Abstract— This research uses Neural Networks to determine two dimensional airfoil geometry using Bezier-PARSEC parameterization. Earlier, Ant Colony Optimization (ACO) techniques have been used to solve combinatorial optimization problems like TSP. This work extends ACO method from TSP problem to design parameters for estimating unknown Bezier-PARSEC parameters that define upper and lower curves of the airfoil. The efficiency and the performance of ACO technique was compared to that of GA. The work established that ACO exhibited improved performance than the GA in terms of optimization time and level of precision achieved. In the next phase, Neural Network is implemented using Cp as input in terms of C l , C d and C m for learning and targeting the corresponding Bezier-PARSEC parameters. Neural Networks including Feed-forward back propagation, Generalized Regression and Radial Basis were implemented and were compared to evaluate their performance. Similar to earlier work with GA and Neural Nets, this work also established Feed-forward back propagation Neural Network as a preferred method for determining the design of airfoil since the technique presented better approximation results than other neural nets. Keywords— Airfoil Optimization, Ant Colony Optimization, Bezier-PARSEC, C p , Neural Network I. INTRODUCTION irfoil design is one of the most challenging processes [1] in development of aircraft aerodynamic surfaces as it affects various aircraft performance parameters like lift, drag, spin-stall, cruise and turning radius [2]. Studies indicate that selecting the right design of airfoil with required characteristics reduces overall cost and improves the performance of air vehicle. Airfoil design largely depends on desire for high lift to drag ratio that is in conflict with the performance requirements [3]. There are two major techniques for designing an airfoil; direct and inverse [4]. First method involves designing a new or modifying an existing airfoil (UIUC Airfoil Database [5] and computing pressure distribution W. Saleem is with School of Mechanical and Manufacturing Engineering National University of Sciences, Pakistan (Phone: +923224362442, e-mail: waqas_jeral@hotmail.com R. Ahmad is currently director research at CIE Building, Research Directorate National University of Sciences and Technology, Pakistan (e-mail: dresearch@nust.edu.pk) A. Kharal is currently Associate Professor at College of Aeronautical Engineering National University of Sciences and Technology, Pakistan (atharkharal@gmail.com ) A. Saleem is with College of Aeronautical Engineering National University of Sciences and Technology (aimen1173@hotmail.com) across the surface to achieve desired set of parameters. This approach may limit the approximation for desired specifications due to inherent limitations in airfoil’s aerodynamics. For faster approximations, reduced degrees of freedoms are required but such reduction results in computational errors like round off, truncation and discretization error. In fact, determining the airfoil geometry should be based on requirements for aircraft’s performance. Thus later method involves using desired operational characteristics and performance parameters unless the airfoil geometry so generated meets the desired criteria. To reduce the computational time and meet the required design criteria various techniques including CFD, fuzzy logic, neural networks [6] and heuristics based algorithms like PSO [7] and GA [8] have been implemented to advantage the aerodynamic design process. This research, largely inspired by Saleem and Kharal [9], uses neural network based approach for airfoil generation exploiting Bezier-PARSEC 3434 parameterization rather than full coordinates for a given Cp. However, this research implements ACO to optimize Bezier-PARSEC unknown parameters instead of GA as in earlier work. II. ARITIFICIAL NEURAL NETWORK In machine learning and data mining, Artificial Neural Network is a set of learning algorithms modeled after neural network structure of the cerebral cortex and is used to approximate functions involving a larger number of the unknown input variables [10] Each neuron receives input from external sources or neighbors in the network, computes output and propagates to other neurons. Another function is the weight adjustments in the connections between neurons. Incremental learning is the technique by gathering information on cumulative error and consequently adjusting weight coefficients, w ij . Mathematically, a Neural Network can be defined as a triple (N, C, w) where N is the set of neurons, C {(i, j)|i, j ∈ N} is a set of connections, and function w((i, j)), shortened as w ij is called weights between neurons i and j. For every neuron, there is an external input ϑ j and an activation function F j to establish the new activation level based on effective input of a neuron S j and is determined by following propagation rule in “(1)”. Comparison of ACO and GA Techniques to Generate Neural Network Based Bezier-PARSEC Parameterized Airfoil Waqas Saleem 1 , Riaz Ahmad 2 , Athar Kharal 3 , Ayman Saleem 4 A (1) Recent Advances in Mathematics ISBN: 978-1-61804-323-8 108