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🔥 Firefly Algorithm (FA) – Overview

Inspired by: Bioluminescent communication of fireflies.Inventor: Xin-She Yang (2008).


Core Idea:

  • Each firefly is attracted to brighter fireflies.

  • Brightness is associated with the objective function (fitness).

  • Movement is influenced by attractiveness and a randomness factor.


✨ Key Mechanisms

  1. Attractiveness (β): Decreases with distance.

  2. Movement: Less bright fireflies move toward brighter ones.

  3. Randomness (α): Adds stochasticity to avoid local optima.

  4. Distance Measure: Typically Euclidean.


🔧 Parameters

  • α: Randomness strength.

  • β0: Base attractiveness.

  • γ: Light absorption coefficient (controls how light fades with distance).

  • n: Number of fireflies.


📌 MATLAB Code: Firefly Algorithm (Minimization Example)

We solve a benchmark sphere function:

f(x)=∑xi^2

% Firefly Algorithm for Sphere Function
clc; clear; close all;

% Problem settings
d = 5;                 % Dimension
n = 20;                % Fireflies
MaxGen = 100;          % Max generations
Lb = -10 * ones(1,d);  % Lower bounds
Ub = 10 * ones(1,d);   % Upper bounds

% Firefly Algorithm parameters
alpha = 0.2;     % Randomness 0--1
beta0 = 1;       % Initial attractiveness
gamma = 1;       % Light absorption coefficient

% Initialize population
x = rand(n,d).*(Ub - Lb) + Lb; % Firefly positions
f = sum(x.^2, 2);              % Objective (sphere)

% Record best
[bestF, idx] = min(f);
bestX = x(idx,:);

% Main loop
for gen = 1:MaxGen
    for i = 1:n
        for j = 1:n
            if f(j) < f(i)
                r = norm(x(i,:) - x(j,:));
                beta = beta0 * exp(-gamma * r^2);
                x(i,:) = x(i,:) + beta*(x(j,:) - x(i,:)) + ...
                         alpha*(rand(1,d)-0.5).*(Ub - Lb);
                % Keep within bounds
                x(i,:) = max(min(x(i,:), Ub), Lb);
                f(i) = sum(x(i,:).^2);
            end
        end
    end

    % Update best
    [currentBestF, idx] = min(f);
    if currentBestF < bestF
        bestF = currentBestF;
        bestX = x(idx,:);
    end
    % Optional: plot convergence
    disp(["Generation", gen, "Best f(x)", bestF])
end

fprintf('\nBest Solution: f(x) = %.6f\n', bestF);

🪐 Comparison: Firefly Algorithm (FA) vs Particle Swarm Optimization (PSO)

Feature

Firefly Algorithm (FA)

Particle Swarm Optimization (PSO)

Inspired by

Flashing behavior of fireflies

Social behavior of bird flocks or fish schools

Interaction Style

One-way (less bright → more bright)

Two-way social sharing (individual & global best)

Brightness concept

Directly linked to objective value

Not explicitly used; instead, personal & global bests

Movement Equation

Attraction-based + random

Velocity-based + inertia + cognitive + social terms

Convergence Speed

Slower but more explorative

Faster in convergence but may get trapped in local optima

Randomness

Explicit (controlled by α)

Implicit (via stochastic velocity updates)

Exploration/Exploitation

Good balance with tunable α, β, γ

Controlled by inertia weight

Population Diversity

High due to selective attraction

Moderate – swarm may collapse around global best

Best Use Cases

Complex, multimodal, high-dimensional problems

Well-understood convex or mildly nonconvex functions

🎯 When to Use Which?

Situation

Recommended

Want more exploration, especially early?

Firefly Algorithm

Require fast convergence on convex/low-dimensional problem?

PSO

Seeking swarm-based global search?

Both are fine, PSO simpler

Highly multimodal objective landscape?

FA preferred due to richer dynamics


💡 Suggestions for Structural Engineering Applications


  • PMM optimization

  • Pile cap design

  • CFRP layout

  • Structural member grouping


Both FA and PSO are viable. But:

  • PSO suits continuous design variable optimization (like reinforcement ratios, dimension tweaks).


  • FA can help in layout problems (pile placement, CFRP anchoring), where distance-based interaction metaphor fits better.


 
 
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