RNA secondary structure prediction is an important field in Bioinformatics. A number of different approaches have been developed to simplify the determination of RNA molecule structures. RNA is a nucleic acid found in living organisms which fulfils a number of important roles in living cells. Knowledge of its structure is crucial in the understanding of its function. Determining RNA secondary structure computationally, rather than by physical means, has the advantage of being a quicker and cheaper method. This dissertation introduces a new Set-based Particle Swarm Optimisation algorithm, known as SetPSO for short, to optimise the structure of an RNA molecule, using an advanced thermodynamic model. Structure prediction is modelled as an energy minimisation problem. Particle swarm optimisation is a simple but effective stochastic optimisation technique developed by Kennedy and Eberhart. This simple technique was adapted to work with variable length particles which consist of a set of elements rather than a vector of real numbers. The effectiveness of this structure prediction approach was compared to that of a dynamic programming algorithm called mfold. It was found that SetPSO can be used as a combinatorial optimisation technique which can be applied to the problem of RNA secondary structure prediction. This research also included an investigation into the behaviour of the new SetPSO optimisation algorithm. Further study needs to be conducted to evaluate the performance of SetPSO on different combinatorial and set-based optimisation problems.