The gate assignment problem (GAP) is crucial for daily airport operations. It is known as a multi-objective combinatorial optimization problem, which is especially challenging in practice due to the problem scale. Nowadays, GAP becomes even more complicated when gates are managed as clusters, each reserved for a special group of airline companies. In this study, an integer programming (IP) model was formulated to describe the problem. Due to the high interconnection among airline groups, it is difficult to decompose the large scale GAP by clusters. To solve the integrated problem, a solution algorithm was developed based on the framework of Non-dominated Sorting Genetic Algorithm II (NSGA-II). A rolling horizon method was further proposed to accelerate the algorithm under the large scale scenario. The realistic operational data of Baiyun airport was used for performance comparison against GUROBI and the rule based method. The numerical experiments showed that the NSGA-II based algorithm could find near optimal solutions under the small scale scenario, and effectively improve the solution quality under the large scale scenario.