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A Suite of Computationally Expensive Shape Optimisation Problems Using Computational Fluid Dynamics

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Parallel Problem Solving from Nature – PPSN XV (PPSN 2018)

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Abstract

In many product design and development applications, Computational Fluid Dynamics (CFD) has become a useful tool for analysis. This is particularly because of the accuracy of CFD simulations in predicting the important flow attributes for a given design. On occasions when design optimisation is applied to real-world engineering problems using CFD, the implementation may not be available for examination. As such, in both the CFD and optimisation communities, there is a need for a set of computationally expensive benchmark test problems for design optimisation using CFD. In this paper, we present a suite of three computationally expensive real-world problems observed in different fields of engineering. We have developed Python software capable of automatically constructing geometries from a given decision vector, running appropriate simulations using the CFD code OpenFOAM, and returning the computed objective values. Thus, users may easily evaluate a decision vector and perform optimisation of these design problems using their optimisation methods without developing custom CFD code. For comparison, we provide the objective values for the base geometries and typical computation times for the test cases presented here.

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Notes

  1. 1.

    Python code for these test problems and relevant instructions are available at: https://bitbucket.org/arahat/cfd-test-problem-suite.

  2. 2.

    Solution repeated using our framework.

References

  1. Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Global Optim. 13(4), 455–492 (1998)

    Article  MathSciNet  Google Scholar 

  2. Naujoks, B., Willmes, L., Bäck, T., Haase, W.: Evaluating multi-criteria evolutionary algorithms for airfoil optimisation. In: Guervós, J.J.M., Adamidis, P., Beyer, H.-G., Schwefel, H.-P., Fernández-Villacañas, J.-L. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 841–850. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45712-7_81

    Chapter  Google Scholar 

  3. Keane, A.J.: Statistical improvement criteria for use in multiobjective design optimization. AIAA J. 44(4), 879–891 (2006)

    Article  Google Scholar 

  4. Forrester, A.I.J., Bressloff, N.W., Keane, A.J.: Optimization using surrogate models and partially converged computational fluid dynamics simulations. In: Proceedings of Mathematical, Physical and Engineering Sciences, vol. 462, no. 2071, pp. 2177–2204 (2006)

    Google Scholar 

  5. Leary, S.J., Bhaskar, A., Keane, A.J.: A derivative based surrogate model for approximating and optimizing the output of an expensive computer simulation. J. Global Optim. 30(1), 39–58 (2004)

    Article  MathSciNet  Google Scholar 

  6. Foli, K., Okabe, T., Olhofer, M., Jin, Y., Sendhoff, B.: Optimization of micro heat exchanger: CFD, analytical approach and multi-objective evolutionary algorithms. Int. J. Heat Mass Transf. 49(5), 1090–1099 (2006)

    Article  Google Scholar 

  7. Hasbun, J.E.: Classical Mechanics with MATLAB Applications. Jones & Bartlett Publishers, Burlington (2012)

    Google Scholar 

  8. Shah, A., Ghahramani, Z.: Pareto frontier learning with expensive correlated objectives. In: International Conference on Machine Learning, pp. 1919–1927 (2016)

    Google Scholar 

  9. Daniels, S.J., Rahat, A.A.M., Tabor, G., Fieldsend, J., Everson, R.: Shape optimisation using computational fluid dynamics and evolutionary algorithms. In: 11th OpenFOAM Workshop, Portugal (2016)

    Google Scholar 

  10. Daniels, S.J., Rahat, A.A.M., Tabor, G., Fieldsend, J., Everson, R.: Automatic shape optimisation of the turbine-99 draft tube. In: 12th OpenFOAM Workshop, Exeter (2017)

    Google Scholar 

  11. Brochu, E., Cora, V.M., De Freitas, N.: A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. arXiv preprint arXiv:1012.2599 (2010)

  12. González, J., Dai, Z., Hennig, P., Lawrence, N.: Batch Bayesian optimization via local penalization. In: Artificial Intelligence and Statistics, pp. 648–657 (2016)

    Google Scholar 

  13. Shahriari, B., Swersky, K., Wang, Z., Adams, R.P., De Freitas, N.: Taking the human out of the loop: a review of Bayesian optimization. Proc. IEEE 104(1), 148–175 (2016)

    Article  Google Scholar 

  14. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization, pp. 105–145. Springer, London (2005). https://doi.org/10.1007/1-84628-137-7_6

    Chapter  MATH  Google Scholar 

  15. Liang, J., Qu, B., Suganthan, P.: Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Technical report, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Nanyang Technological University, Singapore (2014)

    Google Scholar 

  16. Chen, Q., Liu, B., Zhang, Q., Liang, J., Suganthan, P., Qu, B.: Problem definitions and evaluation criteria for CEC 2015 special session on bound constrained single-objective computationally expensive numerical optimization. Technical report, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Nanyang Technological University (2015)

    Google Scholar 

  17. Weller, H., Tabor, G., Jasak, H., Fureby, C.: A tensorial approach to computational continuum mechanics using object orientated techniques. Comput. Phys. 12(6), 620–631 (1998)

    Article  Google Scholar 

  18. Daniels, S.J., Rahat, A.A.M., Tabor, G., Fieldsend, J., Everson, R.: A review of shape distortion methods available in the OpenFoam framework for automated design optimisation. In: Nóbrega, J., Jasak, H. (eds.) OpenFOAM: Selected Papers of the 11th Workshop. Springer, Heidelberg (2018, in Press)

    Google Scholar 

  19. Catmull, E., Clark, J.: Recursively generated B-spline surfaces on arbitrary topological meshes. Comput.-Aided Des. 10(6), 350–355 (1978)

    Article  Google Scholar 

  20. Arfken, G.B., Weber, H.J., Harris, F.E.: Mathematical Methods for Physicists: A Comprehensive Guide. Academic Press, Cambridge (2011)

    MATH  Google Scholar 

  21. Pitz, R., Daily, J.: An experimental study of combustion the turbulent structure of a reacting shear layer formed at a rearward-facing step. Technical report, University of California, Berkeley, California, USA, NASA Contractor Report 165427, August 1981

    Google Scholar 

  22. Nilsson, U.: Description of adjointShapeOptimizationFoam and how to implement new objective functions. Technical report, Chalmers University of Technology (2014)

    Google Scholar 

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Acknowledgements

This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant (reference number: EP/M017915/1).

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Correspondence to Steven J. Daniels or Alma A. M. Rahat .

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Daniels, S.J., Rahat, A.A.M., Everson, R.M., Tabor, G.R., Fieldsend, J.E. (2018). A Suite of Computationally Expensive Shape Optimisation Problems Using Computational Fluid Dynamics. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11102. Springer, Cham. https://doi.org/10.1007/978-3-319-99259-4_24

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  • DOI: https://doi.org/10.1007/978-3-319-99259-4_24

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