There is commercial pressure to design axial compressors exhibiting high levels of performance more quickly. This is despite the performance of these machines approaching an asymptote in recent years, with further gains becoming increasingly difficult to achieve. One tool that can be used to help is optimisation, effectively harnessing the speed of computational analysis to accelerate the design process and unlock additional performance improvements. The greatest potential for optimisation exists at the preliminary design stage, however, current methodologies struggle when applied at this early point in the design process due to inadequate problem formulations, an inability to fulfil the role of enhancing designer understanding and a lack of high-fidelity analysis due to computational cost. The goal of this thesis is to facilitate the use of optimisation in the preliminary aerodynamic design of axial compressors by developing an improved methodology that overcomes these limitations.

The multiple dominance relations (MDR) formulation enables a larger number of performance parameters to be incorporated in a way that accurately reflects the desires of the designer. This is implemented within a Tabu Search (TS) that is capable of providing interpretable design development information to enhance designer understanding. The combined MDRTS algorithm, overcoming the limitations associated with formulation and understanding, outperforms existing methods when applied to analytic, aerofoil and six-stage axial compressor test cases, generating computational savings of up to 80%.

Multi-fidelity techniques are used to accelerate the search by conducting analysis on a "need-to-know'' basis. Computational savings of over 70% are observed compared to the single-fidelity version of the algorithm across the analytic, aerofoil and six-stage axial compressor test cases, enabling high-fidelity analysis to be employed in a computationally efficient manner. The resultant methodology represents a novel and inherently flexible multi-level multi-fidelity optimisation technique.

Application to an N-stage axial compressor test case, in which the optimiser is given control over the number of stages in the machine, demonstrates the capabilities of the accelerated MDRTS approach. The complex design space is effectively navigated, generating computational savings of over 90% compared to existing methodologies and producing designs that are more likely to be of interest to the designer. Interpretable design development information is also provided for this problem to enhance designer understanding. These results show that the improved methodology successfully facilitates the use of optimisation in the preliminary aerodynamic design of axial compressors, overcoming the problems associated with formulation, understanding and speed that limit existing approaches.