The increase in demand for the radio spectrum over the last twenty or so years has been huge, largely due to the surge development of mobile and wireless technologies. Interference between two sets of radio equipment can be a prohibiting factor if the tliei~ respective frequency assignments are not sufficiently separated on the radio spectrum. However, the radio spectrum is a finite resource and as such must be carefully .assigned to avoid excessive and unnecessary use while satisfying as many request of use for radio equipment as possible. This thesis is the result of an investigation into combinatorial optimisation methodologies applied to frequency assignment problems in which we study data, bounds, special cases, representations and algorithms. rvlost of our work concerns the minimum span problem in which an interference free assignment that satisfies frequency separation requirements is required. A comprehensive literature review is presented to give a thorough overview of the work done to date which serves as a basis for the remaining aspects of the thesis. Following this we consider the nature of frequency assignment problems by studying he benchmark data sets and classify them according to some of their inherent properties. This facilitates the generation of artificial data with properties that reflect real-life instances. Further to this we study the concept of 'robustness' of frequency assignments and study the effect of changing networks over time. It is noted that often frequency assignment problems have conflicting objectives. Vve study this in detail by considering the effect of combining objectives. Vve define a bi-criteria frequency assignment problem related to the span of an assignment using a· goal programming approach. We provide a mathematical analysis for this problem and consider the implications of restricting potential interference to co-channel and adjacent channel only. In addition, we provide an optimal solution when the co-channel subgraph has a particular structure. Our primary contribution is the useof a new representation for the minimum span frequency assignment problem that relates the number of acyclic orientations of a graph representing a radio nehvork to the span of frequency assignments. Vve provide results concerning the expected number of acyclic orientations of a graph and show that the solution space of this representation can be significantly smaller than other representations presented in the literature. In addition we define a new Hamming distance for graph orientations that is more suitable for frequency assignments than others proposed in the literature. We demonstrate the viability of this representation computationally by designing a set of simple genetic algorithms for the problem. A comprehensive set of experiments are designed and our algorithms are tested against approaches reported in the literature.