(current_city.keys()))]
while unvisited_cities:
current_city, unvisited_cities = city_select(
pheromone, current_city, unvisited_cities, alpha, beta
)
ant_route.append(next(iter(current_city.keys())))
ant_route.append(0)
ants_route.append(ant_route)

pheromone, best_path, best_distance = pheromone_update(
pheromone,
cities,
pheromone_evaporation,
ants_route,
q,
best_path,
best_distance,
)
return best_path, best_distance

def distance(city1: list[int], city2: list[int]) -> float:
"""
Calculate the distance between two coordinate points
>>> distance([0, 0], [3, 4] )
5.0
>>> distance([0, 0], [-3, 4] )
5.0
>>> distance([0, 0], [-3, -4] )
5.0
"""
return (((city1[0] - city2[0]) ** 2) + ((city1[1] - city2[1]) ** 2)) ** 0.5

def pheromone_update(
pheromone: list[list[float]],
cities: dict[int, list[int]],
pheromone_evaporation: float,
ants_route: list[list[int]],
q: float,  # Pheromone system parameters Q, which is a constant
best_path: list[int],
best_distance: float,
) -> tuple[list[list[float]], list[int], float]:
"""
Update pheromones on the route and update the best route
>>>
>>> pheromone_update(pheromone=[[1.0, 1.0], [1.0, 1.0]],
...                  cities={0: [0,0], 1: [2,2]}, pheromone_evaporation=0.7,
...                  ants_route=[[0, 1, 0]], q=10, best_path=[],
...                  best_distance=float("inf"))
([[0.7, 4.235533905932737], [4.235533905932737, 0.7]], [0, 1, 0], 5.656854249492381)
>>> pheromone_update(pheromone=[],
...                  cities={0: [0,0], 1: [2,2]}, pheromone_evaporation=0.7,
...                  ants_route=[[0, 1, 0]], q=10, best_path=[],
...                  best_distance=float("inf"))
Traceback (most recent call last):
...
IndexError: list index out of range
>>> pheromone_update(pheromone=[[1.0, 1.0], [1.0, 1.0]],
...                  cities={}, pheromone_evaporation=0.7,
...                  ants_route=[[0, 1, 0]], q=10, best_path=[],
...                  best_distance=float("inf"))
Traceback (most recent call last):
...
KeyError: 0
"""
for a in range(len(cities)):  # Update the volatilization of pheromone on all routes
for b in range(len(cities)):
pheromone[a][b] *= pheromone_evaporation
for ant_route in ants_route:
total_distance = 0.0
for i in range(len(ant_route) - 1):  # Calculate total distance
total_distance += distance(cities[ant_route[i]], cities[ant_route[i + 1]])
delta_pheromone = q / total_distance
for i in range(len(ant_route) - 1):  # Update pheromones
pheromone[ant_route[i]][ant_route[i + 1]] += delta_pheromone
pheromone[ant_route[i + 1]][ant_route[i]] = pheromone[ant_route[i]][
ant_route[i + 1]
]

if total_distance < best_distance:
best_path = ant_route
best_distance = total_distance

return pheromone, best_path, best_distance

def city_select(
pheromone: list[list[float]],
current_city: dict[int, list[int]],
unvisited_cities: dict[int, list[int]],
alpha: float,
beta: float,
) -> tuple[dict[int, list[int]], dict[int, list[int]]]:
"""
Choose the next city for ants
>>> city_select(pheromone=[[1.0, 1.0], [1.0, 1.0]], current_city={0: [0, 0]},
...             unvisited_cities={1: [2, 2]}, alpha=1.0, beta=5.0)
({1: [2, 2]}, {})
>>> city_select(pheromone=[], current_city={0: [0,0]},
...             unvisited_cities={1: [2, 2]}, alpha=1.0, beta=5.0)
Traceback (most recent call last):
...
IndexError: list index out of range
>>> city_select(pheromone=[[1.0, 1.0], [1.0, 1.0]], current_city={},
...             unvisited_cities={1: [2, 2]}, alpha=1.0, beta=5.0)
Traceback (most recent call last):
...
StopIteration
>>> city_select(pheromone=[[1.0, 1.0], [1.0, 1.0]], current_city={0: [0, 0]},
...             unvisited_cities={}, alpha=1.0, beta=5.0)
Traceback (most recent call last):
...
IndexError: list index out of range
"""
probabilities = []
for city in unvisited_cities:
city_distance = distance(
unvisited_cities[city], next(iter(current_city.values()))
)
probability = (pheromone[city][next(iter(current_city.keys()))] ** alpha) * (
(1 / city_distance) ** beta
)
probabilities.append(probability)

chosen_city_i = random.choices(
list(unvisited_cities.keys()), weights=probabilities
)[0]
chosen_city = {chosen_city_i: unvisited_cities[chosen_city_i]}
del unvisited_cities[next(iter(chosen_city.keys()))]
return chosen_city, unvisited_cities

if __name__ == "__main__":
best_path, best_distance = main(
cities=cities,
ants_num=10,
iterations_num=20,
pheromone_evaporation=0.7,
alpha=1.0,
beta=5.0,
q=10,
)

print(f"{best_path = }")
print(f"{best_distance = }")
```