The Firefly Algorithm (FA) is a nature-inspired optimization algorithm designed for multimodal optimization. It is compared with other metaheuristics like Particle Swarm Optimization (PSO). The FA is based on the behavior of fireflies, where fireflies are attracted to brighter ones, and their brightness is related to the objective function. The algorithm uses a combination of attraction and randomization to explore the search space efficiently. The attractiveness of fireflies decreases with distance, and the algorithm incorporates a light absorption coefficient to model this. The FA is more effective than PSO in handling multimodal functions due to its natural and efficient handling of multiple optima. The algorithm is implemented with parameters such as brightness, attractiveness, and randomization. The FA is tested on various functions, including the Michalewicz function and Yang's function, showing superior performance in finding global optima. The algorithm is efficient, with a high success rate and quick convergence. It is also suitable for parallel implementation and can be extended to multiobjective optimization. The FA outperforms traditional algorithms like genetic algorithms and PSO in terms of efficiency and success rate. Future research could focus on improving the algorithm's convergence and exploring its applications in combination with other algorithms.The Firefly Algorithm (FA) is a nature-inspired optimization algorithm designed for multimodal optimization. It is compared with other metaheuristics like Particle Swarm Optimization (PSO). The FA is based on the behavior of fireflies, where fireflies are attracted to brighter ones, and their brightness is related to the objective function. The algorithm uses a combination of attraction and randomization to explore the search space efficiently. The attractiveness of fireflies decreases with distance, and the algorithm incorporates a light absorption coefficient to model this. The FA is more effective than PSO in handling multimodal functions due to its natural and efficient handling of multiple optima. The algorithm is implemented with parameters such as brightness, attractiveness, and randomization. The FA is tested on various functions, including the Michalewicz function and Yang's function, showing superior performance in finding global optima. The algorithm is efficient, with a high success rate and quick convergence. It is also suitable for parallel implementation and can be extended to multiobjective optimization. The FA outperforms traditional algorithms like genetic algorithms and PSO in terms of efficiency and success rate. Future research could focus on improving the algorithm's convergence and exploring its applications in combination with other algorithms.