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Generation of Pareto optimal solutions using generalized DEA and PSO

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Abstract

Meta-heuristic methods such as particle swarm optimization and genetic algorithms have been applied in solving multi-objective optimization problems, and have been observed to be useful for generating a good approximation of Pareto optimal solutions. This paper suggests a multi-objective particle swarm optimization (MOPSO) utilizing generalized data envelopment analysis (GDEA) in order to decide adaptively parameters of MOPSO as well as to improve the convergence and the diversity in the search of solutions. In addition, the effectiveness of the proposed method using GDEA will be investigated by comparison with conventional methods through several numerical examples.

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Notes

  1. The particles obtained at each time step are stored temporarily in an external archive, and among them, the non-dominated ones have been kept with the given archive size by the crowding distance and some clustering, and so on. Hereafter, they are called the external best particles.

  2. GDEA results are not so sensitive for \(\alpha \). If there is no prior knowledge for a given optimization problem, \(\alpha \) can be set as a sufficient value such as \(10^{-7}\).

  3. NSGA-II is prominent in generating Pareto optimal solutions, and the MOPSO is a simple and basic algorithm for multi-objective PSO. The implementations have been done by modeFRONTIER 4.2.1.

References

  1. Agrawal, S., Panigrahi, B.K., Tiwari, M.K.: Multiobjective particle swarm algorithm with fuzzy clustering for electrical power dispatch. IEEE Trans. Evol. Comput. 12(5), 529–541 (2008)

    Article  Google Scholar 

  2. Alvarez-Benitez, J.E., Everson, R.M., Fieldsend, J.E.: A MOPSO algorithm based exclusively on Pareto dominance concepts. In: Proceedings of Evolutionary Multi-criterion Optimization (EMO 2005), vol. 3410, pp. 459–473 (2005)

  3. Banker, R.D., Charnes, A., Cooper, W.W.: Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag. Sci. 30, 1078–1092 (1984)

    Article  MATH  Google Scholar 

  4. Charnes, A., Cooper, W.W., Rhodes, E.: Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2(6), 429–444 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  5. Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-objective Problems. Kluwer Academic, Dordrecht (2001)

    Google Scholar 

  6. Coello Coello, C.A., Pulido, G.T., Lechuga, M.S.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 256–279 (2004)

    Article  Google Scholar 

  7. Daneshyari, M., Yen, G.G.: Cultural-based multiobjective particle swarm optimization. IEEE Trans. Syst. Man Cybern. B Cybern. 41(2), 553–567 (2011)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  9. 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 

  10. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization: Theoretical Advances and Applications, Advanced Information and Knowledge Processing. Springer, Berlin, pp. 105–145 (2005)

  11. Durillo, J.J., García-Nieto, J., Nebro, A.J., Coello Coello, C.A., Luna, F., Alba, E.: Multi-objective particle swarm optimizers: an experimental comparison. In: Proceedings of Evolutionary Multi-criterion Optimization (EMO 2009), Lecture Notes in Computer Science, vol. 5467, pp. 495–509 (2009)

  12. Fieldsend , J.E., Singh, S.: A multi-objective algorithm based upon particle swarm optimization, an efficient data structure and turbulence. In: Proceedings of 2002 UK Workshop on Computational Intelligence, pp. 37–44 (2002)

  13. Guo, Y., Li, N., Zhang, H., Ye, T.: Elitist vector evaluated particle swarm optimization for multi-mode resource leveling problems. J. Comput. Inf. Syst. 8(9), 3697–3705 (2012)

    Google Scholar 

  14. Hu, X., Eberhart, R.: Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Proceedings of IEEE Congress Evolutionary Computation, vol. 2, pp. 1677–1681 (2002)

  15. Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann, Los Altos (2001)

    Google Scholar 

  16. Kursawe, F.: A variant of evolution strategies for vector optimization. In: Proceedings of Parallel Problem Solving from Nature I (PPSN-I), pp. 193–197 (1991)

  17. Li, X.: A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Proceedings of Genetic and Evolutionary Computation (GECCO 2003), Lecture Notes in Computer Science, vol. 2723/2003, pp. 37–48 (2003)

  18. Mussetta, M., Pirinoli, P., Selleri, S., Zich, R.E.: Meta-PSO for multi-objective EM problems. In: Nedjah, N., dos Santos Coelho, L., de Macedo Mourelle, L. (eds.) Multi-objective Swarm Intelligent Systems, Studies in Computational Intelligence, vol. 261, pp. 125–150 (2010)

  19. Moore, J., Chapman, R.: Application of particle swarm to multiobjective optimization. Technical report, Department of Computer Science and Software Engineering, Auburn University (1999)

  20. Mostaghim, S., Teich, J.: Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). In: Proceedings of 2003 IEEE Swarm Intelligence Symposium, pp. 26–33 (2003)

  21. Nebro, A.J., Durillo, J.J., García-Nieto, J., Coello Coello, C.A., Luna, F., Alba, E.: SMPSO: a new PSO-based metaheuristic for multi-objective optimization. In: Proceedings of Evolutionary Multi-criterion Optimization (EMO 2009), pp. 495–509 (2009)

  22. Nakayama, H.: Aspiration level approach to interactive multi-objective programming and its applications. In: Pardalos, P.M., Siskos, Y., Zopounidis, C. (eds.) Advances in Multicriteria Analysis. Kluwer Academic, Dordrecht, pp. 147–174 (1995)

  23. Pareto, V.: Manuale di Economia Politica, Societa Editrice Libraria. Milano (trans: Schwier, A.S.) Manual of Political Economy. Macmillan, New York (1906)

  24. Parsopoulos, K.E., Vrahatis, M.N.: Particle swarm optimization method in multiobjective problems. In: Proceedings of 2002 ACM Symposium on Applied Computing, pp. 603–607 (2002)

  25. Reyes Sierra, M., Coello Coello, C.A.: Improving PSO-based multi-objective optimization esing crowding, mutation and \(\epsilon \)-dominance. In: Proceedings of Evolutionary Multi-Criterion Optimization (EMO 2005), vol. 3410, pp. 505–519 (2005)

  26. Reyes-Sierra, M., Coello Coello, C.A.: Multiple objective particle swarm optimizers: a survey of the state-of-art. Int. J. Comput. Intell. Res. 2(3), 287–308 (2006)

    MathSciNet  Google Scholar 

  27. Salazar-Lechuga, M., Rowe, J.E.: Particle swarm optimization and fitness sharing to solve multi-objective optimization problems. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2005), vol. 2, pp. 1204–1211 (2005)

  28. Santana, R.A., Pontes, M.R., Bastos-Filho, C.J.A.: A multiple objective particle swarm optimization approach using crowding distance and roulette wheel. In: Proceedings of IEEE 9th International Conference on Intelligent Systems Design and Applications, pp. 237–242 (2009)

  29. Tanaka, M., Watanabe, H., Furukawa, Y., Tanino, T.: GA-based decision support system for multicriteria optimization. In: Proceedings of the 1995 International Conference of Systems, Man, and Cybernetics, vol. 2, pp. 1556–1561 (1995)

  30. Toscano, G., Coello Coello, C.A.: Using clustering techniques to improve the performance of a multi-objective particle swarm optimizer. In: Proceedings of Genetic and Evolutionary Computation (GECCO 2004), Lecture Notes in Computer Science, vol. 3102/2004, pp. 225–237 (2004)

  31. Toscano-Pulido, G., Coello Coello, C.A., Santana-Quintero, L.V.: EMOPSO: a multi-objective particle swarm optimizer with emphasis on efficiency. In: Proceedings of Evolutionary Multi-Criterion Optimization (EMO 2007), Lecture Notes in Computer Science, vol. 4403, pp. 272–285 (2007)

  32. Tulkens, H.: On FDH efficiency: some methodological issues and applications to retail banking, courts, and urban transit. J. Prod. Anal. 4, 183–210 (1993)

    Article  Google Scholar 

  33. Wu, D., Ogawa, M., Suzuki, Y., Ogai, H., Kusaka, J.: Modified Multi-objective particle swarm optimization: application to optimization of diesel engine control parameter. SICE J. Control, Meas. Syst. Integr. 3(5), 315–323 (2011)

    Article  Google Scholar 

  34. Yun, Y.B., Nakayama, C.H., Arakawa, M.: Multiple criteria decision making with generalized DEA and an aspiration level method. Eur. J. Oper. Res. 158(3), 697–706 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  35. Yun, Y.B., Nakayama, H., Tanino, T.: A generalized model for data envelopment analysis. Eur. J. Oper. Res. 157(1), 87–105 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  36. Yun, Y.B., Nakayama, C.H., Tanino, C.T., Arakawa, M.: Generation of efficient frontiers in multi-objective optimization problems by generalized data envelopment analysis. Eur. J. Oper. Res. 129(3), 586–595 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  37. Yun, Y.B., Yoon, C.M., Nakayama, H.: Genetic algorithm for multi-objective optimization using GDEA. Adv. Nat. Comput. III 3612, 409–416 (2005)

    Article  Google Scholar 

  38. Zhang, Q., Mahfouf, M.: A modified PSO with a dynamically varying population and its application to the multi-objective optimal design of alloy steels. In: Proceedings of IEEE Conference on Evolutionary Computation (CEC 2009), pp. 3241–3248 (2009)

  39. Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications, Ph. D. thesis, Swiss Federal Institute of Technology (ETH), Shaker Verlag (1999)

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Authors and Affiliations

  1. Kansai University, 3-3-35 Yamate, Suita, Osaka, 564-8680, Japan

    Yeboon Yun

  2. Konan University, 8-9-1 Okamoto, Higashinada, Kobe, 658-8501, Japan

    Hirotaka Nakayama

  3. Pukyong National University, 599-1 Daeyeon 3-dong, Nam-gu, Busan, 608-737, Korea

    Min Yoon

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  1. Yeboon Yun
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  3. Min Yoon
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Correspondence to Yeboon Yun.

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Yun, Y., Nakayama, H. & Yoon, M. Generation of Pareto optimal solutions using generalized DEA and PSO. J Glob Optim 64, 49–61 (2016). https://doi.org/10.1007/s10898-015-0314-3

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