Firefly Algorithm MATLAB Implementation

This document presents a standard MATLAB implementation of the Firefly Algorithm, a nature-inspired optimization technique模仿生物发光昆虫的集体行为. The algorithm模拟萤火虫通过亮度相互吸引的机制进行全局优化, with applications spanning engineering design, machine learning, and computational mathematics. The implementation workflow follows these computational steps: First, initialize firefly positions and luminosity values within the search space. Then, determine movement directions by calculating attractiveness based on relative brightness and Euclidean distance. Subsequently, update positions through attraction forces with randomized exploration components. Iterate until convergence criteria are met. Below is the annotated MATLAB code:

% Algorithm initialization parameters n = 50; % Population size (number of fireflies) m = 5; % Problem dimensionality Lb = -10 * ones(1, m); % Lower bounds of search space Ub = 10 * ones(1, m); % Upper bounds of search space gamma = 1; % Light absorption coefficient alpha = 0.2; % Randomization parameter for exploration beta0 = 1; % Base attractiveness at zero distance tmax = 100; % Maximum generations epsilon = 1e-6; % Convergence tolerance % Initialize firefly population with uniform distribution x = rand(n, m) .* (Ub - Lb) + Lb; I = zeros(n, 1); % Luminosity/intensity values % Evaluate initial fitness using benchmark function for i = 1:n I(i) = benchmark_func(x(i,:)); % User-defined objective function end % Main optimization loop t = 1; while t <= tmax % Dual-loop attraction mechanism: brighter fireflies attract dimmer ones for i = 1:n for j = 1:n if I(j) > I(i) % Brighter firefly found r = norm(x(i,:) - x(j,:)); % Euclidean distance beta = beta0 * exp(-gamma * r^2); % Distance-dependent attractiveness % Position update with attraction and randomization x(i,:) = x(i,:) + beta * (x(j,:) - x(i,:)) + alpha * (rand(1,m)-0.5); end end end % Re-evaluate fitness after movement for i = 1:n I(i) = benchmark_func(x(i,:)); end % Convergence check: stop if population diversity drops below threshold if max(I) - min(I) < epsilon break end t = t + 1; end % Extract optimal solution [~, idx] = max(I); xopt = x(idx,:); % Optimal position fopt = I(idx); % Optimal fitness value disp(['xopt = ' num2str(xopt)]); disp(['fopt = ' num2str(fopt)]);

This implementation demonstrates core swarm intelligence principles with distance-based attractiveness calculations and stochastic exploration. The code structure allows easy adaptation to various optimization problems by modifying the benchmark_func objective function and parameter settings.