Title:
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Combinatorial optimisation approaches to frequency assignment
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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.
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