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Multi-objective Swarm Intelligence pp 75–103Cite as

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

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Part of the book series: Studies in Computational Intelligence ((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.

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References

  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)

    Article  Google Scholar 

  2. Conover, W.J.: Practical Nonparametric Statistics, 3rd edn, pp. 272–286. Wiley, New York (1999)

    Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  6. Venkatraman, S., Yen, G.G.: A generic framework for constrained optimization using genetic algorithms. IEEE Trans. Evol. Comput. 9(4), 424–435 (2005)

    Article  Google Scholar 

  7. de Lima, P., Yen, G.G.: Multiple objective evolutionary algorithm for temporal linguistic rule extraction. ISA Trans. 44(2), 315–327 (2005)

    Article  Google Scholar 

  8. Zitzler, E.: Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. Dissertation, Swiss Federal Institute Technology, Zurich (1999)

    Google Scholar 

  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)

    Article  Google Scholar 

  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 2003

    Google Scholar 

  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 Center

    Google Scholar 

  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 Press

    Google Scholar 

  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 Press

    Google Scholar 

  14. Schaffer, D.J.: Multiple objective optimization with vector evaluated genetic algorithms. Ph.D. Thesis, Vanderbilt University (1984)

    Google Scholar 

  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. Shi, Y., Eberhart, R.: Empirical study of particle swarm optimization. In: Congress on Evolutionary Computation (CEC’1999), Piscataway, NJ, (1999), pp. 1945–1950. IEEE Press

    Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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 Center

    Google Scholar 

  21. Baumgartner, U., Magele, Ch., Renhart, W.: Pareto optimality and particle swarm optimization. IEEE Trans. Magn. 40(2), 1172–1175 (2004)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  23. Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the Pareto archived evolution strategy. Evol. Comput. 8(2), 149–172 (2000)

    Article  Google Scholar 

  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. 459–473

    Google Scholar 

  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)

    Article  Google Scholar 

  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 Press

    Google Scholar 

  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 Press

    Google Scholar 

  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 Press

    Google Scholar 

  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. Ray, T., Liew, K.M.: A swarm metaphor for multiobjective design optimization. Eng. Optim. 34(2), 141–153 (2002)

    Article  Google Scholar 

  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 Press

    Google Scholar 

  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 Press

    Google Scholar 

  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. 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. 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 Center

    Google Scholar 

  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. Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan kaufmann Publishers Inc., San Francisco (2001)

    Google Scholar 

  38. Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diverisity in evolutionary multi-objective optimization. Evol. Comput. 10, 263–282 (2002)

    Article  Google Scholar 

  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 Center

    Google Scholar 

  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 2003

    Google Scholar 

  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 Press

    Google Scholar 

  42. Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. 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. Blackwell, T., Branke, J.: Multiswarms, exclusion, and anticonvergence in dynamic environments. IEEE Trans. Evol. Comput. 10(4), 459–472 (2006)

    Article  Google Scholar 

  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. Grefenstette, J.: Optimization of control parameters for genetic algorithms. IEEE Trans. Syst., Man, Cybern. SMC–16(1), 122–128 (1986)

    Article  Google Scholar 

  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. Hu, X., Eberhart, R.: Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Proceedings of the 2002 Congress on Evolutionary Computation, (2002), IEEE Press

    Google Scholar 

  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. 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. 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 2004

    Google Scholar 

  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)

    MathSciNet  Google Scholar 

  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. 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. 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. 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. 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 2001

    Google Scholar 

  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. 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. 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. Zitzler, E.: Evolutionary algorithms for multiobjective optimization: methods and applications. Shaker (1999)

    Google Scholar 

  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. 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)

    MathSciNet  Google Scholar 

  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. 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. 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. 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. Kennedy, James, Eberhart, Russell C.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)

    Google Scholar 

  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. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67 (1997)

    Google Scholar 

  74. Fieldsend, J., Everson, R., Singh, S.: Using unconstrained elite archives for Multi-objective optimisation. IEEE Trans. Evol. Comput. 7, 305–323 (2003)

    Article  Google Scholar 

  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. 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. Fieldsend, J.: Multi-objective particle swarm optimization methods. Technical Report No. 419, Department of Computer Science, University of Exeter (2004)

    Google Scholar 

  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)

    Article  Google Scholar 

  79. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Fourth IEEEInternational Conference on Neural Networks, pp. 1942–1948 (1995)

    Google Scholar 

  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 0-3064-6762-3

    Google Scholar 

  81. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester, U.K (2001). ISBN 0-471-87339-X

    Google Scholar 

  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 Center

    Google Scholar 

  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)

    Article  Google Scholar 

  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 2003

    Google Scholar 

  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. 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 2004

    Google Scholar 

  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 Press

    Google Scholar 

  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 Press

    Google Scholar 

  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. 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. 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 2002

    Google Scholar 

  92. Engelbrecht, P.A.: Fundamentals of Computational Swarm Intelligence.Wiley (2005)

    Google Scholar 

  93. Coello, C., Pulido, G., Lechunga, M.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 256–279 (2004)

    Article  Google Scholar 

  94. Hanne, T.: On the convergence of multiobjective evolutionary algorithms. Eur. J. Oper. Res. 117, 553–564 (1999)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  96. Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)

    Article  Google Scholar 

  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 1998

    Google Scholar 

  98. Engelbrecht, Andries P. (ed.): Computational Intelligence: An Introduction. Wiley, England (2002)

    Google Scholar 

  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. 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. 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. 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. 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)

    Article  Google Scholar 

  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. 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. Eberhart, C.R., Dobbins, R., Simpson, K.P.: Computational Intelligence PC Tools. Morgan Kaufmann Publishers (1996)

    Google Scholar 

  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)

    Article  Google Scholar 

  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. 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 1989

    Google Scholar 

  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. 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)

    MathSciNet  Google Scholar 

  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. 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. 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. 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)

    Article  Google Scholar 

  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. Li, X.: Better spread and convergence: particle swarm multiobjective optimization using the maximin fitness. In: GECCO, pp. 117–128 (2004)

    Google Scholar 

  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. 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 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Siksha ‘O’ Anusandhan University, Bhubaneswar, 751030, India

    Swagatika Devi & Alok Kumar Jagadev

  2. Department of Information & Communication Technology, Fakir Mohan University, Balasore, 756019, India

    Sachidananda Dehuri

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  1. Swagatika Devi
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  2. Alok Kumar Jagadev
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  3. Sachidananda Dehuri
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Correspondence to Alok Kumar Jagadev .

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Editors and Affiliations

  1. Department of Information and Communication Technology, Fakir Mohan University, Balasore, India

    Satchidananda Dehuri

  2. Department of Computer Science and Engineering, Siksha 'O' Anusandhan University, Bhubaneswar, India

    Alok Kumar Jagadev

  3. Gandhi Institute for Technological Advancement, Bhubaneswar, India

    Mrutyunjaya Panda

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Devi, S., Jagadev, A.K., Dehuri, S. (2015). Comparison of Various Approaches in Multi-objective Particle Swarm Optimization (MOPSO): Empirical Study. In: Dehuri, S., Jagadev, A., Panda, M. (eds) Multi-objective Swarm Intelligence. Studies in Computational Intelligence, vol 592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46309-3_3

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