This paper addresses a vehicle sequencing problem for adjacent intersections under the framework of Autonomous Intersection Management (AIM). In the context of AIM, autonomous vehicles are considered to be independent individuals and the traffic control aims at deciding on an efficient vehicle passing sequence. Since there are considerable vehicle passing combinations, how to find an efficient vehicle passing sequence in a short time becomes a big challenge, especially for more than one intersection. In this paper, we present a technique for combining certain vehicles into some basic groups with reference to some properties discussed in our earlier works. A genetic algorithm based on these basic groups is designed to find an optimal or a near-optimal vehicle passing sequence for each intersection. Computational experiments verify that the proposed genetic algorithms can response quickly for several intersections. Simulations with continuous vehicles are carried out with application of the proposed algorithm or existing traffic control methods. The results show that the traffic condition can be significantly improved by our algorithm.