Efficiency Improvement of Evolutionary Multiobjective Optimization Methods for CFD-Based Shape Optimization

Abstract

This dissertation presents an efficient optimization methodology to solve the CFD-based shape optimization problems. This methodology is based on evolutionary algorithms (EAs) for their well-known derivative-free property as well as the advantages in dealing with multiobjective optimization problems (MOOPs) and providing the global optimal solutions. Meanwhile, the approximation models and the deterministic optimization methods are combined with EA to improve the optimization efficiency and the local convergence. The optimization process consists of two parts: the design space exploration using EA (global search) and the convergence acceleration using deterministic methods (local search). When solving a shape optimization problem, the optimizer controls the whole optimization process. The shape variation and flow simulation are incorporated to perform the objective function evaluations and construct the database for the training of the approximation models. Free form deformation (FFD) is employed for the shape variation because it directly modifies the computational grids required by the flow solver and provides a flexible deformation by only moving a small number of the control points. The flow simulation is performed using the in-house developed finite-volume flow solver FASTEST. A modified, elitist evolutionary method NSGA-II is employed as the global explorer. During the evolutionary optimization process, in some generations the online and locally trained RBFN models are utilized to substitute the expensive function evaluations conducted by the high-fidelity flow solver. The adaptive exchange between the exactly and approximately evaluated generations is accomplished through an approximation control procedure. Afterwards, using the achieved results as the starting points, two derivative-free trust-region algorithms DFO and CONDOR are chosen to perform the local search. The proposed optimization methodology is first applied to several analytical and numerical optimization problems, and the optimization results show that it works well for both convex and non-convex Pareto front. The incorporation of approximation models overcomes the requirement of large number of computationally expensive function evaluations. Compared to conventional EA, this hybrid optimization method is able to achieve a set of optimal solutions with good diversity and better convergence with much less computational cost. Furthermore, the influence of RBFN construction methods and the number of solutions in the initial database on the approximation accuracy, as well as the performance of two local search methods, DFO and CONDOR, are studied in this work. Another contribution of the present work is to provide a methodology to construct the approximation model by combining the interpolation methods (spline interpolation or radial basis function interpolation) with the proper orthogonal decomposition (POD) technique in order to approximate the complete flow region in an efficient manner. Applied in the optimization process, this kind of surrogate model has the ability not only to predict the objective functions but also to provide a detailed estimation of the underlying flow region. The efficiency and accuracy of the POD-based approximation models as well as the quality of the optimization results are investigated by two shape optimization test cases.