The gate assignment problem (GAP) aims at assigning gates to aircraft considering operational efficiency of airport and satisfaction of passengers. Unlike the existing works, we model the GAP as a bi-objective constrained optimization problem. The total walking distance of passengers and the total robust cost of the gate assignment are the two objectives to be optimized, while satisfying the constraints regarding the limited number of flights assigned to apron, as well as three types of compatibility. A set of real instances is then constructed based on the data obtained from the Baiyun airport (CAN) in Guangzhou, China. A two-phase large neighborhood search (2PLNS) is proposed, which accommodates a greedy and stochastic strategy (GSS) for the large neighborhood search; both to speed up its convergence and to avoid local optima. The empirical analysis and results on both the synthetic instances and the constructed real-world instances show a better performance for the proposed 2PLNS as compared to many state-of-the-art algorithms in literature. An efficient way of choosing the tradeoff from a large number of nondominated solutions is also discussed in this article.