This paper introduces a new metaheuristic algorithm, the Lévy-flight Firefly Algorithm (LFA), which combines Lévy flights with the search strategy of the Firefly Algorithm (FA). The FA, inspired by the flashing behavior of fireflies, is known for its effectiveness in solving global optimization problems. By incorporating Lévy flights, which are characterized by a power-law step-length distribution, the LFA aims to enhance the exploration capabilities of the FA. The authors outline the basic principles of the FA, including the attractiveness of fireflies being proportional to their brightness, which is determined by the objective function. They then extend this to the LFA, where the attractiveness function is modified to include a decay factor based on the distance between fireflies, following the Lévy flight pattern. The paper includes a detailed implementation of the LFA, including the pseudo-code and parameter choices. The authors validate the LFA using the Ackley function and a non-smooth test function, demonstrating its ability to find global optima efficiently. They also compare the LFA with Particle Swarm Optimization (PSO) and Genetic Algorithms (GA), showing that the LFA outperforms both in terms of efficiency and success rate. The results suggest that the LFA is particularly effective in solving NP-hard problems and has potential for further research, including sensitivity studies on parameters and combining with other algorithms. The paper concludes by highlighting the promising nature of the LFA for global optimization tasks.This paper introduces a new metaheuristic algorithm, the Lévy-flight Firefly Algorithm (LFA), which combines Lévy flights with the search strategy of the Firefly Algorithm (FA). The FA, inspired by the flashing behavior of fireflies, is known for its effectiveness in solving global optimization problems. By incorporating Lévy flights, which are characterized by a power-law step-length distribution, the LFA aims to enhance the exploration capabilities of the FA. The authors outline the basic principles of the FA, including the attractiveness of fireflies being proportional to their brightness, which is determined by the objective function. They then extend this to the LFA, where the attractiveness function is modified to include a decay factor based on the distance between fireflies, following the Lévy flight pattern. The paper includes a detailed implementation of the LFA, including the pseudo-code and parameter choices. The authors validate the LFA using the Ackley function and a non-smooth test function, demonstrating its ability to find global optima efficiently. They also compare the LFA with Particle Swarm Optimization (PSO) and Genetic Algorithms (GA), showing that the LFA outperforms both in terms of efficiency and success rate. The results suggest that the LFA is particularly effective in solving NP-hard problems and has potential for further research, including sensitivity studies on parameters and combining with other algorithms. The paper concludes by highlighting the promising nature of the LFA for global optimization tasks.