Skip to main content
SpringerLink
Log in

Recent Developments in Evolutionary Multi-Objective Optimization

  • Chapter
  • First Online:
Trends in Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 142))

Abstract

By now evolutionary multi-objective optimization (EMO) is an established and a growing field of research and application with numerous texts and edited books, commercial software, freely downloadable codes, a biannual conference series running successfully since 2001, special sessions and workshops held at all major evolutionary computing conferences, and full-time researchers from universities and industries from all around the globe. In this chapter, we discuss the principles of EMO through an illustration of one specific algorithm and an application to an interesting real-world bi-objective optimization problem. Thereafter, we provide a list of recent research and application developments of EMO to paint a picture of some salient advancements in EMO research. Some of these descriptions include hybrid EMO algorithms with mathematical optimization and multiple criterion decision-making procedures, handling of a large number of objectives, handling of uncertainties in decision variables and parameters, solution of different problem-solving tasks better by converting them into multi-objective problems, runtime analysis of EMO algorithms, and others. The development and application of EMO to multi-objective optimization problems and their continued extensions to solve other related problems has elevated the EMO research to a level which may now undoubtedly be termed as an active field of research with a wide range of theoretical and practical research and application opportunities.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B.V. Babu and M. L. Jehan. Differential evolution for multi-objective optimization. In Proceedings of the 2003 Congress on Evolutionary Computation (CEC’2003), volume 4, pages 2696–2703. IEEE Press, Piscataway NJ, 2003.

    Google Scholar 

  2. M. Basseur and E. Zitzler. Handling uncertainty in indicator-based multiobjective optimization. International Journal of Computational Intelligence Research, 2(3):255–272, 2006.

    Article  Google Scholar 

  3. S. Bleuler, M. Brack, and E. Zitzler. Multiobjective genetic programming: Reducing bloat using SPEA2. In Proceedings of the 2001 Congress on Evolutionary Computation, pages 536–543. IEEE Press, Piscataway NJ, 2001.

    Google Scholar 

  4. P. A. N. Bosman and D. Thierens. The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Transactions on Evolutionary Computation, 7(2), 2003.

    Google Scholar 

  5. J. Branke. Evolutionary Optimization in Dynamic Environments. Springer-Verlag, Heidelberg, Germany, 2001.

    Google Scholar 

  6. J. Branke and K. Deb. Integrating user preferences into evolutionary multi-objective optimization. In Y. Jin, editor, Knowledge Incorporation in Evolutionary Computation, pages 461–477. Springer-Verlag, Heidelberg, Germany, 2004.

    Google Scholar 

  7. J. Branke, K. Deb, H. Dierolf, and M. Osswald. Finding knees in multi-objective optimization. In Parallel Problem Solving from Nature (PPSN-VIII), volume 3242 of Lecture Notes in computer Science, pages 722–731. Springer-Verlag, Heidelberg, Germany, 2004.

    Google Scholar 

  8. J. Branke, K. Deb, K. Miettinen, and R. Slowinski. Multiobjective Optimization: Interactive and Evolutionary Approaches. Springer-Verlag, Berlin, Germany, 2008.

    Google Scholar 

  9. D. Brockhoff and E. Zitzler. Dimensionality reduction in multiobjective optimization: The minimum objective subset problem. In K. H. Waldmann and U. M. Stocker, editors, Operations Research Proceedings 2006, pages 423–429. Springer-Verlag, Berlin, 2007.

    Google Scholar 

  10. D. Brockhoff and E. Zitzler. Offline and online objective reduction in evolutionary multiobjective optimization based on objective conflicts. TIK Report 269, Institut für Technische Informatik und Kommunikationsnetze, ETH Zürich, 2007.

    Google Scholar 

  11. C. A. C. Coello and M. S. Lechuga. MOPSO: A proposal for multiple objective particle swarm optimization. In Congress on Evolutionary Computation (CEC’2002), volume 2, pages 1051–1056. IEEE Service Center, Piscataway NJ, 2002.

    Google Scholar 

  12. C. A. C. Coello and G. Toscano. A micro-genetic algorithm for multi-objective optimization. Technical Report Lania-RI-2000-06, Laboratoria Nacional de Informatica Avanzada, Xalapa, Veracruz, Mexico, 2000.

    Google Scholar 

  13. C. A. C. Coello, D. A. VanVeldhuizen, and G. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer, Boston, MA, 2002.

    Google Scholar 

  14. C. A. Coello Coello. Treating objectives as constraints for single objective optimization. Engineering Optimization, 32(3):275–308, 2000.

    Article  Google Scholar 

  15. C. A. Coello Coello, A. H. Aguirre, and E. Zitzler, editors. Evolutionary Multi-Criterion Optimization: Third International Conference, volume 3410 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 2005.

    Google Scholar 

  16. D. W. Corne, J. D. Knowles, and M. Oates. The Pareto envelope-based selection algorithm for multiobjective optimization. In Proceedings of the Sixth International Conference on Parallel Problem Solving from Nature VI (PPSN-VI), volume 1917 of Lecture Notes in Computer Science, pages 839–848. Springer-Verlag, Berlin, Germany, 2000.

    Google Scholar 

  17. V. Coverstone-Carroll, J. W. Hartmann, and W. J. Mason. Optimal multi-objective low-thurst spacecraft trajectories. Computer Methods in Applied Mechanics and Engineering, 186(2–4): 387–402, 2000.

    Article  Google Scholar 

  18. T. R. Cruse. Reliability-based Mechanical Design. Marcel Dekker, New York, 1997.

    Google Scholar 

  19. K. Deb. Multi-objective Optimization Using Evolutionary Algorithms. Wiley, Chichester, UK, 2001.

    Google Scholar 

  20. K. Deb and R. B. Agrawal. Simulated binary crossover for continuous search space. Complex Systems, 9(2):115–148, 1995.

    Google Scholar 

  21. K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2):182–197, 2002.

    Article  Google Scholar 

  22. K. Deb and T. Goel. A hybrid multi-objective evolutionary approach to engineering shape design. In Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization (EMO-01), volume 1993 of Lecture Notes in Computer Science, pages 385–399. Springer-Verlag, Heidelberg, Germany, 2001.

    Google Scholar 

  23. K. Deb and H. Gupta. Introducing robustness in multi-objective optimization. Evolutionary Computation Journal, 14(4):463–494, 2006.

    Article  Google Scholar 

  24. K. Deb, S. Gupta, D. Daum, J. Branke, A. Mall, and D. Padmanabhan. Reliability-based optimization using evolutionary algorithms. IEEE Transactions on Evolutionary Computation, doi 10.1109/TEVC.2009.2014361, 2009.

    Google Scholar 

  25. K. Deb and A. Kumar. Interactive evolutionary multi-objective optimization and decision-making using reference direction method. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2007), pages 781–788. The Association of Computing Machinery, New York, 2007.

    Google Scholar 

  26. K. Deb and A. Kumar. Light beam search based multi-objective optimization using evolutionary algorithms. In Proceedings of the Congress on Evolutionary Computation (CEC-07), pages 2125–2132. IEEE Press, Piscataway NJ, 2007.

    Google Scholar 

  27. K. Deb and P. K. S. Nain. An evolutionary multi-objective adaptive meta-modeling procedure using artificial neural networks. In Evolutionary Computation in Dynamic and Uncertain Environments, pages 297–322. Springer-Verlag, Berlin, Germany, 2007.

    Google Scholar 

  28. K. Deb, U. B. Rao, and S. Karthik. Dynamic multi-objective optimization and decision-making using modified NSGA-II: A case study on hydro-thermal power scheduling bi-objective optimization problems. In Proceedings of the Fourth International Conference on Evolutionary Multi-Criterion Optimization (EMO-2007), volume 4403 of Lecture Notes in ComputerScience, 2007.

    Google Scholar 

  29. K. Deb and D. Saxena. Searching for Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. In Proceedings of the World Congress on Computational Intelligence (WCCI-2006), pages 3352–3360. IEEE Press, Piscataway NJ, 2006.

    Google Scholar 

  30. K. Deb and A. Srinivasan. Innovization: Innovating design principles through optimization. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2006), pages 1629–1636, The Association of Computing Machinery, New York, 2006.

    Google Scholar 

  31. K. Deb, J. Sundar, N. Uday, and S. Chaudhuri. Reference point based multi-objective optimization using evolutionary algorithms. International Journal of Computational Intelligence Research, 2(6):273–286, 2006.

    Google Scholar 

  32. K. Deb, R. Tiwari, M. Dixit, and J. Dutta. Finding trade-off solutions close to KKT points using evolutionary multi-objective optimization. In Proceedings of the Congress on Evolutionary Computation (CEC-2007), pages 2109–2116. IEEE Press, Piscataway NJ, 2007.

    Google Scholar 

  33. K. Deb, P. Zope, and A. Jain. Distributed computing of pareto-optimal solutions using multi-objective evolutionary algorithms. In Proceedings of the Second Evolutionary Multi-Criterion Optimization (EMO-03) Conference, volume 2632 of Lecture Notes in Computer Science, pages 535–549. Spriinger Verlag, Berlin, Germany, 2003.

    Google Scholar 

  34. X. Du and W. Chen. Sequential optimization and reliability assessment method for efficient probabilistic design. ASME Journal of Mechanical Design, 126(2):225–233, 2004.

    Article  Google Scholar 

  35. M. A. El-Beltagy, P. B. Nair, and A. J. Keane. Metamodelling techniques for evolutionary optimization of computationally expensive problems: Promises and limitations. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-1999), pages 196–203. Morgan Kaufmmann, San Mateo, CA, 1999.

    Google Scholar 

  36. M. Emmerich and B. Naujoks. Metamodel-assisted multiobjective optimisation strategies and their application in airfoil design. In Adaptive Computing in Design and Manufacture VI, pages 249–260. Springer, London, UK, 2004.

    Google Scholar 

  37. M. T. M. Emmerich, K. C. Giannakoglou, and B. Naujoks. Single and multiobjective evolutionary optimization assisted by gaussian random field metamodels. IEEE Transactions on Evolutionary Computation, 10(4):421–439, 2006.

    Article  Google Scholar 

  38. M. Farina and P. Amato. A fuzzy definition of optimality for many criteria optimization problems. IEEE Transactions on Systems, Man and Cybernetics Part A: Systems and Humans, 34(3):315–326, 2004.

    Article  Google Scholar 

  39. M. Fleischer. The measure of Pareto optima: Applications to multi-objective optimization. In Proceedings of the Second International Conference on Evolutionary Multi-Criterion Optimization (EMO-2003), volume 1993 of Lecture Notes in Computer Science, pages 519–533. Springer-Verlag, Berlin, Germany, 2003.

    Google Scholar 

  40. L. J. Fogel, A. J. Owens, and M. J. Walsh. Artificial Intelligence Through Simulated Evolution. Wiley, New York, 1966.

    Google Scholar 

  41. C. Fonseca, P. Fleming, E. Zitzler, K. Deb, and L. Thiele. Proceedings of the Second Evolutionary Multi-Criterion Optimization (EMO-03) Conference, volume 2632 of Lecture Notes in Computer Science. Springer-Verlag, Heidelberg, Germany, 2003.

    Book  Google Scholar 

  42. C. M. Fonseca, V. Grunert da Fonseca, and L. Paquete. Exploring the performance of stochastic multiobjective optimisers with the second-order attainment function. In C. A. Coello Coello, A. Hernández Aguirre, and E. Zitzler, editors, Third International Conference on Evolutionary Multi-Criterion Optimization, EMO-2005, volume 3410 of Lecture Notes in Computer Science, pages 250–264. Springer-Verlag, Berlin, Germany, 2005.

    Google Scholar 

  43. C. M. Fonseca and P. J. Fleming. Genetic algorithms for multiobjective optimization: Formulation, discussion, and generalization. In Proceedings of the Fifth International Conference on Genetic Algorithms, pages 416–423, 1993.

    Google Scholar 

  44. C. M. Fonseca and P. J. Fleming. On the performance assessment and comparison of stochastic multiobjective optimizers. In H.-M. Voigt, W. Ebeling, I. Rechenberg, and H.-P. Schwefel, editors, Parallel Problem Solving from Nature (PPSN IV), volume 1141 of Lecture Notes in Computer Science, pages 584–593. Springer-Verlag, Berlin, Germany, 1996.

    Chapter  Google Scholar 

  45. K. C. Giannakoglou. Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Progress in Aerospace Science, 38(1):43–76, 2002.

    Article  Google Scholar 

  46. O. Giel. Expected runtimes of a simple multi-objective evolutionary algorithm. In Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), pages 1918–1925. IEEE Press, Piscataway NJ, 2003.

    Google Scholar 

  47. O. Giel and P. K. Lehre. On the effect of populations in evolutionary multi-objective optimization. In Proceedings of the 8th Annual Genetic and Evolutionary Computation Conference (GECCO 2006), pages 651–658. ACM Press, New York, 2006.

    Google Scholar 

  48. D. E. Goldberg. Genetic Algorithms for Search, Optimization, and Machine Learning. Addison-Wesley, Reading MA, 1989.

    Google Scholar 

  49. D. E. Goldberg and J. Richardson. Genetic algorithms with sharing for multimodal function optimization. In Proceedings of the First International Conference on Genetic Algorithms and Their Applications, pages 41–49, 1987.

    Google Scholar 

  50. M. Gravel, W. L. Price, and C. Gagné. Scheduling continuous casting of aluminum using a multiple objective ant colony optimization metaheuristic. European Journal of Operational Research, 143(1):218–229, 2002.

    Article  Google Scholar 

  51. J. Handl and J. D. Knowles. An evolutionary approach to multiobjective clustering. IEEE Transactions on Evolutionary Computation, 11(1):56–76, 2007.

    Article  Google Scholar 

  52. M. P. Hansen and A. Jaskiewicz. Evaluating the quality of approximations to the non-dominated set. IMM Report IMM-REP-1998-7, Institute of Mathematical Modelling, Technical University of Denmark, Lyngby, 1998.

    Google Scholar 

  53. J. H. Holland. Adaptation in Natural and Artificial Systems. MIT Press, Ann Arbor, MI, 1975.

    Google Scholar 

  54. J. Horn, N. Nafploitis, and D. E. Goldberg. A niched Pareto genetic algorithm for multi-objective optimization. In D. Fogel, editor, Proceedings of the First IEEE Conference on Evolutionary Computation, pages 82–87. IEEE Press, Piscataway, NJ, 1994.

    Chapter  Google Scholar 

  55. J. Jahn. Vector Optimization. Springer-Verlag, Berlin, Germany, 2004.

    Google Scholar 

  56. H. Jin and M.-L. Wong. Adaptive diversity maintenance and convergence guarantee in multiobjective evolutionary algorithms. In Proceedings of the Congress on Evolutionary Computation (CEC-2003), pages 2498–2505. IEEE Press, Piscataway, NJ, 2003.

    Google Scholar 

  57. E. D. De Jong, R. A. Watson, and J. B. Pollack. Reducing bloat and promoting diversity using multi-objective methods. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), pages 11–18. Morgan Kaufmann, San Mateo, CA, 2001.

    Google Scholar 

  58. V. Khare, X. Yao, and K. Deb. Performance scaling of multi-objective evolutionary algorithms. In Proceedings of the Second Evolutionary Multi-Criterion Optimization (EMO-03) Conference, volume 2632 of Lecture Notes in Computer Science, pages 376–390, 2003.

    Google Scholar 

  59. J. Knowles and D. Corne. Quantifying the effects of objective space dimension in evolutionary multiobjective optimization. In Proceedings of the Fourth International Conference on Evolutionary Multi-Criterion Optimization (EMO-2007), volume 4403 of Lecture Notes in Computer Science, pages 757–771. Springer-Verlag, Berlin, Germany, 2007.

    Google Scholar 

  60. J. D. Knowles and D. W. Corne. Approximating the non-dominated front using the Pareto archived evolution strategy. Evolutionary Computation Journal, 8(2):149–172, 2000.

    Article  Google Scholar 

  61. J. D. Knowles and D. W. Corne. On metrics for comparing nondominated sets. In Congress on Evolutionary Computation (CEC-2002), pages 711–716. IEEE Press, Piscataway, NJ, 2002.

    Google Scholar 

  62. J. D. Knowles, D. W. Corne, and K. Deb, editors. Multiobjective Problem Solving from Nature. Springer Natural Computing Series. Springer-Verlag, Berlin, 2008.

    Google Scholar 

  63. P. Korhonen and J. Laakso. A visual interactive method for solving the multiple criteria problem. European Journal of Operational Reseaech, 24:277–287, 1986.

    Article  Google Scholar 

  64. R. Kumar and N. Banerjee. Analysis of a multiobjective evolutionary algorithm on the 0-1 knapsack problem. Theoretical Computer Science, 358(1):104–120, 2006.

    Article  Google Scholar 

  65. H. T. Kung, F. Luccio, and F. P. Preparata. On finding the maxima of a set of vectors. Journal of the Association for Computing Machinery, 22(4):469–476, 1975.

    Google Scholar 

  66. M. Laumanns, L. Thiele, K. Deb, and E. Zitzler. Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation, 10(3):263–282, 2002.

    Article  Google Scholar 

  67. M. Laumanns, L. Thiele, and E. Zitzler. Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean Functions. IEEE Transactions on Evolutionary Computation, 8(2):170–182, 2004.

    Article  Google Scholar 

  68. M. Laumanns, L. Thiele, E. Zitzler, E. Welzl, and K. Deb. Running time analysis of multi-objective evolutionary algorithms on a simple discrete optimization problem. In M. Guervós, P. Adamidis, H.-G. Beyer, J. L. Fernández-Villacañas Martín, and H.-P. Schwefel, editors, Proceedings of the Seventh Conference on Parallel Problem Solving from Nature (PPSN-VII), volume 2439 of Lecture Notes in Computer Science, pages 44–53. Springer-Verlag, Berlin, Germany, 2002.

    Chapter  Google Scholar 

  69. D. H. Loughlin and S. Ranjithan. The neighborhood constraint method: A multiobjective optimization technique. In T. Bäck, editor, Proceedings of the Seventh International Conference on Genetic Algorithms, pages 666–673. Morgan Kaufmann, San Francisco, CA, 1997.

    Google Scholar 

  70. M. Luque, K. Miettinen, P. Eskelinen, and F. Ruiz. Three different ways for incorporating preference information in interactive reference point based methods. Technical Report W-410, Helsinki School of Economics, Helsinki, Finland, 2006.

    Google Scholar 

  71. P. R. McMullen. An ant colony optimization approach to addessing a JIT sequencing problem with multiple objectives. Artificial Intelligence in Engineering, 15:309–317, 2001.

    Article  Google Scholar 

  72. K. Miettinen. Nonlinear Multiobjective Optimization. Kluwer, Boston, 1999.

    Google Scholar 

  73. S. Mostaghim and J. Teich. Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In 2003 IEEE Swarm Intelligence Symposium Proceedings, pages 26–33. IEEE Service Center, Piscataway, NJ, 2003.

    Google Scholar 

  74. P. K. S. Nain and K. Deb. Computationally effective search and optimization procedure using coarse to fine approximations. In Proceedings of the Congress on Evolutionary Computation (CEC-2003), pages 2081–2088. IEEE Press, Piscataway, NJ, 2003.

    Google Scholar 

  75. F. Neumann and I. Wegener. Minimum spanning trees made easier via multi-objective optimization. In GECCO ’05: Proceedings of the 2005 conference on Genetic and evolutionary computation, pages 763–769. ACM, New York, 2005.

    Google Scholar 

  76. S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, and T. Murata, editors. Evolutionary Multi-Criterion Optimization, 4th International Conference, EMO 2007, Matsushima, Japan, March 5-8, 2007, Proceedings, volume 4403 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 2007.

    Google Scholar 

  77. A. Osyczka. Evolutionary algorithms for single and multicriteria design optimization. Physica-Verlag, Heidelberg, Germany, 2002.

    Google Scholar 

  78. R. S. Rosenberg. Simulation of Genetic Populations with Biochemical Properties. Ph.D. thesis, University of Michigan, Ann Arbor, MI, 1967.

    Google Scholar 

  79. G. Rudolph. Convergence analysis of canonical genetic algorithms. IEEE Transactions on Neural Network, 5(1):96–101, 1994.

    Article  Google Scholar 

  80. D. Sasaki, M. Morikawa, S. Obayashi, and K. Nakahashi. Aerodynamic shape optimization of supersonic wings by adaptive range multiobjective genetic algorithms. In E. Zitzler, K. Deb, L. Thiele, C. A. Coello Coello, and D. Corne, editors, Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization (EMO 2001), volume 1993 of Lecture Notes in Computer Science, pages 639–652. Springer-Verlag, Berlin, Germany, 2001.

    Chapter  Google Scholar 

  81. C. G. Sauer. Optimization of multiple target electric propulsion trajectories. In AIAA 11th Aerospace Science Meeting, 1973. Paper Number 73-205.

    Google Scholar 

  82. Z. M. Saul and C. A. C. Coello. A proposal to hybridize multi-objective evolutionary algorithms with non-gradient mathematical programming techniques. In Proceedings of the Parallel Problem Solving from Nature (PPSN-2008), volume 5199 of Lecture Notes in Computer Science, pages 837–846. Springer-Verlag, Berlin, Germany, 2008.

    Google Scholar 

  83. D. K. Saxena and K. Deb. Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: Employing correntropy and a novel maximum variance unfolding. In S. Obayashi, K. Deb, C. Poloni, T. Hiroyasu, and T. Murata, editors, Proceedings of the Fourth International Conference on Evolutionary Multi-Criterion Optimization (EMO-2007), volume 4403 of Lecture Notes in Computer Science, pages 772–787. Springer-Verlag, Berlin, Germany, 2007.

    Chapter  Google Scholar 

  84. J. D. Schaffer. Some Experiments in Machine Learning Using Vector Evaluated Genetic Algorithms. Ph.D. thesis, Vanderbilt University, Nashville, TN, 1984.

    Google Scholar 

  85. P. Shukla and K. Deb. On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods. European Journal of Operational Research, 181(3):1630–1652, 2007.

    Article  Google Scholar 

  86. K. Sindhya, K. Deb, and K. Miettinen. A local search based evolutionary multi-objective optimization technique for fast and accurate convergence. In G. Rudolph, T. Jansen, S. M. Lucas, C. Poloni, and N. Beume, editors, Proceedings of the Paralle Problem Solving From Nature (PPSN-2008), Lecture Notes in Computer Science, pages 815–824. Springer-Verlag, Berlin, Germany, 2008.

    Chapter  Google Scholar 

  87. N. Srinivas and K. Deb. Multi-objective function optimization using non-dominated sorting genetic algorithms. Evolutionary Computation Journal, 2(3):221–248, 1994.

    Article  Google Scholar 

  88. L. Thiele, K. Miettinen, P. Korhonen, and J. Molina. A preference-based interactive evolutionary algorithm for multiobjective optimization. Technical Report W-412, Helsingki School of Economics, Finland, 2007.

    Google Scholar 

  89. D. Van Veldhuizen and G. B. Lamont. Multiobjective evolutionary algorithms: Analyzing the state-of-the-art. Evolutionary Computation Journal, 8(2):125–148, 2000.

    Article  Google Scholar 

  90. A. P. Wierzbicki. The use of reference objectives in multiobjective optimization. In G. Fandel and T. Gal, editors, Multiple Criteria Decision Making Theory and Applications, pages 468–486. Springer-Verlag, Berlin, Germany, 1980.

    Google Scholar 

  91. E. Zitzler, K. Deb, L. Thiele, C. A. C. Coello, and D. W. Corne. Proceedings of the First Evolutionary Multi-Criterion Optimization (EMO-01) Conference, volume 1993 of Lecture Notes in Computer Science. Springer-Verlag, Heidelberg, Germany, 2001.

    Book  Google Scholar 

  92. E. Zitzler and S. Künzli. Indicator-based selection in multiobjective search. In Conference on Parallel Problem Solving from Nature (PPSN VIII), volume 3242 of Lecture Notes in Computer Science, pages 832–842. Springer-Verlag, Berlin, Germany, 2004.

    Google Scholar 

  93. E. Zitzler, M. Laumanns, and L. Thiele. SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In K. C. Giannakoglou, D. T. Tsahalis, J. Périaux, K. D. Papailiou, and T. Fogarty, editors, Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, pages 95–100. International Center for Numerical Methods in Engineering (CIMNE), 2001.

    Google Scholar 

  94. E. Zitzler and L. Thiele. Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation, 3(4):257–271, 1999.

    Article  Google Scholar 

  95. E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. G. Fonseca. Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation, 7(2):117–132, 2003.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, PIN 208016, India

    Kalyanmoy Deb

  2. Department of Business Technology, Helsinki School of Economics, FIN-00101, Helsinki, Finland

    Kalyanmoy Deb

Authors
  1. Kalyanmoy Deb
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kalyanmoy Deb .

Editor information

Editors and Affiliations

  1. Dept. Engineering Science, University of Auckland, Auckland, New Zealand

    Matthias Ehrgott

  2. Depto. Engenharia e Gestao, Instituto Superior Tecnico, Av. Prof.Dr. Cavaco Silva, Porto Salvo, 2780-990, Portugal

    José Rui Figueira

  3. Faculty of Economics, University of Catania, Corso Italia 55, Catania, 95129, Italy

    Salvatore Greco

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Deb, K. (2010). Recent Developments in Evolutionary Multi-Objective Optimization. In: Ehrgott, M., Figueira, J., Greco, S. (eds) Trends in Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 142. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5904-1_12

Download citation

Publish with us

Policies and ethics

Search

Navigation