Optimisation of Airfoils using Parallel Genetic Algorithms

This paper describes a parallel genetic algorithm which is linked to CFD analysis for the design of optimal airfoils. The method has been implemented on a variety of parallel architec-tures, and results to illustrate its application are presented. A common problem with genetic algorithms (or GAs) is how to maintain diversity of the gene pool and avoid premature convergence of the population. Subdivision of the population into semi-isolated subpopulations (commonly referred to as`demes') not only helps signiicantly in this regard, but is ideally suited to implementation on a network of workstations. The basic ideas behind the GA are described in excellent texts such as 1], and only a brief outline can be given here. The GA always starts with a population of trial solutions to the optimisation problem (generally that of minimising a cost function); these trial solutions may be randomly generated for the problem. In this work, a member of the population (a trial solution) corresponds to a particular airfoil geometry, which is encoded as a string specifying the values of the design variables. The string may be an array of real or binary numbers, and can be viewed as a chromosome in which the array positions correspond to positions along the string and are analogous to genes. We prefer a real number encoding, and have generally used the locations of the vertices of the control polygon of a B-spline to represent the airfoil geometry, g.1a. Direct encoding, and shape modiication functions have also been tried. The population of strings or chromosomes is then allowed to evolve, by preferentially selecting the tter individuals for reproduction. Fitness for reproduction is evaluated by the ow solver, normally far more expensive in CFD optimization than other GA operations. The selection schemes used comprise binary tournament and roulette wheel selection 1]. Selection plays a central role in controlling the GA; if over-extreme, it can produce too rapid convergence. The simple reciprocal relation between the values of the cost returned by the evaluation and corresponding tness values is altered here by remapping the distribution of tness values, (termed``tness scaling') in order to innuence selection by modifying the tness. The selection is also treated here asèlitist', so that the best of a generation is always carried through to the next; a uniformly slightly mutated copy of the best is also carried through. Reproduction involves the mutation and crossover of genes to produce new oospring. Mutations …