Gaussian Mutation-based Firefly Algorithm for Enhanced Optimization

The Gaussian Mutation-based Firefly Algorithm (GMFA) is an enhanced intelligent optimization technique that integrates the classical Firefly Algorithm (FA) with Gaussian mutation strategies to improve global search performance and convergence rates. Core Algorithm Mechanism Firefly Attraction Mechanism: Fireflies attract each other based on brightness, where individuals with lower brightness move toward those with higher brightness, simulating natural firefly mating behavior. Brightness typically correlates with objective function values - better values (e.g., smaller in minimization problems) indicate higher brightness. In code implementation, this involves calculating Euclidean distances between fireflies and updating positions using attraction formulas with exponential decay factors. Gaussian Mutation Operation: During iterations, Gaussian random perturbations are introduced to firefly positions. The Gaussian mutation's mean and variance are adjustable parameters, where smaller random disturbances help escape local optima and enhance exploration capabilities. Implementation typically uses numpy.random.normal() or equivalent functions to generate Gaussian-distributed random steps. Adaptive Parameter Adjustment: As iterations progress, attraction coefficients and mutation intensities gradually decrease, allowing the algorithm to focus more on local refinement during later stages. This can be programmed using linear or exponential decay functions for parameter modulation. Role of Benchmark Functions Benchmark functions (such as Sphere, Rosenbrock, etc.) validate algorithm performance across various scenarios including unimodal, multimodal, and high-dimensional landscapes. By comparing convergence speed and solution accuracy, the effectiveness of Gaussian mutation strategies can be quantitatively evaluated through metrics like convergence curves and statistical tests. Advantages and Application Scenarios Well-suited for continuous optimization problems including engineering parameter tuning and machine learning hyperparameter search. Gaussian mutation balances exploration (global search) and exploitation (local optimization), preventing premature convergence. Simple to implement but requires careful parameter setting (e.g., mutation variance) to avoid excessive randomization. Extension Considerations Further enhancements can incorporate strategies like Lévy Flight for improved long-distance jumping capability, or hybrid approaches combining gradient information for accelerated convergence. Code implementation might involve integrating Lévy flight distributions or gradient descent steps within the position update loop.