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Using MOPSO to Solve Multiobjective Bilevel Linear Problems

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Swarm Intelligence (ANTS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7461))

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Abstract

In this paper we propose a multiobjective particle swarm optimization (MOPSO) algorithm to solve bilevel linear programming problems with multiple objective functions at the upper level. A strategy based on an achievement scalarizing function is proposed for the global best selection and its performance is compared with other selection techniques. The outcomes of the algorithm on some bi-objective instances are compared with those obtained by an exact procedure that we developed before. The results indicate that the algorithm seems to be effective in solving this type of problems. In particular, the proposed selection technique provides a good convergence towards the Pareto front.

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References

  1. Alvarez-Benitez, J.E., Everson, R.M., Fieldsend, J.E.: A MOPSO Algorithm Based Exclusively on Pareto Dominance Concepts. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 459–473. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Alves, M.J., Dempe, S., Júdice, J.J.: Computing the Pareto frontier of a bi-objective bilevel linear problem using a multiobjective mixed-integer programming algorithm. Optimization 61(3), 335–358 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evolut. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  4. Deb, K., Sinha, A.: An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search-algorithm. Evol. Comput. J. 18(3), 403–449 (2010)

    Article  Google Scholar 

  5. 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: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 495–509. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Eichfelder, G.: Multiobjective bilevel optimization. Math. Program. 123(2), 419–449 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Halter, W., Mostaghim, S.: Bilevel optimization of multi-component chemical systems using particle swarm optimization. In: Proc. of the 2006 Congress on Evolutionary Computation (CEC 2006), pp. 1240–1247. IEEE Press (2006)

    Google Scholar 

  8. Li, X.: Better Spread and Convergence: Particle Swarm Multiobjective Optimization Using the Maximin Fitness Function. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 117–128. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  9. Moshirvaziri, K., Amouzegar, M.A., Jacobsen, S.E.: Test problem construction for linear bilevel programming problems. J. Global Optim. 8, 235–243 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. Osman, M.S., Abd El-Wahed, W.F., El Shafei, M.M., Abd El Wahab, H.B.: An approach for solving multi-objective bi-level linear programming based on genetic algorithm. J. Appl. Sci. Res. 6(4), 336–344 (2010)

    Google Scholar 

  11. Raquel, C.R., Naval Jr., P.C.: An effective use of crowding distance in multiobjective particle swarm optimization. In: Beyer, H.-G., Reilly, U.-M.O. (eds.) GECCO 2005, pp. 257–264. ACM Press (2005)

    Google Scholar 

  12. Reyes-Sierra, M., Coello Coello, C.A.: Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and ε-Dominance. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 505–519. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Shi, X., Xia, H.: Model and interactive algorithm of bi-level multi-objective decision-making with multiple interconnected decision makers. J. Multi-Criteria Decsion Analysis 10, 27–34 (2001)

    Article  MATH  Google Scholar 

  14. Wierzbicki, A.: Reference points in vector optimization and decision support. Tech. Rep. IR-98-017, IIASA, Laxenburg, Austria (1998)

    Google Scholar 

  15. Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Trans. Evolut. Comput. 3(4), 257–271 (1999)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Economics, University of Coimbra / INESC Coimbra, Portugal

    Maria João Alves

Authors
  1. Maria João Alves
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Editor information

Editors and Affiliations

  1. IRIDIA, Université Libre de Bruxelles, CoDE, Av. F. Roosevelt 50, CP 194/6, 1050, Brussels, Belgium

    Marco Dorigo , Mauro Birattari  & Thomas Stützle ,  & 

  2. ALBCOM, Department Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Omega 112 Campus Nord, 08034, Barcelona, Spain

    Christian Blum

  3. Instituto de Telecomunicações & Instituto Universitário de Lisboa (ISCTE-IUL), Av. das Foras Armadas, 1649-026, Lisboa, Portugal

    Anders Lyhne Christensen

  4. Department of Computer Science, University of Pretoria, 0002, Pretoria, South Africa

    Andries P. Engelbrecht

  5. Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, S1 3JD, Sheffield, UK

    Roderich Groß

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© 2012 Springer-Verlag Berlin Heidelberg

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Alves, M.J. (2012). Using MOPSO to Solve Multiobjective Bilevel Linear Problems. In: Dorigo, M., et al. Swarm Intelligence. ANTS 2012. Lecture Notes in Computer Science, vol 7461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32650-9_35

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  • DOI: https://doi.org/10.1007/978-3-642-32650-9_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32649-3

  • Online ISBN: 978-3-642-32650-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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