The Firefly Algorithm (FA) is a nature-inspired metaheuristic algorithm that has shown great potential in solving complex optimization problems. This paper proposes a new algorithm, the Lévy-flight Firefly Algorithm (LFA), by integrating Lévy flights into the FA. Lévy flights are characterized by their scale-free search patterns, which are observed in the movement of animals and insects. The LFA combines these properties with the search strategy of the FA, leading to improved performance in global optimization. The FA is based on the flashing behavior of fireflies, where fireflies are attracted to brighter ones. The brightness of a firefly is related to the objective function, and the algorithm uses this to guide the search. The LFA enhances this by incorporating Lévy flights, which allow for more efficient exploration of the search space. The algorithm uses a combination of attraction based on brightness and randomization via Lévy flights to navigate the search space. The LFA has been tested on various optimization problems, including the Ackley function and the Yang's forest function. The results show that the LFA outperforms traditional algorithms like Particle Swarm Optimization (PSO) and Genetic Algorithms (GA) in terms of efficiency and success rate. The algorithm is particularly effective in finding global optima, even in non-smooth and complex landscapes. The LFA is flexible and can be adapted to different problem scales by adjusting parameters such as the attractiveness coefficient, randomization parameter, and Lévy flight parameter. The algorithm's performance is influenced by these parameters, and careful tuning is essential for optimal results. In conclusion, the Lévy-flight Firefly Algorithm offers a powerful approach to global optimization, combining the strengths of the FA with the efficiency of Lévy flights. Future research could focus on further improving the algorithm's convergence and exploring its applications in more complex optimization scenarios.The Firefly Algorithm (FA) is a nature-inspired metaheuristic algorithm that has shown great potential in solving complex optimization problems. This paper proposes a new algorithm, the Lévy-flight Firefly Algorithm (LFA), by integrating Lévy flights into the FA. Lévy flights are characterized by their scale-free search patterns, which are observed in the movement of animals and insects. The LFA combines these properties with the search strategy of the FA, leading to improved performance in global optimization. The FA is based on the flashing behavior of fireflies, where fireflies are attracted to brighter ones. The brightness of a firefly is related to the objective function, and the algorithm uses this to guide the search. The LFA enhances this by incorporating Lévy flights, which allow for more efficient exploration of the search space. The algorithm uses a combination of attraction based on brightness and randomization via Lévy flights to navigate the search space. The LFA has been tested on various optimization problems, including the Ackley function and the Yang's forest function. The results show that the LFA outperforms traditional algorithms like Particle Swarm Optimization (PSO) and Genetic Algorithms (GA) in terms of efficiency and success rate. The algorithm is particularly effective in finding global optima, even in non-smooth and complex landscapes. The LFA is flexible and can be adapted to different problem scales by adjusting parameters such as the attractiveness coefficient, randomization parameter, and Lévy flight parameter. The algorithm's performance is influenced by these parameters, and careful tuning is essential for optimal results. In conclusion, the Lévy-flight Firefly Algorithm offers a powerful approach to global optimization, combining the strengths of the FA with the efficiency of Lévy flights. Future research could focus on further improving the algorithm's convergence and exploring its applications in more complex optimization scenarios.