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A Differential Evolution Algorithm to Semivectorial Bilevel Problems

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Machine Learning, Optimization, and Big Data (MOD 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10710))

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Abstract

Semivectorial bilevel problems (SVBLP) deal with the optimization of a single function at the upper level and multiple objective functions at the lower level of hierarchical decisions. Therefore, a set of nondominated solutions to the lower level decision maker (the follower) exists and should be exploited for each setting of decision variables controlled by the upper level decision maker (the leader). This paper presents a new algorithmic approach based on differential evolution to compute a set of four extreme solutions to the SVBLP. These solutions capture not just the optimistic vs. pessimistic leader’s attitude but also possible follower’s reactions more or less favorable to the leader within the lower level nondominated solution set. The differential evolution approach is compared with a particle swarm optimization algorithm. In this experimental comparison we draw attention to pitfalls associated with the interpretation of results and assessment of the performance of algorithms in SVBLP.

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References

  1. Alves, M.J., Antunes, C.H., Carrasqueira, P.: A PSO approach to semivectorial bilevel programming: pessimistic, optimistic and deceiving solutions. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2015), pp. 599–606 (2015)

    Google Scholar 

  2. Bonnel, H.: Optimality conditions for the semivectorial bilevel optimization problem. Pac. J. Optim. 2, 447–468 (2006)

    MathSciNet  MATH  Google Scholar 

  3. Bonnel, H., Morgan, J.: Semivectorial bilevel optimization problem: penalty approach. J. Optim. Theor. Appl. 131, 365–382 (2006)

    Article  MathSciNet  Google Scholar 

  4. Ankhili, Z., Mansouri, A.: An exact penalty on bilevel programs with linear vector optimization lower level. Eur. J. Oper. Res. 197, 36–41 (2009)

    Article  MathSciNet  Google Scholar 

  5. Zheng, Y., Wan, Z.: A solution method for semivectorial bilevel programming problem via penalty method. J. Appl. Math. Comput. 37, 207–219 (2011)

    Article  MathSciNet  Google Scholar 

  6. Ren, A., Wang, Y.: A novel penalty function method for semivectorial bilevel programming problem. Appl. Math. Model. 40, 135–149 (2016)

    Article  MathSciNet  Google Scholar 

  7. Calvete, H., Galé, C.: On linear bilevel problems with multiple objectives at the lower level. Omega 39, 33–40 (2011)

    Article  Google Scholar 

  8. Liu, B., Wan, Z., Chen, J., Wang, G.: Optimality conditions for pessimistic semivectorial bilevel programming problems. J. Inequal. Appl. 2014, 41 (2014)

    Article  MathSciNet  Google Scholar 

  9. Lv, Y., Chen, J.: A discretization iteration approach for solving a class of semivectorial bilevel programming problem. J. Nonlinear Sci. Appl. 9, 2888–2899 (2016)

    Article  MathSciNet  Google Scholar 

  10. Alves, M.J., Antunes, C.H.: An illustration of different concepts of solutions in semivectorial bilevel programming. In: 2016 IEEE Symposium on Computational Intelligence (SSCI) (2016)

    Google Scholar 

  11. Mezura-Montes, E., Velázquez-Reyes, J., Coello Coello, C.A.: A comparative study of differential evolution variants for global optimization. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 485–492 (2006)

    Google Scholar 

  12. Deb, K., Sinha, A.: Solving bilevel multi-objective optimization problems using evolutionary algorithms. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 110–124. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01020-0_13

    Chapter  Google Scholar 

  13. Sinha, A., Malo, P., Deb, K.: Approximated set-valued mapping approach for handling multiobjective bilevel problems. Comput. Oper. Res. 77, 194–209 (2017)

    Article  MathSciNet  Google Scholar 

  14. Deb, K., Sinha, A.: Constructing test problems for bilevel evolutionary multi-objective optimization. In: 2009 IEEE Congress on Evolutionary Computation, pp. 1153–1160 (2009)

    Google Scholar 

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Acknowledgment

This work was supported by projects UID/MULTI/00308/2013 and SAICTPAC/0004/2015-POCI-01-0145-FEDER-016434.

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Authors and Affiliations

  1. CeBER and Faculty of Economics, University of Coimbra, Coimbra, Portugal

    Maria João Alves

  2. DEEC, University of Coimbra, Polo 2, Coimbra, Portugal

    Carlos Henggeler Antunes

  3. INESC Coimbra, Coimbra, Portugal

    Maria João Alves & Carlos Henggeler Antunes

Authors
  1. Maria João Alves
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  2. Carlos Henggeler Antunes
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Corresponding author

Correspondence to Maria João Alves .

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Editors and Affiliations

  1. University of Catania, Catania, Italy

    Giuseppe Nicosia

  2. University of Florida, Gainesville, FL, USA

    Panos Pardalos

  3. University of Catania, Catania, Italy

    Giovanni Giuffrida

  4. Harvard University, Cambridge, MA, USA

    Renato Umeton

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Alves, M.J., Antunes, C.H. (2018). A Differential Evolution Algorithm to Semivectorial Bilevel Problems. In: Nicosia, G., Pardalos, P., Giuffrida, G., Umeton, R. (eds) Machine Learning, Optimization, and Big Data. MOD 2017. Lecture Notes in Computer Science(), vol 10710. Springer, Cham. https://doi.org/10.1007/978-3-319-72926-8_15

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  • DOI: https://doi.org/10.1007/978-3-319-72926-8_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72925-1

  • Online ISBN: 978-3-319-72926-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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