This dissertation presents an analysis of the angle modulated particle swarm optimisation (AMPSO) algorithm. AMPSO is a technique that enables one to solve binary optimisation problems with particle swarm optimisation (PSO), without any modifications to the PSO algorithm. While AMPSO has been successfully applied to a range of optimisation problems, there is little to no understanding of how and why the algorithm might fail. The work presented here includes in-depth theoretical and emprical analyses of the AMPSO algorithm in an attempt to understand it better. Where problems are identified, they are supported by theoretical and/or empirical evidence. Furthermore, suggestions are made as to how the identified issues could be overcome. In particular, the generating function is identified as the main cause for concern. The generating function in AMPSO is responsible for generating binary solutions. However, it is shown that the increasing frequency of the generating function hinders the algorithm’s ability to effectively exploit the search space. The problem is addressed by introducing methods to construct different generating functions, and to quantify the quality of arbitrary generating functions. In addition to this, a number of other problems are identified and addressed in various ways. The work concludes with an empirical analysis that aims to identify which of the various suggestions made throughout this dissertatioin hold substantial promise for further research.