Firefly algorithm (FA) is a powerful and efficient meta-heuristic algorithm which has shown effective performance in the recent literature when applied to solving engineering optimization problems. FA imitates the flashing behavior of fireflies. FA generates solutions randomly and assumes them as fireflies. However, these algorithms may suffer from premature convergence and poor global exploration when used to optimize complex and high dimension engineering problems. Therefore, this study has proposed a novel FA, called firefly algorithm 1 to 3 (FA1→3), via different types of movements of fireflies in an attempt to improve the global exploration and convergence characteristics of FA. A comprehensive study has been carried out on the CEC2014 test functions to compare FA1→3 with the standard FA and several modern improved FA algorithms to validate its performance. The experimental results demonstrate that FA1→3 has achieved acceptable performance. In addition, it has been applied to six real-world engineering problems to show the optimization capability, robustness, and efficacy of FA1→3 in comparison with modern algorithms As per simulations, FA1→3 has provided suitable performance and higher accuracy than traditional and modified algorithms introduced in the last years. According to simulations, FA1→3 is significantly powerful and robust when dealing with various complex engineering problems and finds the design variables straightforwardly. Note that the source code of the proposed FA1→3 algorithm is publicly available at https://www.optim-app.com/projects/FA.