diff --git a/graphs/ant_colony_optimization_algorithms.py b/graphs/ant_colony_optimization_algorithms.py new file mode 100644 index 000000000..652ad6144 --- /dev/null +++ b/graphs/ant_colony_optimization_algorithms.py @@ -0,0 +1,226 @@ +""" +Use an ant colony optimization algorithm to solve the travelling salesman problem (TSP) +which asks the following question: +"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 = }")