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A discrete squirrel search optimization based algorithm for Bi-objective TSP

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Abstract

This paper presents a novel discrete squirrel search optimization algorithm for the bi-objective traveling salesman problem (TSP). Firstly, the squirrel search algorithm, a single-objective optimization algorithm, needs to be improved to a multi-objective optimization algorithm. This paper designs a mapping fitness function according to the Pareto sorting level and grid density to evaluate all the feasible solutions and applies a selection probability based on the roulette wheel selection. Then, this paper implements this algorithm and other algorithms on classic multi-objective test functions to analyze solutions’ convergence and diversity. It is concluded that it has a good performance in solving multi-objective problems. Moreover, based on this multi-objective squirrel search algorithm, this paper then designs an encoding method to initialize solutions, applies a crossover operator to the squirrel migration process, and utilizes a mutation operator to the squirrel mutation stage. In this case, a discrete squirrel search optimization for the bi-objective traveling salesman problem (TSP) is finally designed. And this paper analyzes the results of this algorithm and other algorithms running on classic bi-objective TSPs. As a result, the presented algorithm’s solutions are also superior to other algorithms for convergence and spread.

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References

  1. Qamar, N., Akhtar, N., & Younas, I. (2018). Comparative analysis of evolutionary algorithms for multi-objective travelling salesman problem[J]. International Journal of Advanced Computer Science and Applications, 9(2), 371–379.

    Article  Google Scholar 

  2. Jiang, D., Zhang, P., Lv, Z., et al. (2016). Energy-efficient multi-constraint routing algorithm with load balancing for smart city applications. IEEE Internet of Things Journal, 3(6), 1437–1447.

    Article  Google Scholar 

  3. Moraes, D. H., Sanches, D. S., da Silva, R. J., et al. (2019). A novel multi-objective evolutionary algorithm based on subpopulations for the bi-objective traveling salesman problem[J]. Soft Computing, 23(15), 6157–6168.

    Article  Google Scholar 

  4. Khan, I., Maiti, M. K., & Basuli, K. (2020). Multi-objective traveling salesman problem: an ABC approach[J]. Applied Intelligence, 50(11), 3942–3960.

    Article  Google Scholar 

  5. Ning, J., Zhao, H., Lan, L., et al. (2019). A Computer-Aided Detection System for the Detection of Lung Nodules Based on 3D-ResNet[J]. Applied Sciences, 9(24), 5544.

    Article  Google Scholar 

  6. Wang, Y., Jiang, D., Huo, L., et al. (2019). A new traffic prediction algorithm to software defined networking[J]. Mobile Networks and Applications, 1–10.

  7. Qi, S., Jiang, D., Huo, L. (2019). A prediction approach to end-to-end traffic in space information networks[J]. Mobile Networks and Applications, 1–10.

  8. Mbiadou Saleu, R. G., Deroussi, L., Feillet, D., et al. (2018). An iterative two-step heuristic for the parallel drone scheduling traveling salesman problem[J]. Networks, 72(4), 459–474.

    Article  MathSciNet  Google Scholar 

  9. Mosayebi, M., Sodhi, M., & Wettergren, T. A. (2021). The Traveling Salesman Problem with Job-times (TSPJ)[J]. Computers & Operations Research, 129, 105226.

    Article  MathSciNet  Google Scholar 

  10. Hacizade, U., & Kaya, I. (2018). Ga based traveling salesman problem solution and its application to transport routes optimization[J]. IFAC-PapersOnLine, 51(30), 620–625.

    Article  Google Scholar 

  11. Jiang, D., Huo, L., & Song, H. (2018). Rethinking behaviors and activities of base stations in mobile cellular networks based on big data analysis[J]. IEEE Transactions on Network Science and Engineering, 7(1), 80–90.

    Article  MathSciNet  Google Scholar 

  12. Barba-González, C., García-Nieto, J., Nebro, A. J., et al. (2018). jMetalSP: a framework for dynamic multi-objective big data optimization[J]. Applied Soft Computing, 69, 737–748.

    Article  Google Scholar 

  13. Jiang, D., Li, W., & Lv, H. (2017). An energy-efficient cooperative multicast routing in multi-hop wireless networks for smart medical applications[J]. Neurocomputing, 220, 160–169.

    Article  Google Scholar 

  14. Qu, B. Y., Zhu, Y. S., Jiao, Y. C., et al. (2018). A survey on multi-objective evolutionary algorithms for the solution of the environmental/economic dispatch problems[J]. Swarm and Evolutionary Computation, 38, 1–11.

    Article  Google Scholar 

  15. Cho, J. H., Wang, Y., Chen, R., et al. (2017). A survey on modeling and optimizing multi-objective systems[J]. IEEE Communications Surveys & Tutorials, 19(3), 1867–1901.

    Article  Google Scholar 

  16. Jiang, D., Wang, Y., Lv, Z., Wang, W., & Wang, H. (2020). An energy-efficient networking approach in cloud services for IIoT networks. IEEE Journal on Selected Areas in Communications, 38(5), 928–941.

    Article  Google Scholar 

  17. Dai, M., Tang, D., Giret, A., et al. (2019). Multi-objective optimization for energy-efficient flexible job shop scheduling problem with transportation constraints[J]. Robotics and Computer-Integrated Manufacturing, 59, 143–157.

    Article  Google Scholar 

  18. Ning, J., Zhao, H., Liu, C. (2020). An improved exhausted-food-sources-identification mechanism for the artificial bee colony algorithm[J]. Wireless Networks, 1–12.

  19. Zaro, F. R., Abido, M. A. (2011). Multi-objective particle swarm optimization for optimal power flow in a deregulated environment of power systems[C]//2011 11th International Conference on Intelligent Systems Design and Applications. IEEE, 1122–1127.

  20. Jiang, D., Huo, L., & Li, Y. (2018). Fine-granularity inference and estimations to network traffic for SDN[J]. PLoS ONE, 13(5), e0194302.

    Article  Google Scholar 

  21. Liu Z, Jiang D, Zhang C, et al. A Novel Fireworks Algorithm for the Protein-Ligand Docking on the AutoDock[J]. Mobile Networks and Applications, 2019: 1–12.

  22. Jiang, D., Wang, Y., Lv, Z., et al. (2019). Big data analysis based network behavior insight of cellular networks for industry 4.0 applications[J]. IEEE Transactions on Industrial Informatics, 16(2): 1310–1320.

  23. Jiang, D., Huo, L., Lv, Z., et al. (2018). A joint multi-criteria utility-based network selection approach for vehicle-to-infrastructure networking[J]. IEEE Transactions on Intelligent Transportation Systems, 19(10), 3305–3319.

    Article  Google Scholar 

  24. Ning, J., Zhang, C., Zhang, B., et al. (2020). Improving the one-position inheritance artificial bee colony algorithm using heuristic search mechanisms[J]. Soft Computing, 24(2), 1271–1281.

    Article  MathSciNet  Google Scholar 

  25. Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition[J]. IEEE Transactions on evolutionary computation, 11(6), 712–731.

    Article  Google Scholar 

  26. Liu, Z., Zhang, C., Zhao, Q., et al. (2019). Comparative study of evolutionary algorithms for protein-ligand docking problem on the AutoDock[C]//International Conference on simulation tools and techniques. Springer, Cham, 598–607.

  27. Xue, B., Zhang, M., & Browne, W. N. (2012). Particle swarm optimization for feature selection in classification: A multi-objective approach[J]. IEEE transactions on cybernetics, 43(6), 1656–1671.

    Article  Google Scholar 

  28. Deb, K., Pratap, A., Agarwal, S., et al. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II[J]. IEEE transactions on evolutionary computation, 6(2), 182–197.

    Article  Google Scholar 

  29. Zitzler E, Laumanns M, Thiele L. SPEA2: Improving the strength Pareto evolutionary algorithm[J]. TIK-report, 2001, 103.

  30. Corne, D. W., Jerram, N. R., Knowles, J. D., et al. (2001). PESA-II: Region-based selection in evolutionary multiobjective optimization[C]//Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, 283–290.

  31. Ning, J., Zhao, Q., Sun, P., et al. (2020). A multi-objective decomposition-based ant colony optimisation algorithm with negative pheromone[J]. Journal of Experimental & Theoretical Artificial Intelligence, 1–19.

  32. Gunantara, N. (2018). A review of multi-objective optimization: Methods and its applications[J]. Cogent Engineering, 5(1), 1502242.

    Article  Google Scholar 

  33. Li, K., Wang, R., Zhang, T., et al. (2018). Evolutionary many-objective optimization: A comparative study of the state-of-the-art[J]. IEEE Access, 6, 26194–26214.

    Article  Google Scholar 

  34. Jiang, D., Wang, W., Shi, L., et al. (2018). A compressive sensing-based approach to end-to-end network traffic reconstruction[J]. IEEE Transactions on Network Science and Engineering, 7(1), 507–519.

    Article  MathSciNet  Google Scholar 

  35. Mirjalili, S. Z., Mirjalili, S., Saremi, S., et al. (2018). Grasshopper optimization algorithm for multi-objective optimization problems[J]. Applied Intelligence, 48(4), 805–820.

    Article  Google Scholar 

  36. Jain, M., Singh, V., & Rani, A. (2019). A novel nature-inspired algorithm for optimization: Squirrel search algorithm[J]. Swarm and evolutionary computation, 44, 148–175.

    Article  Google Scholar 

  37. Wang, Y., & Du, T. (2020). A Multi-objective Improved Squirrel Search Algorithm based on Decomposition with External Population and Adaptive Weight Vectors Adjustment[J]. Physica A: Statistical Mechanics and its Applications, 542, 123526.

    Article  Google Scholar 

  38. Liang, J. J., Qu, B. Y., & Suganthan, P. N. (2013). Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization[J]. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore, 635, 490.

    Google Scholar 

  39. Wang, P., Kong, Y., He, X., et al. (2019). An improved squirrel search algorithm for maximum likelihood DOA estimation and application for MEMS vector hydrophone array[J]. IEEE Access, 7, 118343–118358.

    Article  Google Scholar 

  40. El-Ashmawi, W. H., & Abd Elminaam, D. S. (2019). A modified squirrel search algorithm based on improved best fit heuristic and operator strategy for bin packing problem[J]. Applied Soft Computing, 82, 105565.

    Article  Google Scholar 

  41. Sanaj, M. S., & Prathap, P. M. J. (2020). Nature inspired chaotic squirrel search algorithm (CSSA) for multi objective task scheduling in an IAAS cloud computing atmosphere[J]. Engineering Science and Technology, an International Journal, 23(4), 891–902.

    Article  Google Scholar 

  42. Wang, Y., & Du, T. (2019). An improved squirrel search algorithm for global function optimization[J]. Algorithms, 12(4), 80.

    Article  MathSciNet  Google Scholar 

  43. Zhang, X., Zhao, K., Wang, L., et al. (2020). An improved squirrel search algorithm with reproductive behavior[J]. IEEE Access, 8, 101118–101132.

    Article  Google Scholar 

  44. Mashwani, W. K., Salhi, A., Yeniay, O., et al. (2017). Hybrid non-dominated sorting genetic algorithm with adaptive operators selection[J]. Applied Soft Computing, 56, 1–18.

    Article  Google Scholar 

  45. Bechikh, S., Elarbi, M., & Said, L. B. (2017). Many-objective optimization using evolutionary algorithms: A survey[M]//Recent advances in evolutionary multi-objective optimization (pp. 105–137). Cham: Springer.

    Book  Google Scholar 

  46. Falcón-Cardona, J. G., & Coello, C. A. C. (2020). Indicator-based multi-objective evolutionary algorithms: a comprehensive survey[J]. ACM Computing Surveys (CSUR), 53(2), 1–35.

    Article  Google Scholar 

  47. Sheikholeslami, F., & Navimipour, N. J. (2017). Service allocation in the cloud environments using multi-objective particle swarm optimization algorithm based on crowding distance[J]. Swarm and Evolutionary Computation, 35, 53–64.

    Article  Google Scholar 

  48. Tian, Y., Cheng, R., Zhang, X., et al. (2019). Diversity assessment of multi-objective evolutionary algorithms: performance metric and benchmark problems [research frontier][J]. IEEE Computational Intelligence Magazine, 14(3), 61–74.

    Article  Google Scholar 

  49. Reinelt, G. (1991). TSPLIB—A traveling salesman problem library[J]. ORSA journal on computing, 3(4), 376–384.

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Key Project of National Natural Science Foundation of China (U1908212) and the Fundamental Research Funds for the Central Universities (N2017013, N2017014).

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Authors and Affiliations

  1. Northeastern University, Shenyang, 110819, People’s Republic of China

    Zhuoran Liu, Fanhao Zhang, Xinyuan Wang, Qidong Zhao, Changsheng Zhang & Bin Zhang

  2. Shenyang Normal University, Shenyang, 110034, People’s Republic of China

    Tianhua Liu

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  1. Zhuoran Liu
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  2. Fanhao Zhang
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Correspondence to Bin Zhang.

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Liu, Z., Zhang, F., Wang, X. et al. A discrete squirrel search optimization based algorithm for Bi-objective TSP. Wireless Netw (2021). https://doi.org/10.1007/s11276-021-02653-8

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