Advertisement

Improving the Energy Efficiency of Evolutionary Multi-objective Algorithms

  • J. J. Moreno
  • G. OrtegaEmail author
  • E. Filatovas
  • J. A. Martínez
  • E. M. Garzón
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10049)

Abstract

Problems for which many objective functions have to be simultaneously optimized can be easily found in many fields of science and industry. Solving this kind of problems in a reasonable amount of time while taking into account the energy efficiency is still a relevant task. Most of the evolutionary multi-objective optimization algorithms based on parallel computing are focused only on performance. In this paper, we propose a parallel implementation of the most time consuming parts of the Evolutionary Multi-Objective algorithms with major attention to energy consumption. Specifically, we focus on the most computationally expensive part of the state-of-the-art evolutionary NSGA-II algorithm – the Non-Dominated Sorting (NDS) procedure. GPU platforms have been considered due to their high acceleration capacity and energy efficiency. A new version of NDS procedure is proposed (referred to as EFNDS). A made-to-measure data structure to store the dominance information has been designed to take advantage of the GPU architecture. NSGA-II based on EFNDS is comparatively evaluated with another state-of-art GPU version, and also with a widely used sequential version. In the evaluation we adopt a benchmark that is scalable in the number of objectives as well as decision variables (the DTLZ test suite) using a large number of individuals (from 500 up to 30000). The results clearly indicate that our proposal achieves the best performance and energy efficiency for solving large scale multi-objective optimization problems on GPU.

Keywords

Pareto Front Thread Block Objective Vector Compute Unify Device Architecture Dominance Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Brodtkorb, A.R., Trond, R.H., Sætra, M.L.: Graphics processing unit (GPU) programming strategies and trends in GPU computing. J. Parallel Distrib. Comput. 73(1), 4–13 (2013)CrossRefGoogle Scholar
  2. 2.
    Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J.: PESA-II: region-based selection in evolutionary multiobjective optimization. In: GECCO, pp. 283–290 (2001)Google Scholar
  3. 3.
    Deb, K.: Software Developed at KanGAL: Multi-objective NSGA-II code in C. Revision 1.1.6 (2011). http://www.iitk.ac.in/kangal/codes.shtml
  4. 4.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE T. Evolut. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  5. 5.
    Deb, K., Sundar, J., Bhaskara Rao, N.U.: Reference point based multi-objective optimization using evolutionary algorithms. Int. J. Comput. Intell. Res. 2(3), 273–286 (2006)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: WCCI, pp. 825–830 (2002)Google Scholar
  7. 7.
    Dehuri, S., Ghosh, A., Mall, R.: Parallel multi-objective genetic algorithm for classification rule mining. IETE J. Res. 53(5), 475–483 (2007)CrossRefGoogle Scholar
  8. 8.
    Domínguez, J., Montiel, O., Sepúlveda, R., Medina, N.: High performance architecture for NSGA-II. In: Castillo, O., Melin, P., Kacprzyk, J. (eds.) Recent Advances on Hybrid Intelligent Systems, pp. 451–461. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Durillo, J.J., Nebro, A.J., Luna, F., Alba, E.: A study of master-slave approaches to parallelize NSGA-II. In: IPDPS, pp. 1–8. IEEE (2008)Google Scholar
  10. 10.
    Fang, H., Wang, Q., Tu, Y., Horstemeyer, M.F.: An efficient non-dominated sorting method for evolutionary algorithms. Evol. Comput. 16(3), 355–384 (2008)CrossRefGoogle Scholar
  11. 11.
    Filatovas, E., Kurasova, O., Sindhya, K.: Reference point based multi-objective optimization using evolutionary algorithms. Informatica 26(1), 33–50 (2015)CrossRefGoogle Scholar
  12. 12.
    Gupta, S., Tan, G.: A scalable parallel implementation of evolutionary algorithms for multi-objective optimization on GPUs. In: CEC, pp. 1567–1574. IEEE (2015)Google Scholar
  13. 13.
    Harris, M.: Maxwell: the most advanced CUDA GPU ever made (2014)Google Scholar
  14. 14.
    Hennessy, J.L., Patterson, D.A.: Computer Architecture - A Quantitative Approach, 5th edn. Morgan Kaufmann, San Francisco (2012)zbMATHGoogle Scholar
  15. 15.
    Huang, S., Xiao, S., Feng, W.: On the energy efficiency of graphics processing units for scientific computing. In: IEEE IPDPS 2009, pp. 1–8 (2009)Google Scholar
  16. 16.
    Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. IEEE T. Evolut. Comput. 10(5), 477–506 (2006)CrossRefzbMATHGoogle Scholar
  17. 17.
    Jensen, M.T.: Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms. IEEE T. Evolut. Comput. 7(5), 503–515 (2003)CrossRefGoogle Scholar
  18. 18.
    Knowles, J.D., Corne, D.W.: Approximating the non-dominated front using the Pareto archived evolution strategy. Evol. Comput. 8(2), 149–172 (2000)CrossRefGoogle Scholar
  19. 19.
    Lančinskas, A., Žilinskas, J.: Approaches to parallelize pareto ranking in NSGA-II algorithm. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) PPAM 2011. LNCS, vol. 7204, pp. 371–380. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-31500-8_38 CrossRefGoogle Scholar
  20. 20.
    Lančinskas, A., Żilinskas, J.: Solution of multi-objective competitive facility location problems using parallel NSGA-II on large scale computing systems. In: Manninen, P., Öster, P. (eds.) PARA 2012. LNCS, vol. 7782, pp. 422–433. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-36803-5_31 CrossRefGoogle Scholar
  21. 21.
    McClymont, K., Keedwell, E.: Deductive sort and climbing sort: new methods for non-dominated sorting. Evol. Comput. 20(1), 1–26 (2012)CrossRefGoogle Scholar
  22. 22.
    Miettinen, K.: Nonlinear Multiobjective Optimization. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  23. 23.
    Moreno, J.J., Ortega, G., Filatovas, E., Martínez, J.A., Garzón, E.M.: Using low-power platforms for evolutionary multi-objective optimization algorithms. J. Supercomput (2016). doi: 10.1007/s11227-016-1862-0 Google Scholar
  24. 24.
    Munshi, A., Gaster, B., Mattson, T.G., Fung, J., Ginsburg, D.: OpenCL Programming Guide, 1st edn. Addison-Wesley Professional, Boston (2011)Google Scholar
  25. 25.
    NVIDIA. NVIDIA’s next generation CUDA compute architecture: Kepler GK110 (2012)Google Scholar
  26. 26.
    NVIDIA. CUDA C programming guide. version 7.0 (2015)Google Scholar
  27. 27.
    Ortega, G., Filatovas, E., Garzón, E.M., Casado, L.G.: Non-dominated sorting procedure for pareto dominance ranking on multicore CPU and/or GPU. J. Global Optim. (2016). doi: 10.1007/s10898-016-0468-7 Google Scholar
  28. 28.
    Shi, C., Chen, M., Shi, Z.: A fast nondominated sorting algorithm. In: ICNN, vol. 3, pp. 1605–1610. IEEE (2005)Google Scholar
  29. 29.
    Smutnicki, C., Rudy, J., Żelazny, D.: Very fast non-dominated sorting. Decision Making Manufact. Serv. 8(1–2), 13–23 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE T. Evolut. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar
  31. 31.
    Zhang, X., Ye, T., Cheng, R., Jin, Y.: An efficient approach to non-dominated sorting for evolutionary multi-objective optimization. IEEE T. Evolut. Comput. 19(2), 201–213 (2015)CrossRefGoogle Scholar
  32. 32.
    Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-30217-9_84 CrossRefGoogle Scholar
  33. 33.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Zurich, Switzerland (2001)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • J. J. Moreno
    • 1
  • G. Ortega
    • 1
    Email author
  • E. Filatovas
    • 2
  • J. A. Martínez
    • 1
  • E. M. Garzón
    • 1
  1. 1.Informatics DepartmentUniversity of AlmeríaAlmeríaSpain
  2. 2.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania

Personalised recommendations