This paper by Xin-She Yang explores the application of the Firefly Algorithm (FA) in solving nonlinear design optimization problems. The FA is a metaheuristic algorithm inspired by the flashing behavior of fireflies, which is used to find optimal solutions in complex optimization tasks. The author demonstrates the effectiveness of FA in standard pressure vessel design optimization, achieving a better solution than previously reported in the literature. The paper also introduces several new test functions with singularity or stochastic components, designed to validate the performance of optimization algorithms. These functions include a multimodal nonlinear function, a function with singularities, and a stochastic function, all of which are used to test the robustness and efficiency of the FA. In the engineering application section, the FA is applied to a pressure vessel design problem, where it finds an even better solution compared to the best solution previously obtained using particle swarm optimization (PSO). This highlights the potential of the FA in solving challenging engineering optimization tasks. The paper concludes by discussing the advantages of the FA over other algorithms and the need for further research to develop a theoretical framework for analyzing the convergence of metaheuristic algorithms.This paper by Xin-She Yang explores the application of the Firefly Algorithm (FA) in solving nonlinear design optimization problems. The FA is a metaheuristic algorithm inspired by the flashing behavior of fireflies, which is used to find optimal solutions in complex optimization tasks. The author demonstrates the effectiveness of FA in standard pressure vessel design optimization, achieving a better solution than previously reported in the literature. The paper also introduces several new test functions with singularity or stochastic components, designed to validate the performance of optimization algorithms. These functions include a multimodal nonlinear function, a function with singularities, and a stochastic function, all of which are used to test the robustness and efficiency of the FA. In the engineering application section, the FA is applied to a pressure vessel design problem, where it finds an even better solution compared to the best solution previously obtained using particle swarm optimization (PSO). This highlights the potential of the FA in solving challenging engineering optimization tasks. The paper concludes by discussing the advantages of the FA over other algorithms and the need for further research to develop a theoretical framework for analyzing the convergence of metaheuristic algorithms.