The Firefly Algorithm (FA) is a nature-inspired metaheuristic optimization algorithm based on the flashing behavior of fireflies. This paper presents the application of FA to solve nonlinear design optimization problems, particularly the standard pressure vessel design problem. The results show that FA outperforms previous methods in finding optimal solutions. Additionally, the paper introduces new stochastic test functions with known global optima to validate optimization algorithms. These functions include singularities and randomness, making them suitable for testing the robustness of algorithms. The FA is shown to be effective in solving both deterministic and stochastic optimization problems. The algorithm's performance is demonstrated on various test functions, including a multimodal function with a unique global minimum and a stochastic function with random minima. The FA is also applied to the pressure vessel design problem, where it finds a better solution than existing methods. The paper concludes that FA is a promising optimization algorithm with potential for further research and application in engineering optimization.The Firefly Algorithm (FA) is a nature-inspired metaheuristic optimization algorithm based on the flashing behavior of fireflies. This paper presents the application of FA to solve nonlinear design optimization problems, particularly the standard pressure vessel design problem. The results show that FA outperforms previous methods in finding optimal solutions. Additionally, the paper introduces new stochastic test functions with known global optima to validate optimization algorithms. These functions include singularities and randomness, making them suitable for testing the robustness of algorithms. The FA is shown to be effective in solving both deterministic and stochastic optimization problems. The algorithm's performance is demonstrated on various test functions, including a multimodal function with a unique global minimum and a stochastic function with random minima. The FA is also applied to the pressure vessel design problem, where it finds a better solution than existing methods. The paper concludes that FA is a promising optimization algorithm with potential for further research and application in engineering optimization.