Genetic algorithm for Traveling Salesman Problem

genetic_algorithm/traveling_salesman_problem.py

@@ -0,0 +1,315 @@
+"""
+GENETIC ALGORITHM USING ORDER CROSSOVER,
+SWAP MUTATION AND BINARY TOURNAMENT SELECTION
+TO SOLVE THE TRAVELLING SALESMAN PROBLEM
+https://en.wikipedia.org/wiki/Genetic_algorithm
+https://en.wikipedia.org/wiki/Travelling_salesman_problem
+Author: joydipb01
+"""
+
+import random
+import sys
+
+import numpy as np
+import tsplib95
+
+# Define necessary parameters - population size, total no. of generations, etc:
+TOTAL_POPULATION = 100
+PROB_MUTATION, PROB_CROSSOVER = 0.1, 0.9  # Mutation Probability, Crossover Probability
+TOTAL_GENERATIONS = 100
+
+
+def readinp(filename: str) -> tsplib95.models.Problem:
+    """
+    Loads the Traveling Salesman Problem (TSP) from the provided file using
+    the tsplib95 package. This file should follow the .tsp format and contain
+    city coordinates and possibly other metadata. This file is passed as a
+    command-line argument.
+    Sample .tsp files can be found here:
+    http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/tsp/
+
+    Args:
+    filename (str): Path to the .tsp file.
+
+    Returns:
+    problem (tsplib95.models.Problem): The TSP problem object containing
+    nodes and distances.
+
+    Example:
+    >>> import tsplib95
+    >>> tsp_data = '''
+    ... NAME: sample
+    ... TYPE: TSP
+    ... DIMENSION: 4
+    ... EDGE_WEIGHT_TYPE: EUC_2D
+    ... NODE_COORD_SECTION
+    ... 1 0 0
+    ... 2 1 0
+    ... 3 0 1
+    ... 4 1 1
+    ... EOF
+    ... '''
+    >>> tsp_filename = "sample.tsp"
+    >>> with open(tsp_filename, "w") as f:
+    ...     f.write(tsp_data)
+    >>> prob = readinp('sample.tsp')
+    >>> len(list(prob.get_nodes())) > 0
+    True
+    >>> isinstance(prob, tsplib95.models.StandardProblem)
+    True
+    """
+    problem = tsplib95.load(filename)
+    return problem
+
+
+def fitness(mem: list[int], dist_mat: np.ndarray) -> float:
+    """
+    Calculates the fitness of a given solution (tour). The fitness is the
+    inverse of the total distance of the tour. A shorter distance results in
+    a higher fitness.
+
+    Args:
+    mem (list): A tour (list of city indices) representing a potential solution.
+    dist_mat (numpy array): Distance matrix with pairwise distances between cities.
+
+    Returns:
+    float: The fitness of the tour, which is 1 / total distance of the tour.
+
+    Example:
+    >>> dist_mat = np.array([[0, 2, 9], [2, 0, 3], [9, 3, 0]])
+    >>> mem = [0, 1, 2]
+    >>> round(fitness(mem, dist_mat), 3)
+    0.091
+    """
+    dist = 0
+    for i in range(len(mem)):
+        j = (i + 1) % len(mem)  # Ensures the last city connects to the first city
+        dist += dist_mat[mem[i], mem[j]]
+    fitness = 1.0 / dist  # Fitness is the inverse of total distance
+    return fitness
+
+
+def binary_tournament_selection(
+    popln: list[list[int]], dist_mat: np.ndarray
+) -> tuple[list[int], list[int]]:
+    """
+    Selects two parents from the population using binary tournament selection.
+    Two individuals are randomly chosen, and the one with higher fitness is
+    selected. This process is repeated until two parents are chosen.
+
+    Args:
+    popln (list): The current population of solutions (tours).
+    dist_mat (numpy array): Distance matrix with pairwise distances between cities.
+
+    Returns:
+    tuple: Two selected parent tours from the population.
+
+    Example:
+    >>> dist_mat = np.array([[0, 2, 9], [2, 0, 3], [9, 3, 0]])
+    >>> popln = [[0, 1, 2], [1, 0, 2], [2, 0, 1]]
+    >>> p1, p2 = binary_tournament_selection(popln, dist_mat)
+    >>> p1 in popln and p2 in popln
+    True
+    """
+    select: list[list[int]] = []
+    while len(select) != 2:
+        i, j = random.sample(range(len(popln)), 2)  # Randomly select two individuals
+        if fitness(popln[i], dist_mat) > fitness(popln[j], dist_mat):
+            select.append(popln[i])  # Select the fitter individual
+        else:
+            select.append(popln[j])
+    return select[0], select[1]
+
+
+def order_crossover(
+    p1: list[int], p2: list[int], crossover_prob: float
+) -> tuple[list[int], list[int]]:
+    """
+    Applies order crossover (OX) between two parent solutions with a certain
+    probability. The OX method ensures that the relative order of the cities
+    is preserved in the offspring. If crossover does not occur, the parents
+    are returned unchanged.
+
+    Args:
+    p1 (list): The first parent solution (tour).
+    p2 (list): The second parent solution (tour).
+    crossover_prob (float): The probability of crossover occurring.
+
+    Returns:
+    tuple: Two offspring tours resulting from the crossover.
+
+    Example:
+    >>> random.seed(42)
+    >>> p1 = [0, 1, 2, 3]
+    >>> p2 = [3, 2, 1, 0]
+    >>> child1, child2 = order_crossover(p1, p2, 1.0)
+    >>> child1
+    [0, 2, 1, 3]
+    >>> child2
+    [3, 1, 2, 0]
+    """
+    if random.random() < crossover_prob:  # Perform crossover with given probability
+        c1: list[int] = [-1] * len(p1)
+        c2: list[int] = [-1] * len(p2)
+        start = random.randint(0, len(p1) - 1)
+        end = random.randint(start + 1, len(p1))
+        c1[start:end] = p1[start:end]  # Copy a segment from parent 1 to child 1
+        c2[start:end] = p2[start:end]  # Copy a segment from parent 2 to child 2
+        for i in range(len(p2)):
+            # Fill the remaining cities in child 1 and child 2
+            if p2[i] not in c1:
+                j = i
+                while c1[j] != -1:
+                    j = p2.index(p1[j])
+                c1[j] = p2[i]
+            if p1[i] not in c2:
+                j = i
+                while c2[j] != -1:
+                    j = p1.index(p2[j])
+                c2[j] = p1[i]
+        return c1, c2
+    return p1, p2  # No crossover, return the parents unchanged
+
+
+def swap_mutation(child: list[int], mutation_prob: float, num_cities: int) -> list[int]:
+    """
+    Applies swap mutation to a child solution with a given probability.
+    Two random cities in the tour are swapped to introduce variability.
+
+    Args:
+    child (list): The child solution (tour) to be mutated.
+    mutation_prob (float): The probability of mutation occurring.
+    num_cities (int): The number of cities in the problem.
+
+    Returns:
+    list: The mutated child solution.
+
+    Example:
+    >>> random.seed(42)
+    >>> child = [0, 1, 2, 3]
+    >>> swap_mutation(child, 1.0, 4)
+    [0, 3, 2, 1]
+    """
+    if random.random() < mutation_prob:  # Perform mutation with given probability
+        i, j = random.sample(range(num_cities), 2)  # Randomly select two cities to swap
+        child[i], child[j] = child[j], child[i]  # Swap the cities
+    return child
+
+
+def two_opt_local_search(child: list[int], dist_mat: np.ndarray) -> list[int]:
+    """
+    Applies the 2-opt local search algorithm to improve a solution (tour).
+    It repeatedly checks for pairs of edges in the tour and swaps them if
+    it reduces the total distance of the tour, stopping when no further
+    improvements are found.
+
+    Args:
+    child (list): The solution (tour) to be optimized.
+    dist_mat (numpy array): Distance matrix with pairwise distances between cities.
+
+    Returns:
+    list: The optimized solution after applying 2-opt.
+
+    Example:
+    >>> dist_mat = np.array([[0, 2, 9], [2, 0, 3], [9, 3, 0]])
+    >>> child = [0, 1, 2]
+    >>> two_opt_local_search(child, dist_mat)
+    [0, 1, 2]
+    """
+    while True:
+        improvement = 0
+        best_dist = fitness(child, dist_mat)
+        for i in range(1, len(child) - 1):
+            for j in range(i + 1, len(child)):
+                # Generate a new solution by reversing the order of cities
+                # between i and j
+                new_child = (
+                    child[:i] + list(reversed(child[i : j + 1])) + child[j + 1 :]
+                )
+                new_dist = fitness(new_child, dist_mat)
+                if new_dist > best_dist:  # If the new solution is better, adopt it
+                    child = new_child
+                    improvement = 1
+        if improvement == 0:  # Stop when no further improvements are found
+            break
+    return child
+
+
+# Run the genetic algorithm:
+if __name__ == "__main__":
+    if len(sys.argv) != 2:
+        sys.exit("Usage: traveling_salesman_problem.py <name/path of .tsp file>")
+
+    no_improvement = 0
+
+    prob = readinp(sys.argv[1])
+    n_cities = len(list(prob.get_nodes()))
+
+    # Compute distance matrix:- distance between any two cities
+    dist_mat = np.zeros((n_cities, n_cities))
+    for i in range(n_cities):
+        for j in range(i + 1, n_cities):
+            node1 = prob.node_coords[i + 1]
+            node2 = prob.node_coords[j + 1]
+            dist_mat[i, j] = dist_mat[j, i] = np.linalg.norm(
+                np.array(node1) - np.array(node2)
+            )
+
+    # Generate initial population (first city is taken to be depot by default):
+    popln: list = []
+    while len(popln) < TOTAL_POPULATION:
+        sol_dist = 0.0
+        individual = list(range(n_cities))
+        subindiv = individual[1:]
+        random.shuffle(subindiv)
+        individual[1:] = subindiv
+        popln.append(individual)
+
+    for iteration in range(TOTAL_GENERATIONS):
+        # Binary Tournament Selection:
+        parent1, parent2 = binary_tournament_selection(popln, dist_mat)
+
+        # Order Crossover:
+        child1, child2 = order_crossover(parent1, parent2, PROB_CROSSOVER)
+
+        # Swap Mutation for child-1:
+        child1 = swap_mutation(child1, PROB_MUTATION, n_cities)
+
+        # Swap Mutation for child-2:
+        child1 = swap_mutation(child2, PROB_MUTATION, n_cities)
+
+        # 2-opt for child-1:
+        child1 = two_opt_local_search(child1, dist_mat)
+
+        # 2-opt for child-2:
+        child2 = two_opt_local_search(child2, dist_mat)
+
+        child1_fitness = fitness(child1, dist_mat)
+        child2_fitness = fitness(child2, dist_mat)
+
+        # Individual of worst fitness replaced by fittest of the children:
+        worst_fit = np.argmin([fitness(individual, dist_mat) for individual in popln])
+        if child1_fitness > child2_fitness:
+            popln[worst_fit] = child1
+        else:
+            popln[worst_fit] = child2
+
+        # Sort population based on fitnesses (first member will be the solution):
+        popln.sort(key=lambda member: fitness(member, dist_mat), reverse=True)
+
+        # Checking for improvements in solution:
+        if sol_dist == fitness(popln[0], dist_mat):
+            no_improvement += 1
+        else:
+            sol = popln[0]
+            sol_dist = fitness(sol, dist_mat)
+            print("New fitness at Generation", iteration + 1, "is:", 1 / sol_dist)
+        if (
+            no_improvement == 15
+        ):  # Break if there is no improvement after 15 generations
+            break
+
+    print()
+    fsol = [x + 1 for x in sol]
+    print("Final Solution:", fsol)
+    print("Final Fitness:", 1 / sol_dist)

requirements.txt

@@ -19,6 +19,7 @@ sphinx_pyproject
 statsmodels
 sympy
 tensorflow ; python_version < '3.13'
+tsplib95
 tweepy
 # yulewalker  # uncomment once audio_filters/equal_loudness_filter.py is fixed
 typing_extensions