Comparison of trust-region-based and evolutionary methods for optimization of flow geometries

Optimization has become increasingly important in computer-aided engineering, and applications of engineering optimization to design, control, operations, and planning already exist. Since in the context of numerical flow simulation no information on the gradient information of the objective function is available, or is very difficult to obtain, in such optimization cases it is advantageous to use an optimization technique which does not directly depend on the derivative. The aim of this study is to investigate two optimization techniques, the trust-region-based method and the evolutionary algorithm technique, and compare them quantitatively with respect to efficiency, quality, and working strategy. A tool based on free-form deformation (FFD) is employed for the variation of flow geometry. This simulation tool is the parallel multigrid flow solver FASTEST, which uses a fully conservative finite-volume method for solving the incompressible Navier–Stokes equations on a non-staggered cell-centred grid arrangement. The optimization tools are investigated by considering the optimization of the connection of two pipes with respect to the minimization of the pressure drop. This problem can be considered as a representative test case for a practical three-dimensional flow configuration. †This is an extended and enhanced version of work presented at the mini-symposium on Evolutionary Algorithms: Recent Applications in Engineering and Science organized by Dr William Annicchiarico at the 7th World Congress on Computational Mechanics, Los Angeles, July 2006.

[1]  Michael Schäfer,et al.  Computational Engineering - Introduction to Numerical Methods , 2006 .

[2]  Robert S. Brodkey,et al.  The phenomena of fluid motions , 1967 .

[3]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[4]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[5]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[6]  Michael Schäfer.  Large-Scale Scientific Flow Computations, Large Scale Scientific Computations of Engineering and Environmental Problems , 1998 .

[7]  Frank Vanden Berghen,et al.  CONDOR, a new parallel, constrained extension of Powell's UOBYQA algorithm: experimental results and comparison with the DFO algorithm , 2005 .

[8]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[9]  Ernest Perry,et al.  Aerodynamic shape optimization of internal fluid flow systems , 1998 .

[10]  A. Ronzheimer.  Post-Parameterization of Complex CAD-Based Aircraft-Shapes Using Freeform Deformation , 2002 .

[11]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[12]  Lothar Harzheim,et al.  Shape200: A Program to Create Basis Vectors for Shape Optimization Using Solution 200 of MSC/Nastran , 1997 .

[13]  A parallel multigrid method for the prediction of turbulent flows with reynolds stress closure , 1996 .

[14]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[15]  Michael Schäfer,et al.  Artificial neural networks for shape optimization in CFD , 2004 .

[16]  Kalyanmoy Deb,et al.  Towards a Quick Computation of Well-Spread Pareto-Optimal Solutions , 2003, EMO.

[17]  Franz Durst,et al.  a Parallel Block-Structured Multigrid Method for the Prediction of Incompressible Flows , 1996 .

[18]  O. Pironneau,et al.  SHAPE OPTIMIZATION IN FLUID MECHANICS , 2004 .

[19]  M. J. D. Powell,et al.  UOBYQA: unconstrained optimization by quadratic approximation , 2002, Math. Program..

[20]  Kalyanmoy Deb,et al.  A Comparative Analysis of Selection Schemes Used in Genetic Algorithms , 1990, FOGA.

[21]  Michael Schäfer,et al.  Efficient discretization of pressure-correction equations on non-orthogonal grids , 2003 .

[22]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .