Advertisement

IBEA-SVM: An Indicator-based Evolutionary Algorithm Based on Pre-selection with Classification Guided by SVM

  • Hao-ran Li
  • Fa-zhi HeEmail author
  • Xiao-hu Yan
Article
  • 3 Downloads

Abstract

Multi-objective optimization has many important applications and becomes a challenging issue in applied science. In typical multi-objective optimization algorithms, such as Indicator-based Evolutionary Algorithm (IBEA), all of parents and offspring need to be evaluated in every generation, and then the better solutions of them are selected as the next generation candidates. This leads to a large amount of calculation and slows down convergence rate for IBEA related applications. Our discovery is that the evaluation of evolutionary algorithm is a binary classification in nature and a meaningful preselection method will accelerate the convergence rate. Therefore this paper presents a novel preselection approach to improve the performance of the IBEA, in which a SVM (Support Vector Machine) classifier is adopted to sort the promising solutions from unpromising solutions and then the newly generated solutions are conversely added as train sample to increase the accuracy of the classifier. Firstly, we proposed an online and asynchronous training method for SVM model with empirical kernel. The initial population is randomly generated among population size, which is used as initial training. In the process of training, SVM classifier is modified and perfected to adapt to the evolutionary algorithm sample. Secondly, the classifier divides all the new generated solutions from the whole solution spaces into promising solutions and unpromising ones. And only the promising ones are forwarded for evaluation. In this way, the evaluation time can be greatly reduced and the solution quality can be obviously improved. Thirdly, the promising and unpromising solutions are labeled as new train samples in next generation to refine classifier model. A number of experiments on benchmark functions validates the proposed approach. The results show that IBEA-SVM can significantly outperform previous works.

Keywords

multi-objective optimization SVM IBEA training classification 

MR Subject Classification

35B35 65L15 60G40 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bader J, Zitzler E. HypE: An algorithm for fast hypervolume–based many–objective optimization, Evolutionary Computation, 2011, 19(1): 45–76.Google Scholar
  2. [2]
    Bandaru S, Ng A, Deb K. On the performance of classification algorithms for learning pareto–dominance relations, Evolutionary Computation (CEC), 2014, pp 1139–1146, IEEE.Google Scholar
  3. [3]
    Barnhart C, Johnson E, Jin Y. Branch–and–Price: Column Generation for Solving Huge Integer Programs, Operations Research, 1998, 46(3): 316–329.MathSciNetzbMATHGoogle Scholar
  4. [4]
    Brockhoff D, Zitzler E. Improving hypervolume–based multiobjective evolutionary algorithms by using objective reduction methods, Evolutionary Computation (CEC), 2007, pp 2086–2093, IEEE.Google Scholar
  5. [5]
    Chang C, Lin C. LIBSVM: a library for support vector machines, ACM Transactions on Intelligent Systems and Technology (TIST), 2(3), 27.Google Scholar
  6. [6]
    Chen Y, He F, Wu Y, et al. A local start search algorithm to compute exac. Hausdorff Distance for arbitrary point sets, Pattern Recognition, 2017, 67: 139–148.Google Scholar
  7. [7]
    Chen X, He F, Yu H. A Matting Method Based on Full Feature Coverage, Multimedia Tools and Applications, DOI:10.1007/s11042–018–6690–1.Google Scholar
  8. [8]
    Coello C, Lamont G, Veldhuizen D. Evolutionary algorithms for solving multi–objective problems, 2007, New York: Springer.zbMATHGoogle Scholar
  9. [9]
    Coello C. Twenty Years of Evolutionary Multi–Objective Optimization: A Historical View of the Field, IEEE Computational Intelligence Magazine, 2006, 1(1): 28–36.MathSciNetGoogle Scholar
  10. [10]
    Corne D W, Jerram N R, Knowles J D, et al. PESA–II: region–based selection in evolution–ary multiobjective optimization, Conference on Genetic and Evolutionary Computation, Morgan Kaufmann Publishers Inc, 2001: 283–290.Google Scholar
  11. [11]
    Das S, Suganthan P. Differential evolution: A survey of the state–of–the–art, IEEE transactions on evolutionary computation, 2011, 15(1), 4–31.Google Scholar
  12. [12]
    Deb K, Thiele L, Laumanns M, et al. Scalable multi–objective optimization test problems, Evolu–tionary Computation, 2002, CEC'02, Proceedings of the 2002 Congress on (Vol 1, pp 825–830), IEEE.Google Scholar
  13. [13]
    Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm: NSGA–II, IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182–197.Google Scholar
  14. [14]
    Fan Z, Hu K, Li F. Multi–objective evolutionary algorithms embedded with machine learning A survey, Evolutionary Computation (CEC), 2016, pp 1262–1266, IEEE.Google Scholar
  15. [15]
    Gui W, Zhang H. Asymptotic properties and expectation–maximization algorithm for maximum likelihood estimates of the parameters from Weibull–Logarithmic model, Applied Mathematics–A Journal of Chinese Universities, 2016, 31(4): 425–438.MathSciNetzbMATHGoogle Scholar
  16. [16]
    Kim W, Xiong S, Liang Z. Effect of Loading Symbol of Online Video on Perception of Waiting Time, International Journal of Human–Computer Interaction, 2017(5).Google Scholar
  17. [17]
    Konak A, Coit W. Multi–objective optimization using genetic algorithms: A tutorial, Reliability Engineering System Safety, 2006, 91(9): 992–1007.Google Scholar
  18. [18]
    Laumanns M. SPEA2. Improving the Strength Pareto Evolutionary Algorithm, Technical Report Gloriastrasse, 2001.Google Scholar
  19. [19]
    Li K, He F, Yu H, et al. A parallel and robust object tracking approach synthesizing adap–tive bayesian learning and improved incremental subspace learning, Frontiers Comput Sci, DOI: 10.1007/s11704–018–6442–4.Google Scholar
  20. [20]
    Li K, He F Z, Yu H P. Robust Visual Tracking based on convolutional features with illumination and occlusion handing, Journal of Computer Science and Technology, 2018, 33(1): 223–236.Google Scholar
  21. [21]
    Li K, He F, Yu H, et al. A correlative classifiers approach based on particle filter and sample set for tracking occluded target, Applied Mathematics–A Journal of Chinese Universities, 2017, 32(3): 294–312.MathSciNetGoogle Scholar
  22. [22]
    Li W, Mcmahon C. A Simulated Annealing–based Optimization Approach for Integrated Process Planning and Scheduling, International Journal of Computer Integrated Manufacturing, 2007, 20(1): 80–95.Google Scholar
  23. [23]
    Lin X, Zhang Q, Kwongs S. A decomposition based multiobjective evolutionary algorithm with classification, IEEE Congress on Evolutionary Computation, 2016, pp 3292–3299, IEEE.Google Scholar
  24. [24]
    Lv X, He F, Cai W, et al. A string–wise CRDT algorithm for smart and large–scale collaborative editing systems, Advanced Engineering Informatics, 2017, 33: 397–409.Google Scholar
  25. [25]
    Lv X, He F, Cai W, et al. Supporting selective undo of string–wise operations for collaborative editing systems, Future Generation Computer Systems, 2018, 82: 41–62.Google Scholar
  26. [26]
    Lv X, He F, Cheng Y et al. A novel CRDT–based synchronization method for real–time collabo–rative CA. Systems, Advanced Engineering Informatics, 2018, 38: 381–391.Google Scholar
  27. [27]
    Ni B, He F, Pan Y, et al. Using shapes correlation for active contour segmentation of uterine fibroid ultrasound images in computer–aided therapy, Applied Mathematics–A Journal of Chinese Universities, 2016, 31(1): 37–52.MathSciNetzbMATHGoogle Scholar
  28. [28]
    Sun J, He F, Chen Y, Chen X et al. A multiple template approach for robust tracking of fast motion target, Applied Mathematics–A Journal of Chinese Universities, 2016, 31(2): 177–197.MathSciNetzbMATHGoogle Scholar
  29. [29]
    Tao Q, Zhang M. Mathematical theory of signal analysis vs complex analysis method of harmonic analysis, Applied Mathematics–A Journal of Chinese Universities, 2013, 28(4): 505–530.zbMATHGoogle Scholar
  30. [30]
    Trivedi A, Srinivasan D, Sanyal K, Ghosh A. A Survey of Multiobjective Evolutionary Algorithms based on Decomposition, IEEE Transactions on Evolutionary Computation, 2017, 21(3): 440–462.Google Scholar
  31. [31]
    Van L, Melab N, Talbi E. Gpu computing for parallel local search metaheuristic algorithms, Journal of Supercomputing, 2016, 72(6): 2394–2416.zbMATHGoogle Scholar
  32. [32]
    Wang S, Lu X, Li X, Li W. A systematic approach of process planning and scheduling optimization for sustainable machining, Journal of Cleaner Production, 2015, 87(1): 914–929.Google Scholar
  33. [33]
    Wu Y, He F, Zhang D, et al. Service–oriented feature–based data exchange for cloud–based design and manufacturing, IEEE Transactions on Services Computing, 2018,11: 341–353.Google Scholar
  34. [34]
    Xiong S, Zhao J, et al. A computer–aided design system for foot–feature–based shoe last customiza–tion, International Journal of Advanced Manufacturing Technology, 2010, 46(1–4): 11–19.Google Scholar
  35. [35]
    Yan X, He F, Chen Y. A novel hardware/software partitioning method based on position disturbed particle swarm optimization with invasive weed optimization, Journal of Computer Science and Technology, 2017, 32(2): 340–355.MathSciNetGoogle Scholar
  36. [36]
    Yan X, He F, Hou N, et al. An effcient particle swarm optimization for large–scale hard–ware/software co–design system, International Journal of Cooperative Information Systems, 2018, 27(1): 1741001.Google Scholar
  37. [37]
    Yu H, He F, Pan Y, et al. A novel region–based active–contour model via local patch similarity measure for image segmentation, Multimedia Tools and Appliations, 2018, 77(18), 24097–24119.Google Scholar
  38. [38]
    Yu H, He F, Pan Y. A Novel Segmentation Model for Medical Images with Intensity Inhomogeneity Based on Adaptive Perturbation, Multimedia Tools and Applications, DOI: 10.1007/s11042–018–6735–5.Google Scholar
  39. [39]
    Zhang D J, He F Z, Han S H, et al. Quantitative optimization of interoperability during feature–based data exchange, Integrated Computer–Aided Engineering, 2016, 23(1): 31–50.Google Scholar
  40. [40]
    Zhang D, He F, Han S, et al. An effcient approach to directly compute the exact Hausdorff distance for 3D point sets, Integrated Computer–Aided Engineering, 2017, 24(3): 261–277.Google Scholar
  41. [41]
    Zhang J, Zhou A, Zhang G. A classification and Pareto domination based multiobjective evolu–tionary algorithm, Evolutionary Computation, 2015, pp 2883–2890, IEEE.Google Scholar
  42. [42]
    Zhang Q, Zhou A, Zhao S. Multiobjective optimization test instances for the CEC 2009 spe–cial session and competition, University o. Essex, Colchester, UK and Nanyang technological University, Singapore, special session on performance assessment of multi–objective optimization algorithms, technical report, 2008, 264.Google Scholar
  43. [43]
    Zhang Q, Li H. MOEA/D:A Multiobjective Evolutionary Algorithm Based on Decomposition, IEEE transactions on evolutionary computation, 2007, 11(6): 712–731.Google Scholar
  44. [44]
    Zhang S, He F, Ren W, Yao J. Joint learning of image detail and transmission map for single image dehazing, The Visual Computer, DOI 10.1007/s00371–018–1612–9.Google Scholar
  45. [45]
    Zhou Y, He F, Qiu Y. Optimization of parallel iterated local search algorithms on graphics pro–cessing unit, Journal of Supercomputing, 2016, 72(6): 2394–2416.Google Scholar
  46. [46]
    Zhou Y, He F, Qiu Y. Dynamic Strategy based Parallel Ant Colony Optimization on GPUs for TSPs, Science China Information Sciences, 2017, 60(6): 068–102.Google Scholar
  47. [47]
    Zhou Y, He F, Qiu Y. Parallel ant colony optimization on multi–core simd cpus, Future Genera–tion Computer Systems, 2018, 79(2): 473–487.Google Scholar
  48. [48]
    Zhu H. Avoiding Con icts by Group Role Assignment, IEEE Trans on Systems, Man, and Cy–bernetics: Systems, 2016, 46(4): 535–547.Google Scholar
  49. [49]
    Zhu H. Role–Based Collaboration and the E–CARGO: Revisiting the Developments of the Last Decade, IEEE Systems, Man, and Cybernetics Magazine, 2015, 1(3): 27–35.Google Scholar
  50. [50]
    Zhu H, Zhou M. Role–Based Collaboration and its Kernel Mechanisms, IEEE Trans on Systems, Man, and Cybernetics, Part C: Applications and Reviews, 2006, 36(4): 578–589.Google Scholar
  51. [51]
    Zitzler E, Kunzli S. Indicator–Based Selection in Multiobjective Search, Lecture Notes in Com–puter Science, 2004, 3242: 832–842.Google Scholar
  52. [52]
    Zitzler E, Thiele L. Multiobjective optimization using evolutionary algorithms A comparative case study, Int Conf Parallel Problem Solving from Nature (PPSN–V), 1998, 1498(3): 292–301.Google Scholar
  53. [53]
    Zitzler E, Thiele L, Laumanns M. Performance assessment of multiobjective optimizers: An analysis and review, IEEE Transactions on Evolutionary Computation, 2003, 7(2): 117–132.Google Scholar
  54. [54]
    Zitzler E, Knzli S. Indicator–Based Selection in Multiobjective Search, 2004 Parallel Problem Solving from Nature.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics 2019

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyWuhan UniversityWuhanChina
  2. 2.State Key Laboratory of Digital Manufacturing Equipment and TechnologyHuazhong UniversityWuhanChina

Personalised recommendations