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Comparison of Various Approaches in Multi-objective Particle Swarm Optimization (MOPSO): Empirical Study

  • Swagatika Devi
  • Alok Kumar JagadevEmail author
  • Sachidananda Dehuri
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 592)

Abstract

This chapter presents a study of particle swarm optimization (PSO) method in multi-objective optimization problems. Many of these methods have focused on improving characteristics like convergence, diversity, and computational times by proposing effective ‘archiving’ and ‘guide selection’ techniques. What has still been lacking is an empirical study of these proposals in a common frame-work. In this chapter, an attempt to analyze these methods has been made; discussing their strengths and weaknesses. A multi-objective particle swarm optimization (MOPSO) algorithm, named dynamic multiple swarms in MOPSO is compared with other well known MOPSO techniques in which the number of swarms are adaptively adjusted throughout the search process via dynamic swarm strategy. The strategy allocates an appropriate number of swarms as required to support convergence and diversity criteria among the swarms. Additional novel designs include a PSO updating mechanism to better manage the communication within a swarm and among swarms and an objective space compression and expansion strategy to progressively exploit the objective space during the search process. Comparative study shows that the performance of the variant is competitive in comparison to the selected algorithms on standard benchmark problems. A dynamic MOPSO approach is compared and validated using several test functions and metrics taken from the standard literatures on evolutionary multi-objective optimization. Results indicate that the approach is highly competitive and that can be considered a viable alternative to solve multi-objective optimization problems.

Keywords

Particle swarm optimization MOPSO Dynamic swarm strategy Guide selection Archiving 

References

  1. 1.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)CrossRefGoogle Scholar
  2. 2.
    Conover, W.J.: Practical Nonparametric Statistics, 3rd edn, pp. 272–286. Wiley, New York (1999)Google Scholar
  3. 3.
    Van Veldhuizen, D.A., Lamount, G.B.: Multiobjective evolutionary algorithm research: a history and analysis. Department of Electrical and Computer Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH, Technical Report TR-98-03 (1998)Google Scholar
  4. 4.
    Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms—Part I: a unified formulation. IEEE Trans. Syst., Man, Cybern. A, Syst., Hum. 28(1), 26–37 (1998)CrossRefGoogle Scholar
  5. 5.
    Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms—Part II: application example. IEEE Trans. Syst., Man, Cybern. A, Syst., Hum. 28(1), 38–47 (1998)CrossRefGoogle Scholar
  6. 6.
    Venkatraman, S., Yen, G.G.: A generic framework for constrained optimization using genetic algorithms. IEEE Trans. Evol. Comput. 9(4), 424–435 (2005)CrossRefGoogle Scholar
  7. 7.
    de Lima, P., Yen, G.G.: Multiple objective evolutionary algorithm for temporal linguistic rule extraction. ISA Trans. 44(2), 315–327 (2005)CrossRefGoogle Scholar
  8. 8.
    Zitzler, E.: Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. Dissertation, Swiss Federal Institute Technology, Zurich (1999)Google Scholar
  9. 9.
    Goldstein, M.L., Yen, G.G.: Using evolutionary algorithms for defining the sampling policy of complex n-partite networks. IEEE Trans. Knowl. Data Eng. 17(6), 762–773 (2005)CrossRefGoogle Scholar
  10. 10.
    Buche, D., Muller, S., Koumoutsakos, P.: Self-adaptation for multi-objective evolutionary algorithms. In: Fonseca, M.C., Fleming, J.P., Zitzler, E., Deb, K., Thiele, L. (eds.) Second International Conference on Evolutionary Multi-Criterion Optimization, EMO 2003. Lecture Notes in Computer Science, vol. 2632, pp. 267–281. Springer, Faro April 2003Google Scholar
  11. 11.
    Chow, Chi-kin., Tsui, Hung-tat .: Autonomous agent response learning by a multi-species particle swarm optimization. In: Congress on Evolutionary Computation (CEC’2004), Portland, June 2004, vol. 1, pp. 778–785. IEEE Service CenterGoogle Scholar
  12. 12.
    Srinivasan, D., Seow, H.T.: Particle swarm inspired evolutionary algorithm (PS-EA) for multiobjective optimization problem. In: Congress on Evolutionary Computation (CEC’2003), Canberra, December 2003, vol. 3, pp. 2292–2297. IEEE PressGoogle Scholar
  13. 13.
    Salazar-Lechuga, M., Rowe, J.: Particle swarm optimization and fitness sharing to solve multi-objective optimization problems. In: Congress on Evolutionary Computation (CEC’2005), Edinburgh, September 2005, pp. 1204–1211. IEEE PressGoogle Scholar
  14. 14.
    Schaffer, D.J.: Multiple objective optimization with vector evaluated genetic algorithms. Ph.D. Thesis, Vanderbilt University (1984)Google Scholar
  15. 15.
    Schaffer, D.J.: Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the First International Conference on Genetic Algorithms and their Applications, pp. 93–100. Lawrence Erlbaum (1985)Google Scholar
  16. 16.
    Shi, Y., Eberhart, R.: Empirical study of particle swarm optimization. In: Congress on Evolutionary Computation (CEC’1999), Piscataway, NJ, (1999), pp. 1945–1950. IEEE PressGoogle Scholar
  17. 17.
    Clerc, M., Kennedy, J.: The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evol. Comput. 6(1), 58–73 (2002)CrossRefGoogle Scholar
  18. 18.
    Goldberg, E.D., Richardson, J.: Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the Second International Conference on Genetic Algorithms, pp. 41–49. Lawrence Erlbaum Associates (1987)Google Scholar
  19. 19.
    Tan, K.C., Lee, T.H., Khor, E.F.: Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization. IEEE Trans. Evol. Comput. 5(6), 565–588 (2001)CrossRefGoogle Scholar
  20. 20.
    Mostaghim, S., Teich, J.: Covering paretooptimal fronts by subswarms in multi-objective particle swarm optimization. In: Congress on Evolutionary Computation (CEC’2004), Portland, June 2004, vol. 2, pp. 1404–1411. IEEE Service CenterGoogle Scholar
  21. 21.
    Baumgartner, U., Magele, Ch., Renhart, W.: Pareto optimality and particle swarm optimization. IEEE Trans. Magn. 40(2), 1172–1175 (2004)CrossRefGoogle Scholar
  22. 22.
    Das, I., Dennis, J.: A closer look at drawbacks of minimizing weighted sums of objectives for pareto set generation in multicriteria optimization problems. Struct. Optim. 14(1), 63–69 (1997)CrossRefGoogle Scholar
  23. 23.
    Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the Pareto archived evolution strategy. Evol. Comput. 8(2), 149–172 (2000)CrossRefGoogle Scholar
  24. 24.
    Alvarez-Benitez, J.E., Everson, R.M., Fieldsend, J.E.: A MOPSO algorithm based exclusively on Pareto dominance concepts. In: Third International Conference on Evolutionary MultiCriterion Optimization, Guanajuato, Mexico, 2005, pp. 459–473Google Scholar
  25. 25.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)CrossRefGoogle Scholar
  26. 26.
    Parsopoulos, E.K., Tasoulis, K.D., Vrahatis, N.M.: Multiobjective optimization using parallel vector evaluated particle swarm optimization. In: Proceedings of the IASTED International Conference on Artificial Intelligence and Applications (AIA2004), Innsbruck, Austria, February 2004, vol. 2, pp. 823–828. ACTA PressGoogle Scholar
  27. 27.
    Parsopoulos, E.K., Vrahatis, N.M.: Particle swarm optimization method in multiobjective problems. In: Proceedings of the 2002 ACM Symposium on Applied Computing (SAC’2002), Madrid, Spain (2002), pp. 603–607. ACM PressGoogle Scholar
  28. 28.
    Raquel R.C., Prospero C. Naval, Jr.: An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2005), Washington, DC, USA, June 2005, pp. 257–264. ACM PressGoogle Scholar
  29. 29.
    Ray, T., Kang, T., Chye, K.S.: An evolutionary algorithm for constrained optimization. In: Whitley, D., Goldberg, D., Cantu-Paz, E., Spector, L., Parmee, I., Beyer, Hans-Georg.(eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’2000), pp. 771–777. Morgan Kaufmann, San Francisco (2000)Google Scholar
  30. 30.
    Ray, T., Liew, K.M.: A swarm metaphor for multiobjective design optimization. Eng. Optim. 34(2), 141–153 (2002)CrossRefGoogle Scholar
  31. 31.
    Rudolph, G.: On a multi-objective evolutionary algorithm and its convergence to the pareto set. In: Proceedings of the 5th IEEE Conference on Evolutionary Computation, Piscataway, New Jersey (1998), pp. 511–516. IEEE PressGoogle Scholar
  32. 32.
    Ozcan E., Mohan, K.C.: Particle swarm optimization: Surfing the waves. In: Congress on Evolutionary Computation (CEC’1999), Washington D.C. (1999), pp. 1939–1944. IEEE PressGoogle Scholar
  33. 33.
    Coello Coello, C.A.: A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowl. Inf. Syst. Int. J. 1(3), 269–308 (1999)Google Scholar
  34. 34.
    Ozcan E., Mohan, K.C.: Analysis of a simple particle swarm optimization system. In: Intelligent Engineering Systems Through Artificial Neural Networks, pp. 253–258 (1998)Google Scholar
  35. 35.
    Coello C.A.C., Lechuga, S.M.: MOPSO: a proposal for multiple objective particle swarm optimization. In: Congress on Evolutionary Computation (CEC’2002), Piscataway, NJ, May 2002, vol. 2, pp. 1051–1056. IEEE Service CenterGoogle Scholar
  36. 36.
    Nunes de Castro, L., Timmis, J.: An Introduction to Artificial Immune Systems: A New Computational Intelligence Paradigm. Springer, New York (2002)Google Scholar
  37. 37.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan kaufmann Publishers Inc., San Francisco (2001)Google Scholar
  38. 38.
    Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diverisity in evolutionary multi-objective optimization. Evol. Comput. 10, 263–282 (2002)CrossRefGoogle Scholar
  39. 39.
    Mostaghim, S., Teich, J.: Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium, Indianapolis, IN, April 2003, pp. 26–33. IEEE Service CenterGoogle Scholar
  40. 40.
    Mostaghim, S., Teich, J.: Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium, SIS’03, April 2003Google Scholar
  41. 41.
    Mostaghim, S., Teich, J.: The role of \(\varepsilon \)-dominance in multi objective particle swarm optimization methods. In: Congress on Evolutionary Computation (CEC’2003), Canberra, Australia, December 2003, vol. 3, pp. 1764–1771. IEEE PressGoogle Scholar
  42. 42.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)CrossRefGoogle Scholar
  43. 43.
    Pulido T.G., Coello, C.A.C.: Using clustering techniques to improve the performance of a particle swarm optimizer. In: Proceedings of Genetic and Evolutionary Computation Conference, Seattle, WA, pp. 225–237 (2004)Google Scholar
  44. 44.
    Leong, W.F., Yen, G.G.: PSO-based multiobjective optimization with dynamic population size and adaptive local archives. IEEE Trans. Syst., Man, Cybern. B, Cybern. 38(5), 1270–1293 (2008)CrossRefGoogle Scholar
  45. 45.
    Becerra, R.L., Coello Coello, C.A., Hernndez-Daz, A.G., Caballero, R., Molina, J.: Alternative technique to solve hard multi-objective optimization problems. In: Proceedings of Genetic and Evolutionary Computation Conference, London, U.K, pp. 757–764 (2007)Google Scholar
  46. 46.
    Arabas, J., Michalewicz, Z., Mulawka, J.: GAVaPS-A genetic algorithm with varying population size. In: Proceedings of Congress on Evolutionary Computation, Orlando, FL, pp. 73–78 (1994)Google Scholar
  47. 47.
    Blackwell, T., Branke, J.: Multiswarms, exclusion, and anticonvergence in dynamic environments. IEEE Trans. Evol. Comput. 10(4), 459–472 (2006)CrossRefGoogle Scholar
  48. 48.
    Zhuang, N., Benten, M., Cheung, P.: Improved variable ordering of BBDS with novel genetic algorithm. In: Proceedings of IEEE International Symposium on Circuits and Systems, Atlanta, GA, pp. 414–417 (1996)Google Scholar
  49. 49.
    Grefenstette, J.: Optimization of control parameters for genetic algorithms. IEEE Trans. Syst., Man, Cybern. SMC–16(1), 122–128 (1986)CrossRefGoogle Scholar
  50. 50.
    Fieldsend E.J., Singh, S.: A multi-objective algorithm based upon particle swarm optimisation, an efficient data structure and turbulence. In: The 2002 U.K. Workshop on Computational Intelligence, pp. 34–44 (2002)Google Scholar
  51. 51.
    Hu, X., Eberhart, R.: Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Proceedings of the 2002 Congress on Evolutionary Computation, (2002), IEEE PressGoogle Scholar
  52. 52.
    Pulido, T.G., Coello, C.A.C.: Using clustering techniques to improve the performance of a multi-objective particle swarm optimizer. In: Genetic and EvolutionaryComputation—GECCO 2004. LNCS, vol. 3102, pp. 225–237 (2004)Google Scholar
  53. 53.
    Okabe, T., Jin, Y., Olhofer, M., Sendhoff, B.: On test functions for evolutionary multi-objective optimization. In: Parallel Problem Solving from Nature—PPSN VIII. vol. 3242, pp. 792–802 (2004)Google Scholar
  54. 54.
    Pulido, T.G., Coello, C.A.C.: Using Clustering Techniques to improve the performance of a particle swarm optimizer. In: Genetic and Evolutionary Computation-GECCO 2004, Proceedings of the Genetic and Evolutionary Computation Conference—Part I. Lecture Notes in Computer Science, vol. 3102, pp. 225–237. Springer, June 2004Google Scholar
  55. 55.
    Reyes-Sierra, M., Coello, C.: Multi-objective particle swarm optimizers: a survey of the State-of-the-Art. Int. J. Comput. Intell. Res. 2(3), 287–308 (2006)MathSciNetGoogle Scholar
  56. 56.
    Padhye, N.: Topology optimization of compliant mechanism using multi-objective particle swarm optimization. In: Proceedings of the 2008 GECCO, ACM, pp. 1831–1834 (2008)Google Scholar
  57. 57.
    Parsopoulos, K., Vrahatis, M.: Particle swarm optimization method in multi-objective optimization problems. In: Proceedings of the 2002 ACM Symposium on Applied Computing (SAC 2002), pp. 603–607 (2002)Google Scholar
  58. 58.
    Raquel, R.C., Naval, C.P.: An effective use of crowding distance in multiobjective particle swarm optimization. In: GECOO, pp. 257–264 (2005)Google Scholar
  59. 59.
    Mostaghim, S., Teich, J.: Quad-trees: a data structure for storing pareto-sets in mulit-objective evolutionary algorithms with elitism. In: Evolutionary Computation Based Multi-Criteria Optimization: Theoretical Advances and Applications, pp. 81–104 (2005)Google Scholar
  60. 60.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength pareto evolutionary algorithm. Swiss Federal Institute of Technology (ETH), Zurich, Technical report TIK-Report 103, May 2001Google Scholar
  61. 61.
    Mostaghim, S., Teich, J.: Strategies for finding good local guides in multi- objective particle swarm optimization (MOPSO). In: Proceedings of the IEEE Swarm Intelligence Symposium, 2003. SIS’03, pp. 26–33 (2003)Google Scholar
  62. 62.
    Padhye, N., Branke, J., Mostaghim, S.: A comprehensive comparison of mopso methods: study of convergence and diversity-survey of state of the art. Report under review, submitted to CEC (2009)Google Scholar
  63. 63.
    Wierzbicki, A.P.: The use of reference objectives in multiobjective optimization. Fandel, G., Gal, T. (eds.) Multiple Objective Decision Making, Theory and Application, vol. 6(2) pp. 468–486 (1980)Google Scholar
  64. 64.
    Zitzler, E.: Evolutionary algorithms for multiobjective optimization: methods and applications. Shaker (1999)Google Scholar
  65. 65.
    Papadimitriou, C.H., Yannakakis, M.: On the approximability of trade-offs and optimal access of web sources (extended abstract). In: IEEE Symposium on Foundations of Computer Science (2000)Google Scholar
  66. 66.
    Reyes-Sierra, M., Coello, C.A.C.: Multi-objective particle swarm optimizers: a survey of the state-of-the art. Int. J. Comput. Intell. Res. 2(3), 287–308 (2006)MathSciNetGoogle Scholar
  67. 67.
    Schott, J.R.: Fault tolerant design using single and multicriteria genetic algorithm optimization. Master’s Thesis, Department of Aeronautics and Astonautics, Massachusetts Institute of Technology, Cambridge, MA (1995)Google Scholar
  68. 68.
    Moore, J., Chapman, R.: Application of particle swarm to multiobjective optimization. Department of Computer Science and Software Engineering, Auburn University,Technical report (1999)Google Scholar
  69. 69.
    Li, X.: A non-dominated sorting particle Swarm optimizer for multiobjective optimization. In: Genetic and Evolutionary Computation—GECCO 2003. LNCS, vol. 2723,pp. 37–48 (2003)Google Scholar
  70. 70.
    Everson, R.M., Alvarez-Benitez1 J.E., Fieldsend, J.E.: A mopso algorithm based exclusively on pareto dominance concepts. In: EMO, vol. 3410, pp. 459–473 (2005)Google Scholar
  71. 71.
    Kennedy, James, Eberhart, Russell C.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
  72. 72.
    Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. Technical Report 214, Computer Engineering and Networks Laboratory (TIK), ETH Zurich (2006)Google Scholar
  73. 73.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67 (1997)Google Scholar
  74. 74.
    Fieldsend, J., Everson, R., Singh, S.: Using unconstrained elite archives for Multi-objective optimisation. IEEE Trans. Evol. Comput. 7, 305–323 (2003)CrossRefGoogle Scholar
  75. 75.
    Veldhuizen, D.V., Lamont, G.: Multiobjective Evolutionary Algorithms Research: A History and Analysis. Technical Report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Enginering, Air Force Institute Technology, Wright-Patterson AFB, OH (1998)Google Scholar
  76. 76.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Congress on Evolutionary Computation (CEC2002). vol. 1, pp. 825–830 (2002)Google Scholar
  77. 77.
    Fieldsend, J.: Multi-objective particle swarm optimization methods. Technical Report No. 419, Department of Computer Science, University of Exeter (2004)Google Scholar
  78. 78.
    Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans. Evol. Comput. 10(5), 477–506 (2006)CrossRefGoogle Scholar
  79. 79.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Fourth IEEEInternational Conference on Neural Networks, pp. 1942–1948 (1995)Google Scholar
  80. 80.
    Coello, C.A.C., Van Veldhuizen, A.D., ALamont, B.G.: Evolutionary Algorithms for Solving Multi-objective Problems. Kluwer Academic Publishers, New York, May 2002. ISBN 0-3064-6762-3Google Scholar
  81. 81.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester, U.K (2001). ISBN 0-471-87339-XGoogle Scholar
  82. 82.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-objective Optimization Test Problems. In: Congress on Evolutionary Computation(CEC’2002), Piscataway, NJ, May 2002, vol. 1, pp. 825–830. IEEE Service CenterGoogle Scholar
  83. 83.
    Lu, H., Yen, G.G.: Rank-density-based multiobjective genetic algorithm and benchmark test function study. IEEE Trans. Evol. Comput. 7(4), 325–343 (2003)CrossRefGoogle Scholar
  84. 84.
    Pulido, T.G., Coello, C.A.C.: The micro genetic algorithm 2: towardsonline adaptation in evolutionary multiobjective optimization. In:Fonseca, M.C., Fleming, J.P., Zitzler, E., Deb, K., Thiele, L.(eds.) Evolutionary Multi-Criterion Optimization. SecondInternational Conference, EMO 2003. Lecture Notes in ComputerScience, vol. 2632 pp. 252–266. Springer, Faro, April 2003Google Scholar
  85. 85.
    Tripathi, K.P., Bandyopadhyay, S., Pal. K.S.: Multi-objective particle swarm optimization with time variant inertia and acceleration coefficients. Inf. Sci. 177(22), 5033–5049 (2007)Google Scholar
  86. 86.
    Pulido, T.G., Coello, C.A.C.: Using clustering techniques to improve the performance of a particle swarm optimizer. In: Deb, K., et al. (ed.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO2004). Lecture Notes in Computer Science, vol. 3102, pp. 225–237. Springer, Seattle, June 2004Google Scholar
  87. 87.
    Tan, C.H., Goh, C.K., Tan, K.C., Tay, A.: A cooperative coevolutionary algorithm for multiobjective particle swarm optimization. In: 2007 IEEE Congress on Evolutionary Computation (CEC2007), Singapore, September 2007, pp 3180–3186. IEEE PressGoogle Scholar
  88. 88.
    Clerc, M.: The swarm and the queen: towards a deterministic and adaptative particle swarm optimization. In: Proceedings of the Congress on Evolutionary Computation, (1999), pp. 1951–1957. IEEE PressGoogle Scholar
  89. 89.
    Mostaghim, S., Teich, J., Tyagi, A.: Comparision of data structures for storing pareto-sets in moeas. In: IEEE Proceedings World Congress on Computational Intelligence, pp. 843–849 (2002)Google Scholar
  90. 90.
    Van Veldhuizen, A.D., Lamount, B.G.: Multiobjective evolutionary algorithm research: a history and analysis. Department of Electrical and Computer Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH, Technical Report TR-98- 03 (1998)Google Scholar
  91. 91.
    Fieldsend, E.J., Singh S.: A multiobjective algorithm based upon particle swarm optimisation, an efficient data structure and turbulence. In: Proceedings of the 2002 U.K. Workshop on Computational Intelligence, pp. 37–44. Birmingham, U.K, September 2002Google Scholar
  92. 92.
    Engelbrecht, P.A.: Fundamentals of Computational Swarm Intelligence.Wiley (2005)Google Scholar
  93. 93.
    Coello, C., Pulido, G., Lechunga, M.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 256–279 (2004)CrossRefGoogle Scholar
  94. 94.
    Hanne, T.: On the convergence of multiobjective evolutionary algorithms. Eur. J. Oper. Res. 117, 553–564 (1999)CrossRefzbMATHGoogle Scholar
  95. 95.
    Coello, C.A.C., Pulido, T.G., Lechuga, S.M.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput 8(3), 256–279 (2004)CrossRefGoogle Scholar
  96. 96.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)CrossRefGoogle Scholar
  97. 97.
    Eberhart, C.R., Shi, Y.: Comparison between genetic algorithms and particle swarm optimization. In: Porto, W.V., Saravanan, N., Waagen, D., Eibe, E.A. (eds.) Proceedings of the Seventh Annual Conference on Evolutionary Programming, pp. 611–619. Springer, March 1998Google Scholar
  98. 98.
    Engelbrecht, Andries P. (ed.): Computational Intelligence: An Introduction. Wiley, England (2002)Google Scholar
  99. 99.
    Sierra, R.M., Coello, C.A.C.: Improving PSO-based multiobjective optimization using crowding, mutation and \(\varepsilon \)-dominance. In: Evolutionary Multi-Criterion Optimization Conference, Guanajuato, Mexico, pp. 505–519 (2005)Google Scholar
  100. 100.
    Mostaghim, S., Teich, J.: Strategies for finding good local guides in multi-objective particle swarm optimization. In: Proceedings of IEEE Swarm Intelligence Symposium, Indianapolis, IN, pp. 26–33 (2003)Google Scholar
  101. 101.
    van den Bergh, F.: An Analysis of Particle Swarm Optimizers. Ph.D. Thesis, Faculty of natural and agricultural science, University of Pretoria (2001)Google Scholar
  102. 102.
    Villalobos-Arias, A.M., Pulido, TG., Coello, C.A.C.: A proposal to use stripes to maintain diversity in a multi-objective particle swarm optimizer. In: Proceedings of Swarm Intelligence Symposium, Pasadena, CA, pp. 22–29 (2005)Google Scholar
  103. 103.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  104. 104.
    Fieldsand, J.E., Singh, S.: A multi-objective algorithm based upon particle swarm optimization, an efficient data structure and turbulence. In: Proceedings of U.K. Workshop on Computational Intelligence, Birmingham, U.K.,pp. 37–44 (2002)Google Scholar
  105. 105.
    Zhang, L.B., Zhou, C.G., Liu, X.H., Ma, Z.Q., Ma, M., Liang, Y.C.: Solving multi objective problems using particle swarm optimization. In: Proceedings of Congress on Evolutionary Computation, Canberra, Australia, pp. 2400–2405 (2003)Google Scholar
  106. 106.
    Eberhart, C.R., Dobbins, R., Simpson, K.P.: Computational Intelligence PC Tools. Morgan Kaufmann Publishers (1996)Google Scholar
  107. 107.
    Yen, G.G., Lu, H.: Dynamic multiobjective evolutionary algorithm: adaptive cell-based rank and density estimation. IEEE Trans. Evol. Comput. 7(3), 253–274 (2003)CrossRefGoogle Scholar
  108. 108.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, Perth, pp. 1942–1948 (1995)Google Scholar
  109. 109.
    Deb, K., Goldberg, E.D.: An investigation of niche and species formation in genetic function optimization. In: Schaffer, D.J. (ed.) Proceedings of the Third International Conference on Genetic Algorithms, pp. 42–50. George Mason University, Morgan Kaufmann Publishers, San Mateo, June 1989Google Scholar
  110. 110.
    Okabe, T., Jin, Y., Sendhoff, B., Olhofer, M.: Voronoi-based estimation of distribution algorithm for multi-objective optimization. In: Proceedings of Congress on Evolutionary Computation, Portland, OR, pp. 1594–1601 (2004)Google Scholar
  111. 111.
    Sierra, R.M., Coello, C.A.C.: Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int. J. Comput. Intell. Res. 2(3), 287–308 (2006)MathSciNetGoogle Scholar
  112. 112.
    Sierra RM., Coello, C.A.C.: Improving PSO-based multi-objective optimization using crowding, mutation and \(\varepsilon \)-dominance. In: Evolutionary Multi-Criterion Optimization (EMO 2005). LNCS, vol. 3410, pp. 505–519 (2005)Google Scholar
  113. 113.
    Sierra R.M., Coello, C.A.C.: Improving PSO-based multi-objective optimization using crowding, mutation and \(\varepsilon \)-dominance. In: Third International Conference on Evolutionary Multi-Criterion Optimization, EMO 2005. LNCS vol. 3410, pp. 505–519. Springer (2005)Google Scholar
  114. 114.
    Shi, Y., Eberhart, R.: Parameter selection in particle swarm optimization. In: Evolutionary Programming VII: Proceedings of the Seventh Annual Conference on Evolutionary Programming, pp. 591–600. Springer, New York (1998)Google Scholar
  115. 115.
    Carlos, C.A.C., Pulido, P.T., Lechuga, S.M.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 256–279 (2004)CrossRefGoogle Scholar
  116. 116.
    Coello, C.A.C., Van Veldhuizen, A.D., Lamont, B.G.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, New York (2002)Google Scholar
  117. 117.
    Li, X.: Better spread and convergence: particle swarm multiobjective optimization using the maximin fitness. In: GECCO, pp. 117–128 (2004)Google Scholar
  118. 118.
    Moore, J., Chapman, R.: Application of particle swarm to multiobjective optimization. Department of Computer Science and Software Engineering, Auburn University (1999)Google Scholar
  119. 119.
    Mostaghim, S., Teich. J.: The role of \(\varepsilon \)-dominance in multi objective particle swarm optimization methods. In: The Proceedings of the 2003 Congress on Evolutionary Computation, pp. 1764–1771 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Swagatika Devi
    • 1
  • Alok Kumar Jagadev
    • 1
    Email author
  • Sachidananda Dehuri
    • 2
  1. 1.Department of Computer Science and EngineeringSiksha ‘O’ Anusandhan UniversityBhubaneswarIndia
  2. 2.Department of Information & Communication TechnologyFakir Mohan UniversityBalasoreIndia

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