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The aircraft arrival sequencing and scheduling (ASS) problem is a salient problem in air traffic control (ATC), which proves to be nondeterministic polynomial (NP) hard. This paper formulates the ASS problem in the form of a permutation problem and proposes a new solution framework that makes the first attempt at using an ant colony system (ACS) algorithm based on the receding horizon control (RHC) to solve it. The resultant RHC-improved ACS algorithm for the ASS problem (termed the RHC-ACS-ASS algorithm) is robust, effective, and efficient, not only due to that the ACS algorithm has a strong global search ability and has been proven to be suitable for these kinds of NP-hard problems but also due to that the RHC technique can divide the problem with receding time windows to reduce the computational burden and enhance the solution's quality. The RHC-ACS-ASS algorithm is extensively tested on the cases from the literatures and the cases randomly generated. Comprehensive investigations are also made for the evaluation of the influences of ACS and RHC parameters on the performance of the algorithm. Moreover, the proposed algorithm is further enhanced by using a two-opt exchange heuristic local search. Experimental results verify that the proposed RHC-ACS-ASS algorithm generally outperforms ordinary ACS without using the RHC technique and genetic algorithms (GAs) in solving the ASS problems and offers high robustness, effectiveness, and efficiency.