# Metaheuristic Approaches to Solve a Complex Aircraft Performance Optimization Problem
###### Contents  
* 1 Introduction
* 2.1 Introduction
* 2.2 The 2.3 The 2.4 The 2.5 The 2.6 The 2.7 The 2.8 The 2.9 The 2.1 The 2. Aircraft design is an inherently multidisciplinary, iterative effort. However, conventional design methods weaken the collaborative effect of various disciplines so that aerodynamic, structural, and stability analyses have to be performed in a specific sequence to achieve an optimum of a system. The major limitation of this method relates to an iterative design process and will lead to less efficiency of computations, so it can hardly adapt to the design of a modern aircraft, especially the conceptual design with great potential for innovation in the early stage. Instead, multidisciplinary analysis and optimization (MAO) could take disciplines containing aerodynamics, structure, aircraft flight dynamics, etc. into consideration simultaneously and has been employed in large modern aircraft designs [4; 5; 6; 7; 8; 9]. In light of its capability to overcome the limitations of the conventional method, the MAO technique with the integration of novel algorithms has been applied to solve complex problems in other industry sectors, such as automobile [10; 11], energy [12], mechatronic systems [13], etc. Obviously, a crucial challenge of MAO is its massive computation burden, especially for computational fluid dynamics (CFD) simulations based on Reynolds-averaged Naiver-Stokes (RANS) equations. Though RANS method can simulate intricate turbulence and shedding vortex, the steady flight conditions make up most of the flight time of a large aircraft, hence some viscous-inviscid iteration methods are more suitable for cruise conditions with moderate flow separation [14]. As the disturbance in the cruise condition is weak compared with the steady-state, the small-disturbance theory is valid for the stability analysis. Although a gradient-based algorithm has the advantages of rapidity and effectiveness for solving an optimization problem, it is apt to converge to a local optimal solution and sometimes, it fails in special cases where calculating the partial derivatives is hard or the derivatives are not continuous. Considering these facts, the evolutionary algorithms are suitable to seek the globally optimal solution. Genetic algorithm (GA) is based on [PERSON]'s theory and is used most widely as a global algorithm for this purpose [15; 16]. However, function evaluations in GA are the most time-consuming part as they are usually executed by finite element analysis (FEA) or CFD with high computational demands, for example, a single function evaluation could be of the order of hours or days. Hence, the computational burden of FEA or CFD for design evaluations is the main limitation of GA for solving multidisciplinary optimization problems. To reduce the computational burden and benefit to a great extent of better exploration and exploitation in the design space, metamodel-based optimization has recently found widespread use owing to its promising potential [17; 18; 19; 20; 21; 22; 23]. As a response surface method, genetic programming (GP) is a systematic way of selecting a structure of high-quality global approximations [24]. The program can represent an empirical model to be used for approximation of a response function, and the explicit expression [25], or even algorithms [26], can be entirely attained for optimization. With the high accuracy, approximation models generated by GP have already been used for solving various design optimization problems [27; 28; 29; 18; 21]. In light of the exploitation of the immense potential from a large aircraft conceptual design process and the advantages of GP methodology in support of MAO, an integrated GP metamodel-based optimization method to design a full-scale aircraft subject to aerodynamic, structural and stability constraints is proposed in this paper. Static aeroelasticity and flutter analyses are performed with the MSC/Nastran doublet-lattice method. The stability of flight dynamics is evaluated by the linear small-disturbance method.