Efficient ground handling at airports contributes significantly to the performance of the entire air transport network. In this network, airports are coupled by flights that depend on passenger and crew connections, effective local airport operations, and efficient ground handling resource management. In addition, airport stakeholders must consider different time scales (look-ahead times), process estimates, and both bounded and multiple-dependent solution spaces for their decision-making processes. In this context, we aim to solve the NP-hard problem of combined aircraft turnaround time and airport gate allocation optimization. We developed a hybrid meta-heuristic algorithm based on the Shuffled Frog-Leaping Algorithm (SFLA) and the Grasshopper Optimization Algorithm (GOA). Our hybrid SFLA-GOA approach overcomes the drawback of each algorithm and achieves a preferred solution at a reduced computational cost. We test our approach with a scenario derived from Frankfurt Airport operations, including gate positions, terminal layout, and flight plan information. In all defined problem sizes, the hybrid SFLA-GOA algorithm outperforms an independent implementation of the SFLA algorithm. Also, the SFLA-GOA algorithm provides an improved solution by at least nearly 12% up to 40% over the standard mixed-integer programming solvers.