1 Aerodynamic Optimization Using a Hybrid MOGA-Local Search Method HyoungJin Kim * and Meng-Sing Liou † NASA Glenn Research Center, Cleveland, OH 44135 Abstract A novel adaptive local search method for hybrid multi-objective evolutionary algorithms (MOEAs) was applied to multi-objective aerodynamic optimization problems for convergence improvement. A novel directional operator without explicit gradient information is also adopted, comprising the selection of search direction and a local one-dimensional search. Probability of the directional operator is adaptively changed based on the relative effectiveness of the directional local search operator and evolutionary operators such as crossover and mutation. The adaptive directional operator is combined with a baseline MOEA. Comparisons are made for the baseline and the hybrid MOEA on multi-objective airfoil design optimization problems. Results show that the present adaptive local search strategy enables remarkable enhancement of convergence when a local search is effective, while minimizing unnecessary computation for cases where a local search is not well suited for. 1. INTRODUCTION ulti-objective optimization methods are getting more attention than before as single-objective optimization methodologies are maturing, and trade-offs between conflicting objectives are becoming more critical in modern engineering problems of Multi-disciplinary Design Optimization (MDO). Evolutionary algorithms (EAs) are search algorithms based on genetic evolution and natural selection. EAs are well suited to Multi-Objective Optimization Problems (MOOPs) because they are based on population rather than a single solution and therefore are naturally adaquate to generate distributed solutions on the non-dominated Pareto front. A well-known drawback of an EA is its slow convergence to the optimum solution, especially in regions near the optimum. This behavior is still true to multi-objective evolutionary algorithms (MOEAs) [1-6]. To cope with this problem, hybrid methods combining MOEAs and a local search method have been reported.[7-12] The hybrid methods are also referred to as memetic algorithms. [12] One of major issues for the hybrid methods is that we do not know a priori if conducting local search would be beneficial for a given specific optimization problem; it would be effective for uni-modal problems or in the last stage of optimization process near the true optimum. However, it might be waste of computational budget for multi- modal problems or in the early stages of the evolution process, where exploratory search is more needed for a successful optimization. Effective use of evolutionary and local directional search operators within available computational budget can be implemented by a wise selection of probability for the local search operator, p ls , which determines the number of individuals going through the local search operator [13]. Another Issue for the hybrid algorithms is whether to calculate gradient information explicitly or not. In general cases without any efficient sensitivity analysis code, an explicit calculation of the gradient vector of an objective function by a first order finite differencing requires N dv additional function calls, where N dv is the number of design variables. The computational cost would easily become prohibitive for a larger number of decision variables and expensive function evaluations. In references [14, 15] hybrid methods of MOEAs and gradient-based local search methods are adapted in randomly selected search directions utilizing explicit calculation of gradient information by finite differencing. Both the references show difficulties in improving convergences especially for * NASA Postdoctoral Program (NPP) Senior Fellow, located at Ohio Aerospace Institute, 22800 Cedar Point Road, Senior Member AIAA † Senior Technologist, Aeropropulsion Division, MS 5-11, 21000 Brookpark Road, Associate Fellow AIAA. M 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR> 18th 12 - 15 April 2010, Orlando, Florida AIAA 2010-2911 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.