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Figure 49: Optimal geometries resulting from four optimization runs with different starting populations 4.5.2. Cures to GA-Hardness A standard way to improve GA convergence, already explored in several papers in the literature consists in constructing hybrid algorithms combining the GA with a local search gradient-based algorithm. The most used hybridization technique is the following: the GA is preliminarily run in order to roughly localize basins containing global optima; then, the solution is refined by applying a quick local search method that, using information about the solution gradient, quickly converges to the nearest optimum. Similarly, the coarse-grid solutions provided by the GA is used to initialize a gradient- based method (see 3.2). The fitness-function gradient is approximated by central differences; after about 30 iterations, the solution converges toward a new individual characterized by a better value of the fitness function than both “optimal” individuals detected with the preceding GA runs. The computed drag coefficient is 1.64×10-2 for the NACA0012 and 5.00×10-3 for the optimized airfoil; this value also improve the results previously obtained by the GA. The optimal solution for the inviscid dense gas flow at M=0.95 previously discusses in 4.5.1 is also locally refined by means of the BFGS algorithm. After convergence, an optimal airfoil shape is found , displaying a drag coefficient CD=9.75×10-4. This value is 112PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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