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Genetic Algorithms (GAs) have a good potential of solving the Gate Assignment Problem (GAP) at airport terminals, and the design of feasible and efficient evolutionary operators, particularly, the crossover operator, is crucial to successful implementations. This paper reports an application of GAs to the multi-objective GAP. The relative positions between aircraft rather than their absolute positions in the queues to gates is used to construct chromosomes in a novel encoding scheme, and a new uniform crossover operator, free of feasibility problems, is then proposed, which is effective and efficient to identify, inherit and protect useful common sub-queues to gates during evolution. Extensive simulation studies illustrate the advantages of the proposed GA scheme with uniform crossover operator.