Airport gate assignment is a critical issue in airport operations management. However, limited airport parking spaces and rising fuel costs have caused serious issues with gate assignment. In this paper, an effective multiobjective optimisation model for gate assignment is proposed, with the optimisation objectives of minimising real-time flight conflicts, maximising the boarding bridge rate, and minimising aircraft taxiing fuel consumption. An improved tunicate swarm algorithm based on cosine mutation and adaptive grouping (CG-TSA) is proposed to solve the airport gate assignment problem. First, the Halton sequence is used to initialise the agent positions to improve the initial traversal and allocation efficiency of the algorithm. Second, the population as a whole is adaptively divided into dominant and inferior groups based on fitness values. To improve the searchability of the TSA for the dominant group, an arithmetic optimisation strategy based on ideas related to the arithmetic optimisation algorithm (AOA) is proposed. For the inferior group, the global optimal solution is used to guide the update to improve the convergence speed of the algorithm. Finally, the cosine mutation strategy is introduced to perturb the optimal solution and prevent the target from falling into the local extrema as a way to efficiently and reasonably allocate airport gates. The CG-TSA is validated using benchmark test functions, Wilcoxon rank-sum detection, and CEC2017 complex test functions and the results show that the improved algorithm has good optimality-seeking ability and shows high robustness in the multiobjective optimisation problem of airport gate assignment.