FA Firefly Algorithm

The Firefly Algorithm (FA) is a nature-inspired metaheuristic optimization algorithm that simulates the flashing behavior and attraction patterns of fireflies. This algorithm has demonstrated effectiveness across diverse optimization problems in fields such as finance, engineering, and computer science. In FA implementation, each firefly represents a candidate solution, where its brightness corresponds to the fitness value of the solution. The algorithm operates through three key mechanisms: 1. Brightness comparison: Fireflies compare luminosity using fitness functions 2. Attraction movement: Less bright fireflies move toward brighter ones using attraction formulas 3. Randomization: Incorporates stochastic components for exploration The core mathematical formulation involves: - Light intensity decay: I(r) = I₀/(1+γr²) where I₀ is original intensity, γ is light absorption coefficient - Attraction probability: β(r) = β₀e^(-γr²) with β₀ being maximum attraction - Position update: xᵢ = xᵢ + β(r)(xⱼ - xᵢ) + αε where α is randomization parameter FA shares similarities with other swarm intelligence algorithms like Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Artificial Bee Colony (ABC), but distinguishes itself through its simplicity, efficient convergence properties, and natural attraction-based search mechanism. The algorithm typically requires implementation of distance calculations, brightness updates, and position movement functions in code, making it particularly suitable for multimodal optimization problems where global and local search balance is crucial.