Ant Colony Optimization (ACO): A Comprehensive Guide

Ant Colony Optimization (ACO) is inspired by the foraging behavior of ants. Ants find the shortest path between their colony and a food source using pheromone trails. ACO uses this behavior to solve optimization problems.

Ant Colony Optimization

Key Concepts of ACO

1. Initialization: Define the parameters (number of ants, pheromone levels, etc.) and initialize pheromone trails.
2. Solution Construction: Each ant constructs a solution based on the pheromone trails and a probability distribution.
3. Local Pheromone Update: Update pheromone levels locally as ants move.
4. Global Pheromone Update: Once all ants have constructed their solutions, update the pheromones globally to reinforce the best solutions.
5. Termination: Repeat the process until a stopping criterion is met (e.g., maximum iterations or convergence).

Example Code

Here’s a simple implementation of the ACO algorithm in Python:

import numpy as np

def objective_function(x):
    return np.sum(x**2)

class Ant:
    def __init__(self, num_vars, bounds, alpha=1, beta=1):
        self.position = np.random.uniform(bounds[:, 0], bounds[:, 1], num_vars)
        self.alpha = alpha
        self.beta = beta

    def choose_next_position(self, pheromones, bounds):
        num_vars = len(bounds)
        probabilities = np.zeros(num_vars)
        
        for i in range(num_vars):
            eta = 1 / (np.abs(self.position[i]) + 1e-10)  # heuristic value
            probabilities[i] = (pheromones[i] ** self.alpha) * (eta ** self.beta)
        
        probabilities /= np.sum(probabilities)
        
        next_var = np.random.choice(np.arange(num_vars), p=probabilities)
        self.position[next_var] = np.random.uniform(bounds[next_var, 0], bounds[next_var, 1])
        self.position = np.clip(self.position, bounds[:, 0], bounds[:, 1])

def ant_colony_optimization(func, bounds, num_ants=10, max_iter=100, alpha=1, beta=1, evaporation_rate=0.5):
    num_vars = len(bounds)
    bounds = np.array(bounds)
    pheromones = np.ones(num_vars)
    best_position = None
    best_value = float('inf')

    for _ in range(max_iter):
        ants = [Ant(num_vars, bounds, alpha, beta) for _ in range(num_ants)]
        for ant in ants:
            ant.choose_next_position(pheromones, bounds)
            current_value = func(ant.position)
            if current_value < best_value:
                best_value = current_value
                best_position = ant.position.copy()

        pheromones *= (1 - evaporation_rate)
        for ant in ants:
            pheromones += 1 / (1 + func(ant.position))

    return best_position, best_value

# Example usage
bounds = np.array([(-5, 5), (-5, 5)])
best_position, best_value = ant_colony_optimization(objective_function, bounds)
print(f"Best position: {best_position}")
print(f"Best value: {best_value}")

Best position: [-0.21739703 0.24276673]
Best value: 0.10619715329909586

Ant Colony Optimization (ACO):

• Swarm intelligence: Inspired by ant foraging behavior.
• Pheromone trails: Uses pheromone levels to guide the search for optimal solutions.
• Iterative improvement: Constructs solutions iteratively, updating pheromone levels.

Ant Colony Optimization

Artificial Intelligence — Tutorial #11 “Ant Colony Optimization”

For previous subject go here -> https://medium.com/p/f8b5bf8c5072

For next subject go here -> https://medium.com/p/e7ce818c9ef2

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