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Diversity-Driven Selection Operator for Combinatorial Optimization

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Evolutionary Multi-Criterion Optimization (EMO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12654))

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Abstract

A new selection operator for genetic algorithms dedicated to combinatorial optimization, the Diversity Driven selection operator, is proposed. The proposed operator treats the population diversity as a second objective, in a multiobjectivization framework. The Diversity Driven operator is parameterless, and features low computational complexity. Numerical experiments were performed considering four different algorithms in 24 instances of seven combinatorial optimization problems, showing that it outperforms five classical selection schemes with regard to solution quality and convergence speed. Besides, the Diversity Driven selection operator delivers good and considerably different solutions in the final population, which can be useful as design alternatives.

This work was supported by the Brazilian agencies CNPq, CAPES and FAPEMIG.

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Notes

  1. 1.

    n is the problem size: number of vertices for DCMST, QMST and OCST; number of objects for LinOrder. number of tasks for Scheduling, Makespan and GAP.

References

  1. Bäck, T., Fogel, D.B., Michalewicz, Z. (eds.): Handbook on Evolutionary Computation. Oxford University Press, Oxford (1997)

    MATH  Google Scholar 

  2. Baker, J.E.: Adaptive selection methods for genetic algorithms. In: Proceedings of the 1st International Conference on Genetic Algorithms, pp. 101–111 (1985)

    Google Scholar 

  3. Baker, J.E.: Reducing bias and inefficiency in the selection algorithm. In: Proceedings of the 2nd International Conference on Genetic Algorithms and their Application, pp. 14–21 (1987)

    Google Scholar 

  4. Balachandran, V.: An integer generalized transportation model for optimal job assignment in computer networks. Oper. Res. 24, 742–759 (1976)

    Article  MathSciNet  Google Scholar 

  5. Beasley, J.E.: OR-Library. http://people.brunel.ac.uk/ mastjjb/jeb/orlib/schinfo.html. Accessed 20 Sep 2020

  6. Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Royal Stat. Soc. Ser. B 57(1), 289–300 (1995)

    MathSciNet  MATH  Google Scholar 

  7. Brandstreet, L., While, L., Barone, L.: A fast incremental hypervolume algorithm. IEEE Trans. Evol. Comp. 12(6), 714–723 (2008)

    Article  Google Scholar 

  8. Bui, L.T., Abbass, H.A., Branke, J.: Multiobjective optimization for dynamic environments. In: Proceedings on IEEE Congress on Evolutionary Computation (CEC 2005), Edinburgh, UK, vol. 3, pp. 2349–2356 (2005)

    Google Scholar 

  9. Campelo, F., Takahashi, F.: Sample size estimation for power and accuracy in the experimental comparison of algorithms. J. Heuristics 25(2), 305–338 (2018). https://doi.org/10.1007/s10732-018-9396-7

    Article  Google Scholar 

  10. Carrano, E.G., Ribeiro, G., Cardoso, E., Takahashi, R.H.C.: Subpermutation based evolutionary multiobjective algorithm for load restoration in power distribution networks. IEEE Trans. Evol. Comp. 20, 546–562 (2016)

    Article  Google Scholar 

  11. Carrano, E.G., Wanner, E.F., Takahashi, R.H.C.: A multicriteria statistical based comparison methodology for evaluating evolutionary algorithms. IEEE Trans. Evol. Comp. 15(6), 848–870 (2011)

    Article  Google Scholar 

  12. Carrano, E.G., Takahashi, R.H.C., Fonseca, C.M., Neto, O.M.: Nonlinear network optimization - an embedding vector space approach. IEEE Trans. Evol. Comp. 14(2), 206–226 (2010)

    Article  Google Scholar 

  13. Chicano, F., Alba, E.: Exact computation of the expectation curves of the bit-flip mutation using landscapes theory. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2011), Dublin, Ireland, pp. 2027–2034 (2011)

    Google Scholar 

  14. Cioppa, A., De Stefano, C., Marcelli, A.: Where are the niches? Dynamic fitness sharing. IEEE Trans. Evol. Comp. 11(4), 453–465 (2007)

    Article  Google Scholar 

  15. Cully, A., Demiris, Y.: Quality and diversity optimization: a unifying modular framework. IEEE Trans. Evol. Comput. 22(2), 245–259 (2018)

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Garcia-Najera, A., Bullinaria, J.A.: An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows. Comp. Oper. Res. 38, 287–300 (2011)

    Article  MathSciNet  Google Scholar 

  18. Ginley, B.M., Maher, J., O’Riordan’, C., Morgan, F.: Maintaining healthy population diversity using adaptive crossover, mutation, and selection. IEEE Trans. Evol. Comp. 15(5), 692–714 (2011)

    Article  Google Scholar 

  19. Goldberg, D.E., Lingle, R.: Alleles, loci, and the traveling salesman problem. In: Proceedings of the Conference on Genetic Algorithms, pp. 154–159 (1985)

    Google Scholar 

  20. Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning, 1st edn. Addison-Wesley, Boston (1989)

    MATH  Google Scholar 

  21. Grötschel, M., Jünger, M., Reinelt, G.: Optimal triangulation of large real world input-output matrices. Statistische Hefte 25, 261–295 (1984)

    Article  Google Scholar 

  22. Krishnamoorthy, M., Ernst, A.T., Sharaiha, Y.M.: Comparison of algorithms for the degree constrained minimum spanning tree. J. Heuristics 7, 587–611 (2001)

    Article  Google Scholar 

  23. Landa Silva, J.D., Burke, E.K.: Using diversity to guide the search in multi-objective optimization, chapter 30, pp. 727–751. World Scientific (2004)

    Google Scholar 

  24. Luke, S.: Essentials of Metaheuristics. Lulu (2016). https://cs.gmu.edu/sean/book/metaheuristics/Essentials.pdf

  25. Martins, F.V.C., Carrano, E.G., Wanner, E.F., Takahashi, R.H.C., Mateus, G.R., Nakamura, F.G.: On a vector space representation in genetic algorithms for sensor scheduling in wireless sensor networks. Evol. Comp. 22, 361–403 (2014)

    Article  Google Scholar 

  26. Montgomery, D., Runger, G.: Applied Statistics and Probability for Engineers. Wiley, Newyork (2003)

    MATH  Google Scholar 

  27. Moraglio, A.: Towards a geometric unification of evolutionary algorithms. Ph.D. thesis, University of Essex (2007)

    Google Scholar 

  28. Neumann, A., Gao, W., Wagner, M., Neumann, F.: Evolutionary diversity optimization using multi-objective indicators. In: Proceedings of the Genetic and Evolutionary Computation Conference. ACM (2019)

    Google Scholar 

  29. Pfund, M., Fowler, J.W., Gupta, J.N.D.: A survey of algorithms for single and multi-objective unrelated parallel-machine deterministic scheduling problems. J. Chin. Inst. Ind. Eng. 21, 230–241 (2004)

    Google Scholar 

  30. Reinelt, G.: LOLIB. http://comopt.ifi.uni-heidelberg.de/software/LOLIB/. Accessed 20 Sep 2020

  31. Segura, C., Coello Coello, C.A., Miranda, G., León, C.: Using multi-objective evolutionary algorithms for single-objective optimization. Ann. Oper. Res. 11(3), 201–228 (2013). https://doi.org/10.1007/s10288-013-0248-x

    Article  MathSciNet  MATH  Google Scholar 

  32. Segura, C., Coello Coello, C.A., Segredo, E., Miranda, G., Leon, C.: Improving the diversity preservation of multi-objective approaches used for single-objective optimization. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2013), Cancun, Mexico, pp. 3198–3205 (2013)

    Google Scholar 

  33. Soak, S., Corne, D.W., Ahn, B.: The edge-window-decoder representation for tree-based problems. IEEE Trans. Evol. Comp. 10, 124–144 (2006)

    Article  Google Scholar 

  34. Subtil, R.F., Carrano, E.G., Souza, M.J., Takahashi, R.H.C.: Using an enhanced integer NSGA-II for solving the multiobjective generalized assignment problem. In: Proceedings of the IEEE World Congress on Computational Intelligence, Barcelona, Spain (2010)

    Google Scholar 

  35. Syswerda, G.: Uniform crossover in genetic algorithms. In: Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 2–9 (1989)

    Google Scholar 

  36. Toffolo, A., Benini, E.: Genetic diversity as an objective in multi-objective evolutionary algorithms. Evol. Comp. 11(2), 151–167 (2003)

    Article  Google Scholar 

  37. Wessing, S., Preuss, M., Rudolph, G.: Niching by multiobjectivization with neighbor information: trade-offs and benefits. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2013), Cancun, Mexico, pp. 103–110 (2013)

    Google Scholar 

  38. Zhang, X., Tian, Y., Cheng, R., Jin, Y.: An efficient approach to nondominated sorting for evolutionary multiobjective optimization. IEEE Trans. Evol. Comput. 19(2), 201–213 (2015)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Eduardo G. Carrano & Felipe Campelo

  2. School of Engineering and Applied Science, Aston University, Birmingham, UK

    Felipe Campelo

  3. Department of Mathematics, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Ricardo H. C. Takahashi

Authors
  1. Eduardo G. Carrano
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  2. Felipe Campelo
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  3. Ricardo H. C. Takahashi
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Corresponding author

Correspondence to Ricardo H. C. Takahashi .

Editor information

Editors and Affiliations

  1. Southern University of Science and Technology, Shenzhen, China

    Hisao Ishibuchi

  2. City University of Hong Kong, Kowloon Tong, China

    Qingfu Zhang

  3. Southern University of Science and Technology, Shenzhen, China

    Ran Cheng

  4. University of Exeter, Exeter, UK

    Ke Li

  5. Xi'an Jiaotong University, Xi'an, China

    Hui Li

  6. Xidian University, Xi'an, China

    Handing Wang

  7. East China Normal University, Shanghai, China

    Aimin Zhou

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Carrano, E.G., Campelo, F., Takahashi, R.H.C. (2021). Diversity-Driven Selection Operator for Combinatorial Optimization. In: Ishibuchi, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2021. Lecture Notes in Computer Science(), vol 12654. Springer, Cham. https://doi.org/10.1007/978-3-030-72062-9_15

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  • DOI: https://doi.org/10.1007/978-3-030-72062-9_15

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  • Online ISBN: 978-3-030-72062-9

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