Original Article Multi-point optimization of transonic airfoils using an enhanced genetic algorithm Narjes Timnak and Alireza Jahangirian Abstract In this study, two new techniques are proposed for accelerating the multi-point optimization of an airfoil shape by genetic algorithms. In such multi-point evolutionary optimization, the objective function has to be evaluated several times more than a single-point optimization. Thus, excessive computational time is crucial in these problems particularly, when computational fluid dynamics is used for fitness function evaluation. Two new techniques of preadaptive range operator and adaptive mutation rate are proposed. An unstructured grid Navier–Stokes flow solver with a two-equation k  " turbulence model is used to evaluate the objective function. The new methods are applied for optimum design of a transonic airfoil at two speed conditions. The results show that using the new methods can increase the aerodynamic efficiency of optimum airfoil at each operating condition with about 30% less computational time in comparison with the conventional genetic algorithm approach. Keywords Multi-point design, transonic airfoil, smooth genetic algorithm, Navier–Stokes solver, parallel processing Date received: 30 July 2016; accepted: 27 December 2016 Introduction During past several years, interest in the design of the next generation civilian transonic aircraft has increased. The attention is particularly paid toward the higher transonic velocities while keeping the lift and drag coefficients reasonably unchanged. To achieve such objectives, most of the designers focus on creating a new wing with minimum shock wave strength. Thus, the first step toward designing these wings is typically to optimize 2D airfoils. That is why a substantial amount of research has been performed in the field of airfoil shape optimization. A wing is usually optimized based on the cruise condition requirements because most of the flight- time is in the cruise condition pocket. However, to cover all aspects of aerodynamic design, a practical algorithm requires effective capabilities that may include multiple operating points. This is due to the fact that during the cruise-flight-time, an aircraft may fly at different speeds including a Mach number higher than the design cruise speed. However, this will lead the aircraft to a critical condition because of dramatic increase of the drag coefficient while the lift coefficient is decreasing. Therefore, it is very cru- cial to optimize the wing section not only for design cruise condition but also for maximum speed. 1,2 This will be performed by multi-point optimization. Nowadays, in the realm of aerodynamic shape optimization, among different methods evolutionary algorithms introduce themselves as a powerful tool. Among them, one of the best known algorithms are inspired by Darwin’s theory of natural genetics; ‘‘The Genetic Algorithm (GA).’’ 3 The most important characteristic of GA is that it does not require com- puting the sensitivity of the derivatives, because cal- culating the gradient information especially for nonlinear functions is very complicated. GA also works well when the design parameters are increased, whereas the gradient-based methods have problems. Another important feature of GA is searching the design space from a population of points and not from one special point, which results in a greater likelihood of finding the global optimum point. 3 Proc IMechE Part G: J Aerospace Engineering 0(0) 1–14 ! IMechE 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954410017690549 journals.sagepub.com/home/pig Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran Corresponding author: Alireza Jahangirian, Department of Aerospace Engineering, Amirkabir University of Technology, Tehran 17878, Iran. Email: ajahan@aut.ac.ir