Swarm intelligence algorithms are now among the most widely used soft computing techniques for optimization and computational intelligence. One recent swarm intelligence algorithm that has begun to receive more attention is Accelerated Particle Swarm Optimization (APSO). It is an enhanced version of PSO with global optimization capability, sufficient simplicity and high flexibility. In this paper, we propose the application of the APSO technique to efficiently solve the problem of Query Expansion (QE) in Web Information Retrieval (IR). Unlike prior studies, we introduce a new modelling of QE that aims to find the suitable expanded query from among a set of expanded query candidates. Nevertheless, due to the large number of potential expanded query candidates, it is extremely complex to produce the best one through conventional hard computing methods. Therefore, we propose to consider the problem of QE as a combinatorial optimization problem and address it with APSO. We thoroughly evaluate the proposed APSO for QE using MEDLINE, the world Web's largest medical library. We first conduct a preliminary experiment to tune the APSO parameters. Then, we compare the results to a recent swarm intelligence algorithm called Firefly Algorithm (FA). We also compare the results with three recently published methods for QE that involved Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Bat Algorithm (BA). The experimental analysis demonstrates that the proposed APSO for QE is very competitive and yields substantial improvement over the other methods in terms of retrieval effectiveness and computational complexity.