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Recent research on airport ground movement introduced an Active Routing framework to support multi-objective trajectory-based operations. This results in edges in the airport taxiway graph having multiple costs such as taxi time, fuel consumption and emissions. In such a graph, multiple edges exist between two nodes reflecting different trade-offs among the multiple costs. Aircraft will have to choose the most efficient edge from multiple edges in order to traverse from one node to another respecting various operational constraints. In this paper, we introduce a multi-objective routing and scheduling algorithm based on the enumerative approach that can be used to solve such a multi-objective multi-graph problem. Results using the proposed algorithm for a range of international airports are presented. Compared with other routing and scheduling algorithms, the proposed algorithm can find a representative set of optimal or near optimal solutions in a single run when the sequence of aircraft is fixed. In order to accelerate the search, heuristic functions and a preference-based approach are introduced. We analyse the performance of different approaches and discuss how the structure of the multi-graph affects computational complexity and quality of solutions. • A multi-objective routing and scheduling algorithm is proposed for taxiing aircraft. • The problem is modelled using a multi-objective multi-graph. • Heuristic functions and a preference-based approach are introduced. • The multi-graph structure is analysed w.r.t. complexity and quality of solutions. [ABSTRACT FROM AUTHOR]