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Research Papers: Internal Combustion Engines

Assessment of Multiobjective Genetic Algorithms With Different Niching Strategies and Regression Methods for Engine Optimization and Design

[+] Author and Article Information
Yu Shi, Rolf D. Reitz

Engine Research Center, University of Wisconsin–Madison, 1500 Engineering Drive, Madison, WI 53706

J. Eng. Gas Turbines Power 132(5), 052801 (Mar 05, 2010) (9 pages) doi:10.1115/1.4000144 History: Received April 30, 2009; Revised May 25, 2009; Published March 05, 2010; Online March 05, 2010

In a previous study (Shi, Y., and Reitz, R. D., 2008, “Assessment of Optimization Methodologies to Study the Effects of Bowl Geometry, Spray Targeting and Swirl Ratio for a Heavy-Duty Diesel Engine Operated at High-Load,” SAE Paper No. 2008-01-0949), nondominated sorting genetic algorithm II (NSGA II) (Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T., 2002, “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II  ,” IEEE Trans. Evol. Comput., 6, pp. 182–197) performed better than other popular multiobjective genetic algorithms (MOGAs) in engine optimization that sought optimal combinations of the piston bowl geometry, spray targeting, and swirl ratio. NSGA II is further studied in this paper using different niching strategies that are applied to the objective space and design space, which diversify the optimal objectives and design parameters, accordingly. Convergence and diversity metrics are defined to assess the performance of NSGA II using different niching strategies. It was found that use of design niching achieved more diversified results with respect to design parameters, as expected. Regression was then conducted on the design data sets that were obtained from the optimizations with two niching strategies. Four regression methods, including K-nearest neighbors (KNs), kriging (KR), neural networks (NNs), and radial basis functions (RBFs), were compared. The results showed that the data set obtained from optimization with objective niching provided a more fitted learning space for the regression methods. KNs and KR outperformed the other two methods with respect to prediction accuracy. Furthermore, a log transformation to the objective space improved the prediction accuracy for the KN, KR, and NN methods, except the RBF method. The results indicate that it is appropriate to use a regression tool to partly replace the actual CFD evaluation tool in engine optimization designs using the genetic algorithm. This hybrid mode saves computational resources (processors) without losing optimal accuracy. A design of experiment (DoE) method (the optimal Latin hypercube method) was also used to generate a data set for the regression processes. However, the predicted results were much less reliable than the results that were learned using the dynamically increasing data sets from the NSGA II generations. Applying the dynamical learning strategy during the optimization processes allows computationally expensive CFD evaluations to be partly replaced by evaluations using the regression techniques. The present study demonstrates the feasibility of applying the hybrid mode to engine optimization problems, and the conclusions can also extend to other optimization studies (numerical or experimental) that feature time-consuming evaluations and have highly nonlinear objective spaces.

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Figures

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Figure 6

Comparison of regression methods trained with a data set generated with a DoE method: (a) mean %error for GISFC, (b) mean %error for NOx, (c) mean %error for soot, and (d) legend

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Figure 7

Comparison of regression methods trained with data sets from the optimization process using different niching strategies: %errors of GISFC, (a) mean %error, (b) maximum %error, (c) median %error, (d) minimum %error, (e) standard deviation of the %error, and (f) legend

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Figure 8

Comparison of regression methods trained with data sets from the optimization process using different niching strategies: %errors of NOx, (a) mean %error, (b) maximum %error, (c) median %error, (d) minimum %error, (e) standard deviation of the %error, and (f) legend

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Figure 9

Comparison of regression methods trained with data sets from the optimization process using different niching strategies: %errors of soot, (a) mean %error, (b) maximum %error, (c) median %error, (d) minimum %error, (e) standard deviation of the %error, and (f) legend

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Figure 1

Illustrations of Pareto solutions, ranking, and crowding distance

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Figure 2

Illustration of diversity metric

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Figure 3

Comparison of (a) convergence metric, (b) Pareto front from the optimization using the objective niching, and (c) Pareto front from the optimization using the design niching

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Figure 4

Comparison of performance

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Figure 5

Comparison of (a) diversity metric in the objective space, and (b) diversity metric in the design space

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