A Parallel Genetic Algorithm for Optimal Synthesis of a Morphing Aerofoil

Abstract

This paper describes the optimal synthesis of the internal mechanism for a morphing aerofoil. The accuracy of the process for mapping an initial aerofoil onto a target aerofoil depends on the number of panels in the mechanism. Therefore to achieve a high level of accuracy, a large number of design parameters are involved. Treating the number of precision points as a design parameter leads to an optimisation problem with a variable number of design parameters and hence variable-length chromosomes in its corresponding genetic algorithm. The objective of the optimisation is to minimise the weight of the mechanism subject to a constraint on the permissible deviation of the morphed aerofoil from its target shape. Due to the highly constrained nature of the problem, a full random generation of an initial population of feasible solutions is a very time consuming process. In order to reduce the number of failed attempts in generating feasible individuals in the initial population, a repair process has been employed. Successful repairs reduce the overall computational time, due to saving the computational time normally spent for failed attempts on generating feasible solutions. On the other hand, failed repairs increase the overall computational time through adding computational time for repair process without reducing the number of failed attempts on generating feasible solutions. It has been shown that the average computational time for two algorithms with and without repair process is almost the same, while the algorithm employing the repair mechanism produces better solutions. In order to reduce the computational time, a parallel algorithm has been proposed. Decomposition of the optimisation algorithm into two parallel algorithms is realised by dividing the original problem into two problems. In the first optimisation process, using an approximated objective function, sub-optimised solutions are produced. These solutions, which are the best possible solutions with respect to the deviation of the morphed aerofoil from its target shape, then are passed into the second optimisation process with the original objective function. The parallel algorithm has been compared with a conventional genetic algorithm with respect to its computational efficiency, showing a significant improvement in both computational time and the quality of the produced results.