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Constrained Multi-objective Evolutionary Algorithm

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Evolutionary and Swarm Intelligence Algorithms

Part of the book series: Studies in Computational Intelligence ((SCI,volume 779))

Abstract

Multi-objective optimization problems are common in practice. In practical problems, constraints are also inevitable. The population approach and implicit parallel search ability of evolutionary algorithms have made them popular and useful in finding multiple trade-off Pareto-optimal solutions in multi-objective optimization problems since the past two decades. In this chapter, we discuss evolutionary multi-objective optimization (EMO) algorithms that are specifically designed for handling constraints. Numerical test problems involving constraints and some constrained engineering design problems which are often used in the EMO literature are discussed next. The chapter is concluded with a number of future directions in constrained multi-objective optimization area.

Parts of this chapter is excerpted from author’s 2001 Wiley book [8] and his other publications.

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References

  1. Bhatia, D., Aggarwal, S.: Optimality and duality for multiobjective nonsmooth programming. Eur. J. Oper. Res. 57(3), 360–367 (1992)

    Article  Google Scholar 

  2. Binh, T.T., Korn, U.: MOBES: A multiobjective evolution strategy for constrained optimization problems. In: The Third International Conference on Genetic Algorithms (Mendel 97), pp. 176–182 (1997)

    Google Scholar 

  3. Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making Theory and Methodology. North-Holland, New York (1983)

    MATH  Google Scholar 

  4. Da Cunha, N.O., Polak, E.: Constrained minimization under vector-evaluated criteria in finite dimensional spaces. J. Math. Anal. Appl. 19(1), 103–124 (1967)

    Article  MathSciNet  Google Scholar 

  5. Datta, R., Deb, K. (eds.): Evolutionary Constrained Optimization. Infosys Science Foundation Series, Springer (2015)

    MATH  Google Scholar 

  6. Deb, K.: Optimization for Engineering Design: Algorithms and Examples. Prentice-Hall, New Delhi (1995)

    Google Scholar 

  7. Deb, K.: Evolutionary algorithms for multi-criterion optimization in engineering design. In: Miettinen, K., Neittaanmäki, P., Mäkelä, M.M., Périaux, J. (eds.) Evolutionary Algorithms in Engineering and Computer Science, pp. 135–161. Wiley, Chichester (1999)

    Google Scholar 

  8. Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms. Wiley, Chichester (2001)

    MATH  Google Scholar 

  9. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  10. Deb, K., Datta, R.: A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach. In: Proceedings of the IEEE World Congress on Computational Intelligence (WCCI-2010), pp. 165–172 (2010)

    Google Scholar 

  11. Deb, K., Goldberg, D.E.: An investigation of niche and species formation in genetic function optimization. In: Proceedings of the Third International Conference on Genetic Algorithms, pp. 42–50 (1989)

    Google Scholar 

  12. Deb, K., Jain, H.: An improved NSGA-II procedure for many-objective optimization Part I: Problems with box constraints. Technical Report 2012009, Indian Institute of Technology Kanpur (2012)

    Google Scholar 

  13. Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, Part I: solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577–601 (2014)

    Article  Google Scholar 

  14. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization, pp. 105–145. Springer, London (2005)

    Chapter  Google Scholar 

  15. Drechsler, R.: Evolutionary Algorithms for VLSI CAD. Kluwer Academic Publishers, Boston (1998)

    Book  Google Scholar 

  16. Ehrgott, M.: Multicriteria Optimization. Springer, Berlin (2005)

    MATH  Google Scholar 

  17. Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: formulation, discussion, and generalization. In: Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 416–423. Morgan Kaufmann, San Mateo (1993)

    Google Scholar 

  18. 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. Part A Syst. Hum. 28(1), 26–37 (1998)

    Article  Google Scholar 

  19. Homaifar, A., Lai, S.H.-V., Qi, X.: Constrained optimization via genetic algorithms. Simulation 62(4), 242–254 (1994)

    Article  Google Scholar 

  20. Horn, J., Nafploitis, N., Goldberg, D.E.: A niched Pareto genetic algorithm for multi-objective optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 82–87 (1994)

    Google Scholar 

  21. Huband, S., Barone, L., While, L., Hingston, P.: A scalable multi-objective test problem toolkit. In: Proceedings of the Evolutionary Multi-Criterion Optimization (EMO-2005). Springer, Berlin (2005)

    Google Scholar 

  22. Jain, H., Deb, K.: An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, Part II: Handling constraints and extending to an adaptive approach. IEEE Trans. Evol. Comput. 18(4), 602–622 (2014)

    Article  Google Scholar 

  23. Khare, V., Yao, X., Deb, K.: Performance scaling of multi-objective evolutionary algorithms. In: Proceedings of the Second Evolutionary Multi-Criterion Optimization (EMO-03) Conference (LNCS 2632), pp. 376–390 (2003)

    Google Scholar 

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

    Article  Google Scholar 

  25. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin (1992)

    Book  Google Scholar 

  26. Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evol. Comput. J. 4(1), 1–32 (1996)

    Article  Google Scholar 

  27. Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)

    MATH  Google Scholar 

  28. Osyczka, A., Kundu, S.: A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm. Struct. Optim. 10(2), 94–99 (1995)

    Article  Google Scholar 

  29. Ray, T., Tai, K., Seow, K.C.: An evolutionary algorithm for multiobjective optimization. Eng. Optim. 33(3), 399–424 (2001)

    Article  Google Scholar 

  30. Reklaitis, G.V., Ravindran, A., Ragsdell, K.M.: Engineering Optimization Methods and Applications. Wiley, New York (1983)

    Google Scholar 

  31. Shukla, P., Deb, K.: On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods. Eur. J. Oper. Res. (EJOR) 181(3), 1630–1652 (2007)

    Article  Google Scholar 

  32. Srinivas, N., Deb, K.: Multi-objective function optimization using non-dominated sorting genetic algorithms. Evol. Comput. J. 2(3), 221–248 (1994)

    Article  Google Scholar 

  33. Tanaka, M.: GA-based decision support system for multi-criteria optimization. In: Proceedings of the International Conference on Systems, Man and Cybernetics vol. 2, pp. 1556–1561 (1995)

    Google Scholar 

  34. Van Veldhuizen, D.: Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations. Ph.D. thesis, Dayton, OH: Air Force Institute of Technology (1999). Technical Report No. AFIT/DS/ENG/99-01

    Google Scholar 

  35. Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)

    Article  Google Scholar 

  36. Zhang, Q., Zhou, A., Zhao, S.Z., Suganthan, P.N., Liu, W., Tiwari, S.: Multiobjective optimization test instances for the CEC-2009 special session and competition. Nanyang Technological University, Technical report, Singapore (2008)

    Google Scholar 

  37. Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. J. 8(2), 125–148 (2000)

    Article  Google Scholar 

  38. 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 

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Author information

Authors and Affiliations

  1. Computational Optimization and Innovation (COIN) Laboratory, Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, 48864, USA

    Kalyanmoy Deb

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  1. Kalyanmoy Deb
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Correspondence to Kalyanmoy Deb .

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Editors and Affiliations

  1. South Asian University, New Delhi, Delhi, India

    Jagdish Chand Bansal

  2. ABV-Indian Institute of Information Technology and Management, Gwalior, Madhya Pradesh, India

    Pramod Kumar Singh

  3. Electronics and Communication Sciences Unit (ECSU), Indian Statistical Institute, Kolkata, West Bengal, India

    Nikhil R. Pal

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Deb, K. (2019). Constrained Multi-objective Evolutionary Algorithm. In: Bansal, J., Singh, P., Pal, N. (eds) Evolutionary and Swarm Intelligence Algorithms. Studies in Computational Intelligence, vol 779. Springer, Cham. https://doi.org/10.1007/978-3-319-91341-4_6

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