The issue of gate assignment at modern airports involves coordinating multiple interests, including passenger satisfaction, efficient allocation of airport resources, and control of carbon emissions. A multi-objective nonlinear integer programming model was developed to solve this complex problem, which considering constraints such as flight type, aircraft model, and gate availability. The optimization objectives of model include minimizing passengers' walking distance, maximizing aircraft-gate matching, and minimizing carbon emissions. An improved adaptive genetic algorithm was proposed to solve the gate assignment problem. In the population initialization phase, a combination of random and greedy-perturbation strategies was employed to generate a more diverse initial population. The probabilities of crossover and mutation were adaptively adjusted during the algorithm's iterations. Both crossover-first and mutation-first evolutionary strategies were applied to enhance solution efficiency and global search ability. To validate the effectiveness of the algorithm, some simulation experiments were conducted using operational data from the domestic airport. The improved adaptive genetic algorithm was compared with traditional genetic algorithms and particle swarm optimization algorithms. Results show that the improved algorithm significantly outperforms the others in terms of gate utilization efficiency, passenger satisfaction, and carbon emission control. Furthermore, the effectiveness of the proposed improvement strategies was confirmed through experimental analysis, demonstrating the stability and performance of the algorithm. The proposed model and algorithm provide robust decision support for gate management, contributing to enhanced passenger satisfaction, efficient resource utilization, and sustainable environmental development.