Selected Engineering Applications of Gradient Free Optimisation Using Cuckoo Search and Proper Orthogonal Decomposition

This paper discusses some engineering applications of gradient free optimisation techniques. This is achieved using the development of the cuckoo search algorithm as a case study. The motivations behind using gradient free algorithms are discussed and illustrated using two specific practical examples. The first involves aerofoil shape optimisation, where it is shown that a modified cuckoo search algorithm performs well when applied both to aerofoil inverse design and aerofoil shape optimisation. This example is then used to discuss the use of reduced order modeling to decrease the computational cost of the optimisation process. We discuss which reduced order modeling techniques based on proper orthogonal decomposition are suitable for these optimisation applications. The second example is that of co-volume mesh optimisation, where it is shown that a modified cuckoo search can significantly outperform alternative non-optimisation and gradient based techniques. We conclude by discussing a number of remaining difficulties which may deter engineers from using gradient free techniques, and suggest ways in which these may be alleviated.