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add graphs/ant_colony_optimization_algorithms.py (#11163)
* add ant_colonyant_colony_optimization_algorithms.py * Modify details * Modify type annotation * Add tests for KeyError, IndexError, StopIteration, etc. * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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graphs/ant_colony_optimization_algorithms.py
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226
graphs/ant_colony_optimization_algorithms.py
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"""
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Use an ant colony optimization algorithm to solve the travelling salesman problem (TSP)
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which asks the following question:
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"Given a list of cities and the distances between each pair of cities, what is the
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shortest possible route that visits each city exactly once and returns to the origin
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city?"
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https://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms
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https://en.wikipedia.org/wiki/Travelling_salesman_problem
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Author: Clark
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"""
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import copy
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import random
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cities = {
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0: [0, 0],
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1: [0, 5],
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2: [3, 8],
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3: [8, 10],
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4: [12, 8],
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5: [12, 4],
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6: [8, 0],
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7: [6, 2],
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}
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def main(
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cities: dict[int, list[int]],
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ants_num: int,
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iterations_num: int,
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pheromone_evaporation: float,
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alpha: float,
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beta: float,
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q: float, # Pheromone system parameters Q，which is a constant
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) -> tuple[list[int], float]:
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"""
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Ant colony algorithm main function
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>>> main(cities=cities, ants_num=10, iterations_num=20,
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... pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
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([0, 1, 2, 3, 4, 5, 6, 7, 0], 37.909778143828696)
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>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=5, iterations_num=5,
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... pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
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([0, 1, 0], 5.656854249492381)
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>>> main(cities={0: [0, 0], 1: [2, 2], 4: [4, 4]}, ants_num=5, iterations_num=5,
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... pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
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Traceback (most recent call last):
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...
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IndexError: list index out of range
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>>> main(cities={}, ants_num=5, iterations_num=5,
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... pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
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Traceback (most recent call last):
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...
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StopIteration
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>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=0, iterations_num=5,
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... pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
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([], inf)
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>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=5, iterations_num=0,
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... pheromone_evaporation=0.7, alpha=1.0, beta=5.0, q=10)
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([], inf)
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>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=5, iterations_num=5,
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... pheromone_evaporation=1, alpha=1.0, beta=5.0, q=10)
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([0, 1, 0], 5.656854249492381)
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>>> main(cities={0: [0, 0], 1: [2, 2]}, ants_num=5, iterations_num=5,
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... pheromone_evaporation=0, alpha=1.0, beta=5.0, q=10)
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([0, 1, 0], 5.656854249492381)
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"""
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# Initialize the pheromone matrix
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cities_num = len(cities)
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pheromone = [[1.0] * cities_num] * cities_num
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best_path: list[int] = []
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best_distance = float("inf")
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for _ in range(iterations_num):
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ants_route = []
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for _ in range(ants_num):
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unvisited_cities = copy.deepcopy(cities)
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current_city = {next(iter(cities.keys())): next(iter(cities.values()))}
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del unvisited_cities[next(iter(current_city.keys()))]
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ant_route = [next(iter(current_city.keys()))]
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while unvisited_cities:
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current_city, unvisited_cities = city_select(
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pheromone, current_city, unvisited_cities, alpha, beta
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)
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ant_route.append(next(iter(current_city.keys())))
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ant_route.append(0)
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ants_route.append(ant_route)
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pheromone, best_path, best_distance = pheromone_update(
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pheromone,
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cities,
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pheromone_evaporation,
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ants_route,
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q,
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best_path,
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best_distance,
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)
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return best_path, best_distance
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def distance(city1: list[int], city2: list[int]) -> float:
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"""
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Calculate the distance between two coordinate points
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>>> distance([0, 0], [3, 4] )
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5.0
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>>> distance([0, 0], [-3, 4] )
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5.0
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>>> distance([0, 0], [-3, -4] )
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5.0
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"""
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return (((city1[0] - city2[0]) ** 2) + ((city1[1] - city2[1]) ** 2)) ** 0.5
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def pheromone_update(
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pheromone: list[list[float]],
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cities: dict[int, list[int]],
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pheromone_evaporation: float,
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ants_route: list[list[int]],
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q: float, # Pheromone system parameters Q，which is a constant
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best_path: list[int],
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best_distance: float,
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) -> tuple[list[list[float]], list[int], float]:
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"""
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Update pheromones on the route and update the best route
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>>>
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>>> pheromone_update(pheromone=[[1.0, 1.0], [1.0, 1.0]],
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... cities={0: [0,0], 1: [2,2]}, pheromone_evaporation=0.7,
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... ants_route=[[0, 1, 0]], q=10, best_path=[],
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... best_distance=float("inf"))
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([[0.7, 4.235533905932737], [4.235533905932737, 0.7]], [0, 1, 0], 5.656854249492381)
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>>> pheromone_update(pheromone=[],
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... cities={0: [0,0], 1: [2,2]}, pheromone_evaporation=0.7,
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... ants_route=[[0, 1, 0]], q=10, best_path=[],
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... best_distance=float("inf"))
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Traceback (most recent call last):
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...
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IndexError: list index out of range
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>>> pheromone_update(pheromone=[[1.0, 1.0], [1.0, 1.0]],
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... cities={}, pheromone_evaporation=0.7,
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... ants_route=[[0, 1, 0]], q=10, best_path=[],
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... best_distance=float("inf"))
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Traceback (most recent call last):
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...
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KeyError: 0
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"""
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for a in range(len(cities)): # Update the volatilization of pheromone on all routes
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for b in range(len(cities)):
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pheromone[a][b] *= pheromone_evaporation
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for ant_route in ants_route:
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total_distance = 0.0
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for i in range(len(ant_route) - 1): # Calculate total distance
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total_distance += distance(cities[ant_route[i]], cities[ant_route[i + 1]])
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delta_pheromone = q / total_distance
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for i in range(len(ant_route) - 1): # Update pheromones
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pheromone[ant_route[i]][ant_route[i + 1]] += delta_pheromone
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pheromone[ant_route[i + 1]][ant_route[i]] = pheromone[ant_route[i]][
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ant_route[i + 1]
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]
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if total_distance < best_distance:
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best_path = ant_route
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best_distance = total_distance
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return pheromone, best_path, best_distance
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def city_select(
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pheromone: list[list[float]],
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current_city: dict[int, list[int]],
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unvisited_cities: dict[int, list[int]],
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alpha: float,
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beta: float,
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) -> tuple[dict[int, list[int]], dict[int, list[int]]]:
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"""
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Choose the next city for ants
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>>> city_select(pheromone=[[1.0, 1.0], [1.0, 1.0]], current_city={0: [0, 0]},
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... unvisited_cities={1: [2, 2]}, alpha=1.0, beta=5.0)
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({1: [2, 2]}, {})
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>>> city_select(pheromone=[], current_city={0: [0,0]},
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... unvisited_cities={1: [2, 2]}, alpha=1.0, beta=5.0)
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Traceback (most recent call last):
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...
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IndexError: list index out of range
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>>> city_select(pheromone=[[1.0, 1.0], [1.0, 1.0]], current_city={},
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... unvisited_cities={1: [2, 2]}, alpha=1.0, beta=5.0)
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Traceback (most recent call last):
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...
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StopIteration
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>>> city_select(pheromone=[[1.0, 1.0], [1.0, 1.0]], current_city={0: [0, 0]},
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... unvisited_cities={}, alpha=1.0, beta=5.0)
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Traceback (most recent call last):
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...
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IndexError: list index out of range
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"""
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probabilities = []
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for city in unvisited_cities:
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city_distance = distance(
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unvisited_cities[city], next(iter(current_city.values()))
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)
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probability = (pheromone[city][next(iter(current_city.keys()))] ** alpha) * (
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(1 / city_distance) ** beta
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)
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probabilities.append(probability)
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chosen_city_i = random.choices(
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list(unvisited_cities.keys()), weights=probabilities
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)[0]
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chosen_city = {chosen_city_i: unvisited_cities[chosen_city_i]}
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del unvisited_cities[next(iter(chosen_city.keys()))]
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return chosen_city, unvisited_cities
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if __name__ == "__main__":
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best_path, best_distance = main(
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cities=cities,
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ants_num=10,
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iterations_num=20,
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pheromone_evaporation=0.7,
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alpha=1.0,
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beta=5.0,
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q=10,
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)
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print(f"{best_path = }")
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print(f"{best_distance = }")
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