| Summary: | This thesis considers the frequency assignment problem (FAP), which is a real world problem of assigning frequencies to wireless communication connections (also known as requests) while satisfying a set of constraints in order to prevent a loss of signal quality. This problem has many different applications such as mobile phones, TV broadcasting, radio and military operations. In this thesis, two variants of the FAP are considered, namely the static and the dynamic FAPs. The static FAP does not change over time, while the dynamic FAP changes over time as new requests gradually be-come known and frequencies need to be assigned to those requests effectively and promptly. The dynamic FAP has received little attention so far in the literature com-pared with the static FAP. This thesis consists of two parts: the first part discusses and develops three heuristic algorithms, namely tabu search (TS), ant colony optimization (ACO) and hyper heuris-tic (HH), to solve the static FAP. These heuristic algorithms are chosen to represent different characteristics of heuristic algorithms in order to identify an appropriate solu-tion method for this problem. Several novel and existing techniques have been used to improve the performance of these heuristic algorithms. In terms of TS, one of the nov-el techniques aims to determine a lower bound on the number of frequencies that are required from each domain for a feasible solution to exist, based on the underlying graph colouring model. These lower bounds are used to ensure that we never waste time trying to find a feasible solution with a set of frequencies that do not satisfy the lower bounds, since there is no feasible solution in this search area. Another novel technique hybridises TS with multiple neighbourhood structures, one of which is used as a diversification technique. In terms of ACO, the concept of a well-known graph colouring algorithm, namely recursive largest first, is used. Moreover, some of the key factors in producing a high quality ACO implementation are examined such as differ-ent definitions of visibility and trail, and optimization of numerous parameters. In terms of HH, simple and advanced low level heuristics each with an associated inde-pendent tabu list are applied in this study. The lower bound on the number of fre-quencies that are required from each domain for a feasible solution to exist is also used. Based on the experimental results, it is found that the best performing heuristic algo-rithm is TS, with HH also being competitive, whereas ACO achieves poor perfor-mance. Additionally, TS shows competitive performance compared with other algo-rithms in the literature. In the second part of this thesis, various approaches are designed to solve the dynamic FAP. The best heuristic algorithms considered in the first part of this thesis are used to construct these approaches. It is interesting to investigate whether heuristic algorithms which work well on the static FAP also prove efficient on the dynamic FAP. Addi-tionally, several techniques are applied to improve the performance of these approach-es. One of these, called the Gap technique, is novel. This technique aims to identify a good frequency to be assigned to a given request. Based on the experimental results, it is found that the best approach for the dynamic FAP shows competitive results com-pared with other approaches in the literature. Finally, this thesis proposes a novel ap-proach to solve the static FAP by modelling it as a dynamic FAP through dividing this problem into smaller sub-problems, which are then solved in turn in a dynamic process. The lower bound on the number of frequencies that are required from each domain for a feasible solution to exist, based on the underlying graph colouring model, and the Gap technique are also used. The proposed approach shows the ability to improve the results which have been found by the heuristic algorithms in the first part of this thesis (which solve the static FAP as a whole). Moreover, it shows competitive results com-pared with other algorithms in the literature.
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