Particle swarm optimisation (PSO) is a biologically-inspired, population-based optimisation technique that has been successfully applied to various problems in science and engineering. In the context of semantic technologies, optimisation problems also occur but have rarely been considered as such. This work addresses the problem of ontology alignment, which is the identification of overlaps in heterogeneous knowledge bases backing semantic applications. To this end, the ontology alignment problem is revisited as an optimisation problem. A discrete particle swarm optimisation algorithm is designed in order to solve this optimisation problem and compute an alignment of two ontologies. A number of characteristics of traditional PSO algorithms are partially relaxed in this article, such as fixed dimensionality of particles. A complex fitness function based on similarity measures of ontological entities, as well as a tailored particle update procedure are presented. This approach brings several benefits for solving the ontology alignment problem, such as inherent parallelisation, anytime behaviour, and flexibility according to the characteristics of particular ontologies. The presented algorithm has been implemented under the name MapPSO (ontology mapping using particle swarm optimisation). Experiments demonstrate that applying PSO in the context of ontology alignment is a feasible approach.