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A Cuckoo Quantum Evolutionary Algorithm for the Graph Coloring Problem

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Bio-Inspired Computing: Theories and Applications (BIC-TA 2021)

Abstract

A typical combinatorial optimization problem, Graph Coloring Problem (GCP), has a wide range of applications in the fields of science and engineering. A cuckoo quantum evolutionary algorithm (CQEA) is proposed for the GCP, which is based on the framework of quantum-inspired evolutionary algorithm. To reduce iterations for the search of the chromatic number, the initial quantum population is generated with random initialization assisted by inheritance. Moreover, improvement of global exploration is achieved by incorporating the cuckoo search strategy, and a local search operation, as well as a perturbance strategy, is developed to enhance its performance on GCP. Numerical results show that CQEA has strong exploration and exploitation ability, and is competitive compared with the state-of-the-art heuristic algorithms.

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Notes

  1. 1.

    Zero rows are rows of a matrix where all elements are equal to “0”.

  2. 2.

    http://mat.gsia.cmu.edu/COLOR/instances.html.

References

  1. Mostafaie, T., Modarres, F., Navimipour, N.J.: A systematic study on meta-heuristic approaches for solving the graph coloring problem. Comput. Oper. Res. 120, 104850 (2020)

    Google Scholar 

  2. Djelloul, H., Layeb, A., Chikhi, S.: Quantum inspired cuckoo search algorithm for graph colouring problem. Int. J. Bio-Inspired Comput. 7, 183–194 (2015)

    Article  Google Scholar 

  3. Mahmoudi, S., Lotfi, S.: Modified cuckoo optimization algorithm (MCOA) to solve graph coloring problem. Appl. Soft Comput. 33, 48–64 (2015)

    Article  Google Scholar 

  4. Aranha, C., Toda, K., Kanoh, H.: Solving the graph coloring problem using cuckoo search. In: Tan, Y., Takagi, H., Shi, Y. (eds.) ICSI 2017. LNCS, vol. 10385, pp. 552–560. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61824-1_60

    Chapter  Google Scholar 

  5. Zhou, Y., Zheng, H., Luo, Q., Wu, J., Guangxi, N.: An improved cuckoo search algorithm for solving planar graph coloring problem. Appl. Math. Inf. Sci. 7, 785–792 (2013)

    Article  MathSciNet  Google Scholar 

  6. Silva, A.F., Rodriguez, L.G., Filho, J.F.: The improved Colour Ant algorithm: a hybrid algorithm for solving the graph colouring problem. Int. J. Bio-Inspired Comput. 16, 1–12 (2020)

    Article  Google Scholar 

  7. Mohammadnejad, A., Eshghi, K.: An efficient hybrid meta-heuristic ant system for minimum sum colouring problem. Int. J. Oper. Res. 34, 269–284 (2019)

    Article  MathSciNet  Google Scholar 

  8. Marappan, R., Sethumadhavan, G.: Solution to graph coloring problem using divide and conquer based genetic method. 2016 International Conference on Information Communication and Embedded Systems (ICICES), 1–5 (2016)

    Google Scholar 

  9. Douiri, S.M., Elbernoussi, S.: Solving the graph coloring problem via hybrid genetic algorithms. J. King Saud Univ. Eng. Sci. 27, 114–118 (2015)

    Google Scholar 

  10. Lü, Z., Hao, J.: A memetic algorithm for graph coloring. Eur. J. Oper. Res. 203, 241–250 (2010)

    Article  MathSciNet  Google Scholar 

  11. Moalic, L., Gondran, A.: Variations on memetic algorithms for graph coloring problems. J. Heuristics 24(1), 1–24 (2017). https://doi.org/10.1007/s10732-017-9354-9

    Article  Google Scholar 

  12. Hertz, A., Werra, D.: Using tabu search techniques for graph coloring. Computing 39, 345–351 (2005)

    Article  MathSciNet  Google Scholar 

  13. Bessedik, M., Toufik, B., Drias, H.: How can bees colour graphs. Int. J. Bio-Inspired Comput. 3, 67–76 (2011)

    Article  Google Scholar 

  14. Wang, Z., Wang, D., Bao, X., Wu, T.: A parallel biological computing algorithm to solve the vertex coloring problem with polynomial time complexity. J. Intell. Fuzzy Syst. 40, 3957–3967 (2021)

    Article  Google Scholar 

  15. Han, K., Kim, J.: Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans. Evol. Comput. 6, 580–593 (2002). https://doi.org/10.1109/TEVC.2002.804320

    Article  Google Scholar 

  16. Yang, X., Deb, S.: Engineering optimisation by cuckoo search. Int. J. Math. Modell. Numerical Optim. 1, 330–343 (2010)

    MATH  Google Scholar 

  17. Santillan, J.H., Tapucar, S., Manliguez, C., Calag, V.: Cuckoo search via Lévy flights for the capacitated vehicle routing problem. J. Ind. Eng. Int. 14(2), 293–304 (2017). https://doi.org/10.1007/s40092-017-0227-5

    Article  Google Scholar 

  18. Yang, X.: Cuckoo search for inverse problems and simulated-driven shape optimization. J. Comput. Methods Sci. Eng. 12, 129–137 (2012)

    Google Scholar 

  19. Dökeroglu, T., Sevinç, E.: Memetic teaching-learning-based optimization algorithms for large graph coloring problems. Eng. Appl. Artif. Intell. 102 104282 (2021)

    Google Scholar 

  20. Andreu-Guzmán, J.A., Valencia-Cabrera, L.: A novel solution for GCP based on an OLMS membrane algorithm with dynamic operators. J. Membrane Comput. 2(1), 1–13 (2019). https://doi.org/10.1007/s41965-019-00026-x

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhao, R., et al.: Discrete selfish herd optimizer for solving graph coloring problem. Appl. Intell. 50(5), 1633–1656 (2020). https://doi.org/10.1007/s10489-020-01636-0

    Article  Google Scholar 

  22. Basmassi, M.A., Benameur, L., Chentoufi, J.A.: A novel greedy genetic algorithm to solve combinatorial optimization problem. ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, pp. 117–120 (2020)

    Google Scholar 

  23. Baiche, K., Meraihi, Y., Hina, M.D., Ramdane-Cherif, A., Mahseur, M.: Solving graph coloring problem using an enhanced binary dragonfly algorithm. Int. J. Swarm Intell. Res. 10, 23–45 (2019)

    Article  Google Scholar 

  24. West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice Hall, Upper Saddle River (2001)

    Google Scholar 

  25. Galán, S.F.: Simple decentralized graph coloring. Comput. Optim. Appl. 66(1), 163–185 (2016). https://doi.org/10.1007/s10589-016-9862-9

    Article  MathSciNet  MATH  Google Scholar 

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Xu, Y., Chen, Y. (2022). A Cuckoo Quantum Evolutionary Algorithm for the Graph Coloring Problem. In: Pan, L., Cui, Z., Cai, J., Li, L. (eds) Bio-Inspired Computing: Theories and Applications. BIC-TA 2021. Communications in Computer and Information Science, vol 1565. Springer, Singapore. https://doi.org/10.1007/978-981-19-1256-6_7

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  • DOI: https://doi.org/10.1007/978-981-19-1256-6_7

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