Abstract
Graph coloring problem (GCP) is a classical combinatorial optimization problem and has many applications in the industry. Many algorithms have been proposed for solving GCP. However, insufficient efficiency and unreliable stability still limit their performance. Aiming to overcome these shortcomings, a physarum-based ant colony optimization for solving GCP is proposed in this paper. The proposed algorithm takes advantage of the positive feedback mechanism of the physarum mathematical model to optimize the pheromone matrix updating in the ant colony optimization. Some experiments are implemented to estimate the efficiency and stability of the proposed algorithm compared with typical ant colony optimization and some state-of-art algorithms. According to these results, in terms of the efficiency, stability and computational cost, we can daringly infer that the improved ant colony optimization with the physarum model performs better than the aforementioned for graph coloring. In particular, it is recommended that the model is of rationality and the proposed algorithm is of validity, which will foster a science of color number and computational cost in GCP.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Tayarani-N, M.-H., Prugel-Bennett, A.: On the landscape of combinatorial optimization problems. IEEE Trans. Evol. Comput. 18(3), 420–434 (2014)
Checco, A., Leith, D.J.: Fast, responsive decentralized graph coloring. IEEE/ACM Trans. Netw. 15(6), 3628–3640 (2017)
Topcuoglu, H.R., Demiroz, B., Kandemir, M.: Solving the register allocation problem for embedded systems using a hybrid evolutionary algorithm. IEEE Trans. Evol. Comput. 11(5), 620–634 (2007)
Bessedik, M., Laib, R., Boulmerka, A., Drias, H.: Ant colony system for graph coloring problem. In: International Conference on Computational Intelligence for Modelling Control and Automation, pp. 786–791 (2005)
Liu, Y.C., Xu, J., Pan, L.Q., Wang, S.Y.: DNA solution of a graph coloring problem. J. Chem. Inf. Comput. Sci. 42(3), 524–528 (2002)
Lintzmayer, C.N., Mulati, M.H., Silva, A.F.: Toward better performance of colorant ACO algorithm. In: 30th International Conference of the Chilean Computer Science Society, pp. 256–264 (2011)
Mosa, M.A., Hamouda, A., Marei, M.: Graph coloring and ACO based summarization for social networks. Expert Syst. Appl. 74, 115–126 (2017)
Qin, J., Yin, Y.X., Ban, X.J.: Hybrid discrete particle swarm algorithm for graph coloring problem. J. Chem. Phys. 6(6), 1175–1182 (2011)
Liu, Y.X., et al.: Solving NP-hard problems with Physarum-based ant colony system. IEEE/ACM Trans. Comput. Biol. Bioinf. 14(1), 108–120 (2017)
Zhang, Z.L., Gao, C., Liu, Y.X., Qian, T.: A universal optimization strategy for ant colony optimization algorithms based on the physarum-inspired mathematical model. Bioinspir. Biomim. 9(3), 036006 (2014)
Gao, C., et al.: Does being multi-headed make you better at solving problems? A survey of Physarum-based models and computations. Phys. Life Rev. (2018). https://doi.org/10.1016/j.plrev.2018.05.002
Tero, A., Kobayashi, R., Nakagaki, T.: A mathematical model for adaptive transport network in path finding by true slime mold. J. Theor. Biol. 244(4), 553–564 (2007)
Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B Cybern. 26(1), 29–41 (1996)
Mahmoudi, S., Lotfi, S.: Modified cuckoo optimization algorithm (MCOA) to solve graph coloring problem. Appl. Soft Comput. 33, 48–64 (2015)
Nakagaki, T., Yamada, H., Agota, T.: Intelligence: Maze-solving by an amoeboid organism. Nature 407(6803), 470–470 (2000)
Tero, A., Kobayashi, R., Nakagaki, T.: A coupled-oscillator model with a conservation law for the rhythmic amoeboid movements of plasmodial slime molds. Physica D. 205(1), 125–135 (2005)
Gao, C., Liang, M.X., Li, X.H., Zhang, Z.L., Wang, Z., Zhou, Z.L.: Network community detection based on the Physarum-inspired computational framework. IEEE/ACM Trans. Comput. Biol. Bioinf. 15(6), 1916–1928 (2018)
Gao, C., Chen, S., Li, X.H., Huang, J.J., Zhang, Z.L.: A Physarum-inspired optimization algorithm for load-shedding problem. Appl. Soft Comput. 61, 239–255 (2017)
Jones, J.: Characteristics of pattern formation and evolution in approximations of physarum transport networks. Artif. Life 16(2), 127–153 (2010)
Miyaji, T., Ohnishi, I.: Mathematical analysis to an adaptive network of the Plasmodium system. Hokkaido Math. J. 36(2), 445–465 (2007)
Li, K.: An improved genetic algorithm for solving graph coloring problem. Comput. Mod. 2, 6–11 (2017)
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Nos. 61732019, 61762020), CQ CSTC(Nos. cstc2015gjhz40-002, cstc2018jcyjAX0274) and CERNET Innovation Project (No. NGII20170110). Prof. Chao Gao and Prof. Zili Zhang are the corresponding authors of this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Lv, L., Gao, C., Chen, J., Luo, L., Zhang, Z. (2019). Physarum-Based Ant Colony Optimization for Graph Coloring Problem. In: Tan, Y., Shi, Y., Niu, B. (eds) Advances in Swarm Intelligence. ICSI 2019. Lecture Notes in Computer Science(), vol 11655. Springer, Cham. https://doi.org/10.1007/978-3-030-26369-0_20
Download citation
DOI: https://doi.org/10.1007/978-3-030-26369-0_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26368-3
Online ISBN: 978-3-030-26369-0
eBook Packages: Computer ScienceComputer Science (R0)