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Applied Intelligence

, Volume 47, Issue 2, pp 362–381 | Cite as

Improved multi-objective particle swarm optimization algorithm for optimizing watermark strength in color image watermarking

  • Nitin SaxenaEmail author
  • K. K. Mishra
Article

Abstract

A variant of Multi-Objective Particle Swarm Optimization (MOPSO), named as MOPSOtridist, is proposed in this paper. To improve the performance of existing MOPSO algorithms, new leader selection strategy and personal best (pbest) replacement scheme is introduced in this variant. In existing MOPSO algorithms, selection of leader is done only on the basis of particle’s current position and particle movement history is not taken into account. In MOPSOtridist, this information is used by selecting the most appropriate leader from the archive which has minimum distance from the region where the particle had visited recently. The proposed leader selection strategy efficiently explores the whole Pareto front by attracting the distinct regions explored by different particles. Additionally, a pbest replacement scheme is introduced to handle its stagnation at local optimal solutions by replacing the stagnated pbest of the particle with a new archive member, which is at maximum distance from the particle’s local optimal solutions. This will add diversity and forces those particles to explore other regions. For measuring the distance between particle’s regions and archive member, triangular distance (tridist) is used. The proposed MOPSOtridist algorithm along with other widely known variants of MOPSO, are tested exhaustively over two series of benchmark functions ZDT and DTLZ. The experiment results show that the proposed algorithm outperforms other MOPSO algorithms significantly in terms of standard performance metrics. Further, the proposed variant MOPSOtridist is applied to digital image watermarking problem for colour images in RGB colour space. Results demonstrate that MOPSOtridist efficiently produce optimal values of watermark strength to achieve good trade-offs between imperceptibility and robustness objectives.

Keywords

MOPSO Leader selection Triangular distance Watermarking Imperceptibility Robustness 

References

  1. 1.
    Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings IEEE International Conference of Neural Networking, vol 4, Perth, Australia, pp 1942–1948Google Scholar
  2. 2.
    Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of 6th International Symposium on Micromachine Human Science, Nagoya, Japan, pp 39–43Google Scholar
  3. 3.
    Li X (2003) A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Proceedings of Genetic Evolutionary Computation, pp 37–48Google Scholar
  4. 4.
    Zhang XH, Meng HY, Jiao LC (2005) Intelligent particle swarm optimization in multiobjective optimization, pp 714–719Google Scholar
  5. 5.
    Pulido GT, Coello Coello CA (2004) Using clustering techniques to improve the performance of a particle swarm optimizer. In: Proceedings of Genetic Evolutionary Computation, pp 225–237Google Scholar
  6. 6.
    Yen GG, Leong WF (2009) Dynamic multiple swarms in multiobjective particle swarm optimization. IEEE Trans Syst, Man, Cybern A, Syst, Hum 39(4):890–911CrossRefGoogle Scholar
  7. 7.
    Chow CK, Yuen SY (2012) A multiobjective evolutionary algorithm that diversifies population by its density. IEEE Trans Evol Comput 16(2):149–172CrossRefGoogle Scholar
  8. 8.
    Deb K (2001) Multiobjective optimization using evolutionary algorithms. Wiley, NY, USAzbMATHGoogle Scholar
  9. 9.
    Yen GG, Leong WF (2009) Dynamic multiple swarms in multiobjective particle swarm optimization. IEEE Trans Syst, Man, Cybern A, Syst, Hum 39(4):890–911CrossRefGoogle Scholar
  10. 11.
    Fieldsend JE, Uk EQ, Singh S (2002) A Multi-Objective Algorithm based upon Particle Swarm Optimisation, an Efficient Data Structure and Turbulence. Proceedings of the 2002 U. K. Workshop on Computational Intelligence, pp 37–44Google Scholar
  11. 12.
    Alvarez-Benitez JE, Everson RM, Fieldsend JE (2005) A MOPSO algorithm based exclusively on pareto dominance concepts. Evolutionary Multi-Criterion Optimization, Springer, Berlin HeidelbergCrossRefzbMATHGoogle Scholar
  12. 13.
    Hu W, Yen GG (2013) Density estimation for selecting leaders and maintaining archive in MOSPO. In: Proceedings of IEEE Congress Evolutionary Computation, pp 181–188Google Scholar
  13. 14.
    Yen GG, He Z (2014) Performance Metrics Ensemble for Multiobjective Evolutionary Algorithms. IEEE Trans Evol Comput 18(1):131–144CrossRefGoogle Scholar
  14. 15.
    Coello Coello CA, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279CrossRefGoogle Scholar
  15. 16.
    Reyes-Sierra M, Coello CAC (2006) Multi-objective particle swarm Optimizers: A survey of the state-of-the-art. Int J Comput Intell Res 2(3):287–308MathSciNetGoogle Scholar
  16. 17.
    Pulido GT, Coello Coello CA (2004) Using clustering techniques to improve the performance of a particle swarm optimizer. In: Proceedings of Genetic Evolutionary Computation, pp 225– 237Google Scholar
  17. 18.
    Coello Coello CA, Lechuga MS (2002) MOPSO: A proposal for multiple objective particle swarm optimization. In: Proceedings of Congress Evolutionary Computation, pp 1051–1056Google Scholar
  18. 19.
    Huang VL, Suganthan PN, Liang JJ (2006) Comprehensive learning particle swarm optimizer for solving multiobjective optimization problems. Int J Intell Syst 21(2):209–226CrossRefzbMATHGoogle Scholar
  19. 20.
    Fieldsend JE (2004). Multi-objective particle swarm optimization methods, Department of Computer Science, University of Exeter, Devon, U.K., Technical Report. 418Google Scholar
  20. 21.
    Padhye N, Branke J, Mostaghim S (2009) Empirical comparison of MOPSO methods: Guide selection and diversity preservation. In: Proceedings of IEEE Congress Evolutionary Computation, pp 2516–2523Google Scholar
  21. 22.
    Padhye N (2009) Comparison of archiving methods in multi-objective particle swarm optimization (MOPSO): Empirical study. In: Proceedings of Genetic Evolutionary Computation, pp 1755–1756Google Scholar
  22. 23.
    Mostaghim S, Teich J (2003) Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In: Proceedings of IEEE Congress Swarm Intelligence Symposium, pp 26–33Google Scholar
  23. 24.
    Raquel CR, Nava PC (2005) An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of Genetic Evolutionary Computation, pp 257–264Google Scholar
  24. 25.
    Chiu S-Y et al (2007) Cross-searching strategy for multi-objective particle swarm optimization. In: 2007. CEC 2007. IEEE Congress on Evolutionary Computation. IEEEGoogle Scholar
  25. 26.
    Leung M-F et al (2014) A new strategy for finding good local guides in MOPSO. In: 2014 IEEE Congress on Evolutionary Computation (CEC). IEEEGoogle Scholar
  26. 27.
    Leung M-F et al (2015) A new algorithm based on PSO for Multi-Objective Optimization. In: 2015 IEEE Congress on Evolutionary Computation (CEC). IEEEGoogle Scholar
  27. 28.
    Saxena N, Tripathi A, Mishra KK, Misra AK (2015) Dynamic-PSO: An Improved Particle Swarm Optimizer. In: 2015 IEEE Congress on Evolutionary Computation (CEC). IEEEGoogle Scholar
  28. 29.
    Van den Bergh F (2002) An analysis of particle swarm optimizers. Ph.D. dissertation, Department of Computer Science, University of Pretoria, South AfricaGoogle Scholar
  29. 30.
    Branke J, Mostaghim S (2006) About selecting the personal best in multiobjective particle swarm optimization. In: Proceedings PPSN, pp 523–532Google Scholar
  30. 31.
    Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: Empirical results. Evol Comput 8(2):173–195CrossRefGoogle Scholar
  31. 32.
    Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multiobjective optimization test problems. In: Proceedings of IEEE Congress Evolutionary Computation, pp 825–830Google Scholar
  32. 33.
    Schott JR (1995) Fault tolerant design using single and multicriteria genetic algorithm optimization. Air Force Institute of Technolgy Wright-Patterson AFB, OHGoogle Scholar
  33. 34.
    Veldhuizen V, David A (1999). Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. No. AFIT/DS/ENG/99-01. Air Force Inst of Tech Wright-Pattersonafb OH School of EngineerinGGoogle Scholar
  34. 35.
    Sierra MR, Coello CAC (2004). A new multi-objective particle swarm optimizer with improved selection and diversity mechanisms, Technical Report, CINVESTAV-IPNGoogle Scholar
  35. 36.
    Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison- Welsey, Reading, MAzbMATHGoogle Scholar
  36. 37.
    Storn R, Price KV (1996) Minimizing the real functions of the ICEC 1996 contest by differential evolution. In: Proceedings of IEEE International Conference Evolutionary Computation, pp 842–844Google Scholar
  37. 38.
    Monemizadeh M, Seyedin SA (2009) Optimal DWT-SVD domain image watermarking using multi-objective evolutionary algorithms. World Congress on Computer Science and Information Engineering:259–263Google Scholar
  38. 39.
    Loukhaoukha K, Nabti M, Zebbiche K (2014) A robust SVD-based image watermarking using a multi-objective particle swarm optimization. Opto Electron Rev 22(1):45–54CrossRefGoogle Scholar
  39. 40.
    Hernandez JR, Amado M, Gonzalez FP (2000) DCT-domain watermarking techniques for still for still Images: Detector performance analysis and a new structure. IEEE Trans Image Process 9:55–68CrossRefGoogle Scholar
  40. 41.
    Langelaar G, Setyawan I, Lagendijk R (2000) Watermarking digital image and video data. IEEE Signal Process Mag 17(5):20–46CrossRefGoogle Scholar
  41. 42.
    Barni M, Bartolini F, De Rosa A, Piva A (2003) Optimal decoding and detection of multiplicative watermarks. IEEE Trans Signal Process 51(4):1118–1123CrossRefGoogle Scholar
  42. 43.
    Barni M, Bartolini F, De Rosa A, Piva A (2003) Optimal decoding and detection of multiplicative watermarks. IEEE Trans. Signal Processing 51(4):1118–1123CrossRefGoogle Scholar
  43. 44.
    Briassouli A, Strintzis MG (2004) Locally optimum nonlinearities for DCT watermark detection. IEEE Trans Image Process 13(2):1604–1617CrossRefGoogle Scholar
  44. 45.
    Nikolaidis A, Pitas I (2003) Asymptotically optimal detection for additive watermarking in the DCT and DWT domains. IEEE Trans Image Process 12(5):563–571CrossRefGoogle Scholar
  45. 46.
    Lai CC, Tsai CC (2010) Discrete wavelet transform and singular value decomposition. IEEE Trans Instrum Measur 59(11):3060–3063CrossRefGoogle Scholar
  46. 47.
    Ganic E, Eskicioglu AM (2004) Robust DWT-SVD domain image watermarking: embedding data in all frequencies. In: Proceedings Workshop Multimedia Security, Magdeburg, Germany, pp 166–174Google Scholar
  47. 48.
    Bhatnagar G, Raman B (2009) A new robust reference watermarking scheme based on DWT-SVD. Comput Stand Interfaces 31(5):1002–1013CrossRefGoogle Scholar
  48. 49.
    Rykaczewski R (2007) Comments on –An SVD-based watermarking scheme for protecting rightful ownership. IEEE Trans Multimed 9(2):421–423CrossRefGoogle Scholar
  49. 50.
    Hien TD, Chen Y-W, Nakao Z (2004) “Robust digital watermarking based on principal component analysis’. IJCIA 04(02)Google Scholar
  50. 51.
    Liu R, Tan T (2002) An SVD-based watermarking scheme for protecting rightful ownership. IEEE Trans Multimed 4(1):121–128CrossRefGoogle Scholar
  51. 52.
    un R-S, Horng S-J, Lai J-L, Kao T-W, Chen RJ (2012) An improved SVD based watermarking technique for copy right protection. Expert Syst Appl 39:673–689CrossRefGoogle Scholar
  52. 53.
    Robert S, Torrie J, Dickey D (1997) Principles and procedures of statistics: A biometrical approach. McGraw-Hill, NY, USAGoogle Scholar
  53. 54.
    Zheng Y-J, Chen S-Y (2013) Cooperative particle swarm optimization for multiobjective transportation planning. Applied Intelligence:202–216Google Scholar
  54. 55.
    Lee K-B, Kim J-H (2013) Multiobjective particle swarm optimization with preference-based sort and its application to path following footstep optimization for humanoid robots. IEEE Transactions on Evolutionary Computation:755–766Google Scholar
  55. 56.
    Zheng Y-J, Ling H-F, Xue J-Y, Chen S-Y (2014) Population classification in fire evacuation: a multiobjective particle swarm optimization approach. IEEE Transactions on Evolutionary Computation:70–81Google Scholar
  56. 57.
    Ameli A, Bahrami S, Khazaeli F, Haghifam M-R (2014) A multiobjective particle swarm optimization for sizing and placement of DGs from DG owner’s and distribution company’s viewpoints. IEEE Transactions on Power Delivery:1831–1841Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Computer Science & Engineering DepartmentMotilal Nehru National Institute of Technology AllahabadAllahabadIndia

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