Gaussian Mutation Enhanced Firefly Swarm Optimization Algorithm

The Gaussian Mutation Enhanced Firefly Swarm Optimization Algorithm is an effective approach that integrates the stochastic characteristics of Gaussian distribution to improve the performance of traditional firefly algorithms. The Firefly Swarm Optimization Algorithm is a swarm intelligence optimization technique inspired by the flashing behavior of fireflies in nature, where fireflies move toward each other through attraction to search for optimal solutions. The core innovation of this enhanced algorithm lies in incorporating a Gaussian mutation operator during the position update process of the conventional algorithm. Gaussian mutation generates random numbers following a normal distribution, enabling more flexible exploration of the solution space during the search process. Compared to traditional uniform random mutation, this mutation strategy better balances global exploration and local exploitation capabilities. In code implementation, the Gaussian mutation can be applied using a normal distribution random number generator (e.g., numpy.random.normal() in Python). The position update formula would typically include: new_position = current_position + β * attractiveness + σ * random.gauss(0,1), where σ controls the mutation strength. The enhanced firefly algorithm with Gaussian mutation demonstrates three key advantages: First, it strengthens the algorithm's ability to escape local optima, effectively preventing premature convergence. Second, it accelerates convergence speed, enabling faster approximation to global optimal solutions. Third, it enhances algorithm robustness, improving adaptability to different types of optimization problems. This improved algorithm is particularly suitable for complex nonlinear optimization problems, such as engineering design optimization and parameter tuning. Through appropriate configuration of Gaussian mutation parameters (mean and variance), developers can adjust the algorithm's exploration-exploitation balance for specific problems, achieving superior optimization results. The mutation strength parameter σ can be dynamically adjusted using adaptive strategies like σ = σ_max - (σ_max - σ_min) * (current_iteration/max_iterations).