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Knowledge and Information Systems

, Volume 1, Issue 3, pp 269–308 | Cite as

A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques

  • Carlos A. Coello CoelloEmail author
Critical Reviews

Abstract

This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described with its advantages and disadvantages, its degree of applicability and some of its known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed.

Keywords

Multiobjective optimization multicriteria optimization vector optimization genetic algorithms evolutionary algorithms artificial intelligence. 

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References

  1. 1.
    F. J. Aherne, N. A. Thacker, P. I. Rockett. Optimal pairwise geometric histograms. In: A. F. Clark (ed.), Electronic Proceedings of the Eighth British Machine Vision Conference, BMVC97, University of Essex, United Kingdom, 1997. URL: http://peipa.essex.ac.uk/bmva/bmvc97/papers/071/bmvc.html Google Scholar
  2. 2.
    R. Allenson. Genetic algorithms with gender for multi-function optimisation, Technical Report EPCC-SS92-01, Edinburgh Parallel Computing Centre, Edinburgh, Scotland, 1992.Google Scholar
  3. 3.
    A. D. Belegundu, D. V. Murthy, R. R. Salagame, E. W. Constants. Multiobjective optimization of laminated ceramic composites using genetic algorithms. In: Fifth AIAA/USAF/NASA Symposium on Multidisciplinary Analysis and Optimization, Panama City, Florida, AIAA, 1994, Paper 84-4363-CP, pp. 1015-1022Google Scholar
  4. 4.
    P. J. Bentley, J. P. Wakefield. Finding acceptable solutions in the pareto-optimal range using multiobjective genetic algorithms. In: Proc. 2nd On-Line World Conference on Soft Computing in Engineering Design and Manufacturing (WSC2), June 1997, URL: http://users.aol.com/docbentley/dispaper.htm
  5. 5.
    A. Charnes, W. W. Cooper. Management Models and Industrial Applications of Linear Programming, Volume 1, J hn Wiley: New York, 1961.zbMATHGoogle Scholar
  6. 6.
    Y. L. Chen, C. C. Liu. Multiobjective VAR planning using the goal-attainment method, IEE Proc. Generation, Transmission and Distribution, 141(3), 227–232, 1994.CrossRefGoogle Scholar
  7. 7.
    A. Chipperfield, P. Fleming. Gas turbine engine controller design using multiobjective genetic algorithms. In: A. M. S. Zalzala (ed.) Proc. First IEE/IEEE International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, GALESIA ’95, Halifax Hall, University of Sheffield, UK, September 1995, IEEE, pp. 214–219.CrossRefGoogle Scholar
  8. 8.
    C. A. Coello Coello, A. D. Christiansen. MOSES: A multiobjective optimization tool for engineering design, Engineering Optimization, 31(3), pp. 337–368, 1998.CrossRefGoogle Scholar
  9. 9.
    C.A. Coello Coello, A. D. Christiansen. Two new GA-based methods for multiobjective optimization, Civil Engineering Systems, 15(3), pp. 207–243, 1998.CrossRefGoogle Scholar
  10. 10.
    C. A. Coello Coello, A. D. Christiansen, A. H. Aguirre. Using a new GA-based multiobjective optimization technique for the design of robot arms, Robotica, 16(4), July–au]gust, pp. 401–414, 1998.CrossRefGoogle Scholar
  11. 11.
    C. A. Coello Coello, F. S. Hernández, F. A. Farrera. Optimal design of reinforced concrete beams using genetic algorithms, Expert Systems with Applications: An International Journal, 12(1), pp. 101–108, 1997.CrossRefGoogle Scholar
  12. 12.
    C. A. Coello Coello. An Empirical study of evolutionary techniques for multiobjective optimization in engineering design, PhD thesis, Department of Computer Science, Tulane University, New Orleans, LA, 1996.Google Scholar
  13. 13.
    D. Cvetković, I. Parmee, E. Webb. Multi-objective Optimisation and Preliminary Airframe Design, In Ian Parmee, editor, The Integration of Evolutionary and Adaptive Computing Technologies with Product/System Design and Realisation, pp. 255-267, Plymouth, United Kingdom, April 1998, Springer-Verlag.Google Scholar
  14. 14.
    K. Deb. Multi-objective genetic algorithms: Problem difficulties and construction of test problems, Technical Report CI-49/98, Dortmund: Department of Computer Science/LS11, University of Dortmund, Germany, 1998.Google Scholar
  15. 15.
    K. Deb, D. E. Goldberg. An investigation of niche and species formation in genetic function optimization. In: J. David Schaffer (ed.), Proc. Third International Conference on Genetic Algorithms, San Mateo, California, June 1989, George Mason University, Morgan Kau]fmann Publishers, pp. 42-50.Google Scholar
  16. 16.
    L. Duckstein. Multiobjective optimization in structural design: The model choice problem. In: E. Atrek, R. H. Gallagher, K. M. Ragsdell, O. C. Zienkiewicz (eds.), New Directions in Optimum Structural Design, John Wiley and Sons, 1984, pp. 459-481.Google Scholar
  17. 17.
    C. M. Fonseca, P. J. Fleming. Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In: S. Forrest (ed.), Proc. Fifth International Conference on Genetic Algorithms, San Mateo, California, University of Illinois at Urbana-Champaign, Morgan Kau]ffman Publishers, 1993, pp. 416–423.Google Scholar
  18. 18.
    C. M. Fonseca, P. J. Fleming. An overview of evolutionary algorithms in multiobjective optimization, Technical report, Department of au]tomatic Control and Systems Engineering, University of Sheffield, Sheffield, UK, 1994.Google Scholar
  19. 19.
    C. M. Fonseca, P. J. Fleming. Multiobjective optimization and multiple constraint handling with evolutionary algorithms I: A unified formulation, Technical Report 564, University of Sheffield, Sheffield, UK, January 1995.Google Scholar
  20. 20.
    C. M. Fonseca, P. J. Fleming. Multiobjective optimization and multiple constraint handling with evolutionary algorithms II: Application example, Technical Report 565, University of Sheffield, Sheffield, UK, January 1995.Google Scholar
  21. 21.
    C. M. Fonseca, P. J. Fleming. An overview of evolutionary algorithms in multiobjective optimization, Evolutionary Computation 3(1), 1–16, 1995.CrossRefGoogle Scholar
  22. 22.
    C. M. Fonseca, P. J. Fleming. Nonlinear system identification with multiobjective genetic algorithms. In: Proc. 13th World Congress of IFAC, San Francisco, California, 1996, pp. 187-192.Google Scholar
  23. 23.
    C. M. Fonseca, P. J. Fleming. On the performance assessment and comparison of stochastic multiobjective optimizers. In: H.-M. Voigt, W. Ebeling, I. Rechenberg, H.-P. Schwefel (eds.), Parallel Problem Solving from Nature—PPSN IV, Lecture Notes in Computer Science, Springer-Verlag: Berlin, Germany, 1996, pp.584–593.CrossRefGoogle Scholar
  24. 24.
    M. P. Fourman. Compaction of symbolic layout using genetic algorithms. In: Genetic Algorithms and Their Applications: Proceedings of the First International Conference on Genetic Algorithms, Lawrence Erlbau]m, 1985, pp. 141–153.Google Scholar
  25. 25.
    M. Gen, K. Ida, Y. Li. Solving bicriteria solid transportation problem with fuzzy numbers by genetic algorithm, Int. J. Computers and Industrial Engineering 29, 537–543, 1995.CrossRefGoogle Scholar
  26. 26.
    M. Gen, R. Cheng. Genetic Algorithms and Engineering Design, John Wiley and Sons, Inc.: New York, 1997.Google Scholar
  27. 27.
    D. E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company: Reading, Massachusetts, 1989.zbMATHGoogle Scholar
  28. 28.
    D. E. Goldberg, K. Deb. A comparison of selection schemes used in genetic algorithms. In: G.J. E. Rawlins (ed.), Foundations of Genetic Algorithms, Morgan Kau]fmann, San Mateo, California, 1991, pp. 69-93.Google Scholar
  29. 29.
    D. E. Goldberg, J. Richardson. Genetic algorithm with sharing for multimodal function optimization. In: J. J. Grefenstette (ed.), Genetic Algorithms and Their Applications: Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Erlbau]m, 1987, pp. 41–49.Google Scholar
  30. 30.
    G. W. Greenwood, X. S. Hu, J. G. D’Ambrosio. Fitness functions for multiple objective optimization problems: Combining preferences with pareto rankings. In: R. K. Belew, M. D. Vose (eds.), Foundations of Genetic Algorithms 4, Morgan Kau]fmann, San Mateo, California, 1997, pp. 437–455.Google Scholar
  31. 31.
    J. J. Grefenstette. GENESIS: A system for using genetic search procedures. In: Proc. 1984 Conference on Intelligent Systems and Machines, 1984, pp.161-165.Google Scholar
  32. 32.
    Y. Y. Haimes, W. Hall, H. Freedman. Multi-Objective Optimization in Water Resources Systems: The Surrogate Trade-Off Method, Elsevier: Amsterdam, 1975.Google Scholar
  33. 33.
    P. Hajela, C. Y. Lin. Genetic search strategies in multicriterion optimal design, Structural Optimization 4, 99–107, 1992.CrossRefGoogle Scholar
  34. 34.
    M. R. Hilliard, G. E. Liepins, M. Palmer, G. Rangarajen. The computer as a partner in algorithmic design: au]tomated discovery of parameters for a multiobjective scheduling heuristic. In: R. Sharda, B. L. Golden, E. Wasil, O. Balci, W. Stewart (eds.), Impacts of Recent Computer Advances on Operations Research, North-Holland: New York, 1989.Google Scholar
  35. 35.
    J. H. Holland. Adaptation in Natural and Artificial Systems. An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, Second Edition, MIT Press: Cambridge, Massachusetts, 1992.Google Scholar
  36. 36.
    J. Horn, N. Nafpliotis. Multiobjective optimization using the niched pareto genetic algorithm, Technical Report IlliGAl Report 93005, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA, 1993.Google Scholar
  37. 37.
    J. P. Ignizio. Goal Programming and Extensions, Heath, Lexington, Massachusetts, 1976.Google Scholar
  38. 38.
    J. P. Ignizio. The determination of a subset of efficient solutions via goal programming, Computing and Operations Research 3, 9–16, 1981.CrossRefGoogle Scholar
  39. 39.
    Y. Ijiri. Management Goals and Accounting for Control, North-Holland: Amsterdan, 1965.Google Scholar
  40. 40.
    H. Ishibuchi, T. Murata. Multi-objective genetic local search algorithm. In: T. Fukuda, T. Furuhashi (eds.), Proc. 1996 International Conference on Evolutionary Computation, Nagoya, Japan, IEEE, 1996, pp. 119–124.Google Scholar
  41. 41.
    W. Jakob, M. Gorges-Schleuter, C. Blume. Application of genetic algorithms to task planning and learning. In: R. Männer, B. Manderick (eds.), Parallel Problem Solving from Nature, 2nd Workshop, Lecture Notes in Computer Science, Amsterdam, 1992. North-Holland: Amsterdam, pp. 291–300.Google Scholar
  42. 42.
    G. Jones, R. D. Brown, D. E. Clark, P. Willett, R. C. Glen. Searching databases of two-dimensional and three-dimensional chemical structures using genetic algorithms. In: S. Forrest (ed.), Proc. Fifth International Conference on Genetic Algorithms, San Mateo, California, Morgan Kau]fmann, 1993, pp. 597-602.Google Scholar
  43. 43.
    H. Jutler. Liniejnaja modiel z nieskolkimi celevymi funkcjami (linear model with several objective functions), Ekonomika i matematiceckije Metody 3, 397–406, 1967, (in Polish).Google Scholar
  44. 44.
    J. R. Koza. Genetic Programming. On the Programming of Computers by Means of Natural Selection, The MIT Press, 1992.Google Scholar
  45. 45.
    H. W. Kuhn, A. W. Tucker. Nonlinear programming. In: J. Neyman (ed.), Proc. Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, California, University of California Press, 1951, pp. 481–492.Google Scholar
  46. 46.
    A. Gaspar Kunha, P. Oliveira, J. A. Covas. Use of genetic algorithms in multicriteria optimization to solve industrial problems. In: T. Bäck (ed.), Proc. Seventh International Conference on Genetic Algorithms, San Mateo, California, Michigan State University, Morgan Kau]fmann Publishers, 1997, pp. 682–688.Google Scholar
  47. 47.
    F. Kursawe. A variant of evolution strategies for vector optimization. In: H. P. Schwefel, R. Männer (eds.), Parallel Problem Solving from Nature, 1st Workshop, PPSN I, Berlin, Germany, Lecture Notes in Computer Science 496, Springer-Verlag, 1991, pp. 193-197Google Scholar
  48. 48.
    G. E. Liepins, M. R. Hilliard, J. Richardson, M. Palmer. Genetic algorithms application to set covering and travelling salesman problems. In: D. E. Brown, C. C. White (eds.), Operations Research and Artificial Intelligence: The Integration of Problem-Solving Strategies, Kluwer Academic: Norwell, Massachusetts, 1990, pp. 29–57.CrossRefGoogle Scholar
  49. 49.
    J. G. Lin. Maximal vectors and multi-objective optimization, J. Optimization Theory and Applications 18(1), 41–64, 1976.MathSciNetzbMATHCrossRefGoogle Scholar
  50. 50.
    J. Lis, A. E. Eiben. A multi-sexual genetic algorithm for multiobjective optimization. In: T. Fukuda, T. Furuhashi (eds.), Proc. 1996 International Conference on Evolutionary Computation, Nagoya, Japan, IEEE, 1996, pp. 59–64.Google Scholar
  51. 51.
    X. Liu, D. W. Begg, R. J. Fishwick. Genetic approach to optimal topology/controller design of adaptive structures, Int. J. Numerical Methods in Engineering 41, 815–830, 1998.zbMATHCrossRefGoogle Scholar
  52. 52.
    D. H. Loughlin, S. Ranjithan. The neighborhood constraint method: A genetic algorithm-based multiobjective optimization technique. In: T. Bäck (ed.), Proc. Seventh International Conference on Genetic Algorithms, San Mateo, California, Michigan State University, Morgan Kau]fmann Publishers, 1997, pp. 666–673.Google Scholar
  53. 53.
    S. M. Mahfoud. Crowding and preselection revisited. In: R Männer, B. Manderick (eds.), Parallel Problem Solving from Nature 2nd Workshop, North-Holland: Amsterdam, 1992.Google Scholar
  54. 54.
    Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs, Second Edition, Springer-Verlag, 1992.Google Scholar
  55. 55.
    E. Michielssen, D. S. Weile. Electromagnetic system design using genetic algorithms. In: Genetic Algorithms and Evolution Strategies in Engineering and Computer Science, John Wiley and Sons, England, 1995, 267–288.Google Scholar
  56. 56.
    M. Mitchell. An Introduction to Genetic Algorithms, MIT Press: Cambridge, Massachusetts, 1996.Google Scholar
  57. 57.
    J. Nash. The bargaining problem, Econometrica 18, 155–162, 1950.MathSciNetzbMATHCrossRefGoogle Scholar
  58. 58.
    S. Obayashi. Pareto genetic algorithm for aerodynamic design using the Navier-Stokes equations. In: D. Quagliarella, J. Périau]x, C. Poloni, G. Winter (eds.), Genetic Algorithms and Evolution Strategies in Engineering and Computer Science. Recent Advances and Industrial Applications, John Wiley and Sons: West Susex, England, 1997, Chapter 12, pp. 245–266.Google Scholar
  59. 59.
    A. Osyczka. An approach to multicriterion optimization problems for engineering design. Computer Methods in Applied Mechanics and Engineering 15, 309–333, 1978.zbMATHCrossRefGoogle Scholar
  60. 60.
    A. Osyczka. An approach to multicriterion optimization for structural design. In: Proc. International Symposium on Optimal Structural Design, University of Arizona, 1981.Google Scholar
  61. 61.
    A. Osyczka, J. Koski. Selected works related to multicriterion optimization methods for engineering design. In: Proc. Euromech Colloquium, University of Siegen, 1982.Google Scholar
  62. 62.
    A. Osyczka, S. Kundu. A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm, Structural Optimization 10, 94–99, 1995.CrossRefGoogle Scholar
  63. 63.
    A. Osyczka. Optimization of the steady state parameters for machine tool gear trains, Int. J. Machine Tool Design and Research 15, 31–68, 1975.CrossRefGoogle Scholar
  64. 64.
    A. Osyczka. Multicriterion Optimization in Engineering with FORTRAN programs, Ellis Horwood Limited, 1984.Google Scholar
  65. 65.
    A. Osyczka. Multicriteria optimization for engineering design. In: J. S. Gero (ed.), Design Optimization, Academic Press, 1985, pp. 193-227.Google Scholar
  66. 66.
    V. Pareto. Cours D’Economie Politique, volume I and II, F. Rouge: Lau]sanne, 1896.Google Scholar
  67. 67.
    I. C. Parmee, G. Purchase. The development of a directed genetic search technique for heavily constrained design spaces. In: I. C. Parmee (ed.), Adaptive Computing in Engineering Design and Control ’94, Plymouth, UK, University of Plymouth, 1994, pp. 97–102.Google Scholar
  68. 68.
    J. Périau]x, M. Sefrioui, B. Mantel. Ga multiple objective optimization strategies for electromagnetic backscattering. In: D. Quagliarella, J. Périau]x, C. Poloni, G. Winter (eds.), Genetic Algorithms and Evolution Strategies in Engineering and Computer Science. Recent Advances and Industrial Applications, John Wiley and Sons: West Sussex, England, 1997, Chapter 11, pp. 225–243.Google Scholar
  69. 69.
    C. Poloni, V. Pediroda. GA coupled with computationally expensive simulations: Tools to improve efficiency. In: D. Quagliarella, J. Périau]x, C. Poloni, G. Winter (eds.), Genetic Algorithms and Evolution Strategies in Engineering and Computer Science. Recent Advances and Industrial Applications, John Wiley and Sons: West Sussex, England, 1997, Chapter 13, pp. 267–288.Google Scholar
  70. 70.
    D. Powell, M. M. Skolnick. Using genetic algorithms in engineering design optimization with non-linear constraints. In: S. Forrest (ed.), Proc. Fifth International Conference on Genetic Algorithms, San Mateo, California, University of Illinois at Urbana-Champaign, Morgan Kau]fmann Publishers, 1993, pp. 424–431Google Scholar
  71. 71.
    D. Quagliarella, A. Vicini. Coupling genetic algorithms and gradient based optimization techniques. In: D. Quagliarella, J. Périau]x, C. Poloni, G. Winter (eds.), Genetic Algorithms and Evolution Strategies in Engineering and Computer Science. Recent Advances and Industrial Applications, John Wiley and Sons: West Sussex, England, 1997, Chapter 14,pp. 289–309.Google Scholar
  72. 72.
    S. Ranjithan, J. W. Eheart, J. C. Liebman. Incorporating fixed-cost component of pumping into stochastic groundwater management: A genetic algorithm-based optimization approach, Eos Transactions AGU 73(14), 125, 1992, Spring meeting supplement.Google Scholar
  73. 73.
    S. Rao. Game theory approach for multiobjective structural optimization, Computers and Structures 25(1), 119–127, 1986.CrossRefGoogle Scholar
  74. 74.
    S. S. Rao. Multiobjective optimization in structural design with uncertain parameters and stochastic processes, AIAA Journal 22(11), 1670–1678, 1984.zbMATHCrossRefGoogle Scholar
  75. 75.
    S. S. Rao. Game theory approach for multiobjective structural optimization, Computers and Structures 25(1), 119–127, 1987.MathSciNetzbMATHCrossRefGoogle Scholar
  76. 76.
    J. T. Richardson, M. R. Palmer, G. Liepins, Mike Hilliard. Some guidelines for genetic algorithms with penalty functions. In: J. D. Schaffer (ed.), Proc. Third International Conference on Genetic Algorithms, George Mason University,Morgan Kau]fmann Publishers, 1989, pp. 191–197.Google Scholar
  77. 77.
    B. J. Ritzel, J. Wayland Eheart, S. Ranjithan. Using genetic algorithms to solve a multiple objective groundwater pollution containment problem, Water Resources Research 30(5), 1589–1603 1994.CrossRefGoogle Scholar
  78. 78.
    K. Rodríguez-Vázquez, C. M. Fonseca, P. J. Fleming. Multiobjective genetic programming: A nonlinear system identification application. In: J. R. Koza (ed.), Late Breaking Papers at the Genetic Programming 1997 Conference, Stanford University, California, 1997, pp. 207–212.Google Scholar
  79. 79.
    M. A. Roseman, J. S. Gero. Reducing the pareto optimal set in multicriteria optimization, Engineering Optimization 8, 189–206, 1985.CrossRefGoogle Scholar
  80. 80.
    R. S. Rosenberg. Simulation of genetic populations with biochemical properties, PhD thesis, University of Michigan, Ann Harbor, Michigan, 1967.Google Scholar
  81. 81.
    Günter Rudolph. On a multi-objective evolutionary algorithm and its convergence to the pareto set. In: Proc. 5th IEEE Conference on Evolutionary Computation, Piscataway, New Jersey, IEEE Press, 1998, pp. 511–516.Google Scholar
  82. 82.
    E. Sandgren. Multicriteria design optimization by goal programming. In: H. Adeli (ed.), Advances in Design Optimization, Chapman &; Hall, London, 1994, pp. 225–265.Google Scholar
  83. 83.
    J. D. Schaffer. Multiple objective optimization with vector evaluated genetic algorithms. In: Genetic Algorithms and Their Applications: Proceedings of the First International Conference on Genetic Algorithms, Lawrence Erlbau]m, 1985, pp. 93–100.Google Scholar
  84. 84.
    H. P. Schwefel. Numerical Optimization of Computer Models, John Wiley and Sons: Great Britain, 1981.zbMATHGoogle Scholar
  85. 85.
    R. Solich. Zadanie programowania liniowego z wieloma funkcjami celu (linear programming problem with several objective functions), Przeglad Statystyczny 16, 24–30, 1969, (in Polish).Google Scholar
  86. 86.
    N. Srinivas, K. Deb. Multiobjective optimization using nondominated sorting in genetic algorithms, Technical report, Department of Mechanical Engineering, Indian Institute of Technology, Kanput, India, 1993.Google Scholar
  87. 87.
    N. Srinivas, K. Deb. Multiobjective optimization using nondominated sorting in genetic algorithms, Evolutionary Computation 2(3), 221–248, 1994.CrossRefGoogle Scholar
  88. 88.
    T. J. Stanley, Trevor Mudge. A parallel genetic algorithm for multiobjective microprocessor design. In: L. J. Eshelman (ed.), Proc. Sixth International Conference on Genetic Algorithms, San Mateo, California, University of Pittsburgh, Morgan Kau]fmann Publishers, 1995, pp. 597–604.Google Scholar
  89. 89.
    P. D. Surry, N. J. Radcliffe, I. D. Boyd. A multi-objective approach to constrained optimisation of gas supply networks: The COMOGA method. In: T. C. Fogarty (ed.), Evolutionary Computing. AISB Workshop. Selected Papers, Lecture Notes in Computer Science, Springer-Verlag: Sheffield, UK, 1995, pp. 166–180.Google Scholar
  90. 90.
    G. Syswerda, J. Palmucci. The application of genetic algorithms to resource scheduling. In: R. K. Belew, L. B. Booker (eds.), Proc. Fourth International Conference on Genetic Algorithms, San Mateo, California, Morgan Kau]fmann, 1991, pp. 502–508.Google Scholar
  91. 91.
    H. Tamaki, H. Kita, S. Kobayashi. Multi-objective optimization by genetic algorithms: A review. In: T. Fukuda, T. Furuhashi (eds.), Proc. 1996 International Conference on Evolutionary Computation, Nagoya, Japan, IEEE, 1996, pp. 517–522.Google Scholar
  92. 92.
    H. Tamaki, M. Mori, M. Araki, H. Ogai. Multicriteria optimization by genetic algorithms: A case of scheduling in hot rolling process. In: Proc. 3rd APORS, 1995, pp. 374-381.Google Scholar
  93. 93.
    K. C. Tan, Y. Li. Multi-objective genetic algorithm based time and frequency domain design unification of linear control systems, Technical Report CSC-97007, Department of Electronics and Electrical Engineering, University of Glasglow, Glasglow, Scotland, 1997.Google Scholar
  94. 94.
    D. S. Todd, P. Sen. A multiple criteria genetic algorithm for containership loading. In: T. Bäck (ed.), Proc. Seventh International Conference on Genetic Algorithms, San Mateo, California, Michigan State University, Morgan Kau]fmann Publishers, 1997, pp. 674–681.Google Scholar
  95. 95.
    C. H. Tseng, T. W. Lu. Minimax multiobjective optimization in structural design, Int. J. Numerical Methods in Engineering 30, 1213–1228, 1990.zbMATHCrossRefGoogle Scholar
  96. 96.
    M. Valenzuela-Rendón, E. Uresti-Charre. A non-generational genetic algorithm for multiobjective optimization. In: T. Bäck (ed.), Proc. Seventh International Conference on Genetic Algorithms, San Mateo, California, Michigan State University, Morgan Kau]fmann Publishers, 1997, 658–685.Google Scholar
  97. 97.
    G. Vedarajan, L. C. Chan, D. E. Goldberg. Investment portfolio optimization using genetic algorithms. In: J. R. Koza (ed.), Late Breaking Papers at the Genetic Programming 1997 Conference, Stanford University, California, Stanford Bookstore, 1997, pp. 255–263.Google Scholar
  98. 98.
    D. A. Van Veldhuizen, G. B. Lamont. Evolutionary computation and convergence to a pareto front. In: J. R. Koza (ed.), Late Breaking Papers at the Genetic Programming 1998 Conference, Stanford University, California, Stanford University Bookstore, 1998, pp. 221–228.Google Scholar
  99. 99.
    D. A. Van Veldhuizen, G. B. Lamont. Multiobjective evolutionary algorithm research: A history and analysis, Technical Report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, Ohio, 1998.Google Scholar
  100. 100.
    S. Voget, M. Kolonko. Multidimensional optimization with a fuzzy genetic algorithm, J. Heuristics, 4(3):221–244, September 1998.zbMATHCrossRefGoogle Scholar
  101. 101.
    C. White, A. Sage, S. Dozono. A model of multiattribute decision-making and tradeoff weight determination under uncertainty, IEEE Trans. Systems, Man, and Cybernetics, SMC-14, 223-229, 1984.Google Scholar
  102. 102.
    P. B. Wienke, C. Lucasius, G. Kateman. Multicriteria target optimization of analytical procedures using a genetic algorithm, Analytical Chimica Acta 265(2), 211–225, 1992.CrossRefGoogle Scholar
  103. 103.
    P. B. Wilson, M. D. Macleod. Low implementation cost IIR digital filter design using genetic algorithms. In: IEE/IEEE Workshop on Natural Algorithms in Signal Processing, Chelmsford, UK, 1993, pp. 4/1–4/8.Google Scholar
  104. 104.
    X. Yang, M. Gen. Evolution program for bicriteria transportation problem. In: M. Gen, T. Kobayashi (eds.), Proc. 16th International Conference on Computers and Industrial Engineering, Ashikaga, Japan, 1994, 451–454.Google Scholar
  105. 105.
    E. Zitzler, L. Thiele. An evolutionary algorithm for multiobjective optimization: The strength pareto approach, Technical Report 43, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, May 1998.Google Scholar
  106. 106.
    E. Zitzler, L. Thiele. Multiobjective optimization using evolutionary algorithms—A comparative study. In: A. E. Eiben (ed.), Parallel Problem Solving from Nature V, Amsterdam, Springer-Verlag, 1998, pp. 292–301.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Singapore Pte. Ltd. 1999

Authors and Affiliations

  1. 1.Laboratorio Nacional de Informatica AvanzadaXalapaMéxico

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