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# IOSO vs Genetic Algorithm (comparison on practical optimization problem)

Dear Colleagues,

Here we would like to offer you the summary from a published work concernign the optimization of industrial object. The work describes the application of parallel IOSO algorithms and parallel genetic algorithm PGA for the solution of optimization of 3D serpentine cooling passage inside a turbine blade.

The geometry of the blade and the internal serpentine cooling passages were parameterized using surface patch analytic formulation, which provides very high degree of flexibility, second order smoothness and a minimum number of parameters. The design variable set defines the geometry of the turbine blade coolant passage including blade wall thickness distribution and blade internal strut configurations. A parallel three-dimensional thermoelasticity finite element analysis (FEA) code from the ADVENTURE project at the University of Tokyo was used to perform automatic thermal and stress analysis of different blade configurations. The same code can also analyze nonlinear (large/plastic deformation) thermoelasticity problems for complex 3-D configurations. The objective of the optimization was to make stresses throughout the blade as uniform as possible. Constraints were that the maximum temperature and stress at any point in the blade were less than the maximum allowable values. A robust semi-stochastic constrained optimizer (IOSO) and a parallel genetic algorithm (PGA) were used to solve this problem while running on an inexpensive distributed memory parallel computer.

For each design, a series of modules is required to turn a given set of design variables into optimization objective and constraint function values. The flow of data between these modules is depicted graphically in Figure 1.

Figure 3: Modules used for automatic parallel FEA

The outer blade shape was considered to be fixed and to be provided by the user at the beginning of the design optimization. The shapes of the internal coolant passages were parameterized using analytical shape functions. All together a total of 42 continuous design variables were used to uniquely describe a design. Sample geometry and the generated surface mesh are shown in Figures 2-3

Figure 2: Internally cooled blade example. Figure 3: Triangular surface mesh for blade example.

A total of 12 analyses were performed per iteration for IOSO method. For PGA, 36 designs were evaluated per generation. A converged result was found by the IOSO optimizer in 70 Iterations (only 840 model evaluations). The PGA run was terminated before a converged result was found. The convergence history for the objective function for both PGA and IOSO is shown in Figure 4.

Figure 4: Objective function convergence history

The initial and the IOSO optimized passages configurations are shown in Figures 5 and 6. Principal stresses on the surface of the blade with the initial shape of the coolant passage is shown in Figure 7, while the IOSO optimized coolant passage offers lower and more uniform stress field (Figure 8). Temperature distributions for the initial design and the IOSO optimized design are shown in Figures 9, 10.

Figure 5 Passage shape in *x-z *plane for initial design. Figure 6: Passage shape in *x-z *plane for IOSO optimized design.

Figure 7: Principal stress contours for initial design. Figure 8: Principal stress contours for IOSO optimized design.

Figure 9: Temperature contours for initial design. Figure 10: Temperature contours for IOSO optimized design

To see the full paper look at http://cfdlab.uta.edu/~brian/papers/asme-gt2003-38180.pdf

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