Implementing ant colony algorithm to solve TSP problem based on Matlab (source code + data attached)

Ant Colony Optimization (ACO) is a heuristic optimization algorithm based on the behavior of ant groups. It simulates the behavior of ants when looking for food. In the Traveling Salesman Problem (TSP), the ant colony algorithm can be used to solve the shortest path problem.

introduce

The TSP problem means that a traveling salesman wants to travel between multiple cities. There is a certain distance between each city. The traveling salesman needs to find a shortest path that allows him to pass through each city once and finally return to the departure city. This problem is a classic combinatorial optimization problem, and its solution space grows exponentially, so traditional exhaustive search methods are often difficult to implement in practical applications.

Ant colony algorithm simulates the behavior of ants when searching for food and uses the mechanism of pheromone deposition and volatilization among ants to find the optimal path. The basic idea of ​​​​the algorithm is that ants will leave behind a substance called pheromone during the search process. The higher the concentration of pheromone, the better the path selection. When ants choose a path, they will tend to choose a path with a higher pheromone concentration, so that the entire group gradually converges to the optimal solution.

Implementation steps

In Matlab, the ant colony algorithm can be implemented to solve the TSP problem through the following steps:

1. Initialization parameters: including city coordinates, number of ants, initial pheromone concentration, pheromone volatilization coefficient, pheromone update rate, etc.

2. Calculate the distance between cities: Calculate the distance matrix between cities based on city coordinates.

3. Initialize the pheromone matrix: Set the initial pheromone concentration on all paths to a small constant.

4. Iterative search: Repeat the following steps until the stopping condition is reached:
   a. Each ant selects the next city based on pheromone concentration and distance.
   b. Update the path and total path length of each ant.
   c. Update the pheromone concentration on the path passed by each ant.
   d. Update the global optimal path and total path length.

5. Output results: Output the global optimal path and total path length.

Simple case

The following is a simple Matlab code example that implements the ant colony algorithm to solve the TSP problem:

function [best_path, best_length] = ant_colony_tsp(cities, num_ants, num_iterations, alpha, beta, rho, q)
    num_cities = size(cities, 1);
    distances = pdist2(cities, cities);
    pheromones = ones(num_cities, num_cities) * 0.01;
    best_path = [];
    best_length = Inf;
    
    for iteration = 1:num_iterations
        paths = zeros(num_ants, num_cities);
        lengths = zeros(num_ants, 1);
        
        for ant = 1:num_ants
            visited = zeros(1, num_cities);
            current_city = randi(num_cities);
            visited(current_city) = 1;
            paths(ant, 1) = current_city;
            
            for step = 2:num_cities
                probabilities = (pheromones(current_city, :) .^ alpha) .* ((1 ./ distances(current_city, :)) .^ beta);
                probabilities(visited) = 0;
                probabilities = probabilities / sum(probabilities);
                
                next_city = randsample(num_cities, 1, true, probabilities);
                visited(next_city) = 1;
                paths(ant, step) = next_city;
                lengths(ant) = lengths(ant) + distances(current_city, next_city);
                current_city = next_city;
            end
            
            lengths(ant) = lengths(ant) + distances(current_city, paths(ant, 1));
            
            if lengths(ant) < best_length
                best_length = lengths(ant);
                best_path = paths(ant, :);
            end
        end
        
        delta_pheromones = zeros(num_cities, num_cities);
        
        for ant = 1:num_ants
            for step = 1:num_cities
                current_city = paths(ant, step);
                next_city = paths(ant, mod(step, num_cities) + 1);
                delta_pheromones(current_city, next_city) = delta_pheromones(current_city, next_city) + q / lengths(ant);
            end
        end
        
        pheromones = (1 - rho) * pheromones + delta_pheromones;
    end
end

When using this function, you need to input the city coordinate matrix, the number of ants, the number of iterations, pheromone parameters alpha and beta, pheromone volatilization coefficient rho, and pheromone update rate q. The function returns the optimal path and total path length.

cities = [0, 0; 1, 1; 2, 2; 3, 3; 4, 4];  % 城市坐标矩阵
num_ants = 10;  % 蚂蚁数量
num_iterations = 100;  % 迭代次数
alpha = 1;  % 信息素参数
beta = 2;  % 信息素参数
rho = 0.5;  % 信息素挥发系数
q = 1;  % 信息素更新速率

[best_path, best_length] = ant_colony_tsp(cities, num_ants, num_iterations, alpha, beta, rho, q);
disp('Best path:');
disp(best_path);
disp('Best length:');
disp(best_length);

The city coordinate matrix in this code is a 5x2 matrix, representing the coordinates of 5 cities. The function will return the optimal path and total path length.

Through the above steps, we can use Matlab to implement the ant colony algorithm to solve the TSP problem. The ant colony algorithm is an efficient heuristic optimization algorithm that has good results in solving combinatorial optimization problems such as TSP problems.

Source code + data download

Implementing ant colony algorithm to solve TSP problem based on Matlab (source code + data): https://download.csdn.net/download/m0_62143653/88366393