Skip to main content
SpringerLink
Log in

Innovative Clustering-Driven Techniques for Enhancing Initial Solutions in Euclidean Traveling Salesman Problems with Machine Learning Integration

  • Research Article-Computer Engineering and Computer Science
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Integrating machine learning techniques within metaheuristics has shown promise for effectively solving combinatorial problems like the Traveling Salesman Problem (TSP). However, key challenges remain in initializing metaheuristics to balance exploration and exploitation across vast search spaces. This paper introduces a novel clustering-driven technique for constructing high-quality initial solutions to Euclidean TSP instances. Our method uses hierarchical hybrid clustering with K-means, affinity propagation, and density peaks clustering to recursively partition cities into a compressed quadtree structure. A rigorous assessment using the Davies–Bouldin index and Gini coefficient optimizes intra- and inter-cluster quality and balance at each level. The multi-tiered decomposition strategically abstracts complex optimization landscapes into localized clusters that are solved efficiently in parallel within each using heuristics such as nearest neighbor and ant colony optimization. A genetic networking heuristic then interconnects independent intra-cluster solutions to construct unified inter-cluster routes. The clustering-guided initialization provides a diverse population of initialized tours that balance global exploration against localized exploitation. To validate our method, we conduct experiments using the generated solutions to seed a simulated annealing metaheuristic. This experimental evaluation will demonstrate this technique’s ability to initialize metaheuristics for TSP instances closer to optimality compared to traditional methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Algorithm 1
Algorithm 2
Algorithm 3
Fig. 2
Fig. 3
Algorithm 4
Algorithm 5
Algorithm 6
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Karimi-Mamaghan, M.; Mohammadi, M.; Meyer, P.; Karimi-Mamaghan, A.M.; Talbi, E.-G.: Machine learning at the service of meta-heuristics for solving combinatorial optimization problems: a state-of-the-art. Eur. J. Oper. Res. 296, 393–422 (2022)

    Article  MathSciNet  Google Scholar 

  2. Cook, W.J., Applegate, D.L., Bixby, R.E., & Chvatal, V.: The traveling salesman problem: a computational study (Princeton university press, 2011).

  3. Ahsini, Y.; et al.: The electric vehicle traveling salesman problem on digital elevation models for traffic-aware urban logistics. Algorithms 16, 402 (2023)

    Article  Google Scholar 

  4. Arkhipov, D.I.; Wu, D.; Wu, T.; Regan, A.C.: A parallel genetic algorithm framework for transportation planning and logistics management. Ieee Access 8, 106506–106515 (2020)

    Article  Google Scholar 

  5. Kyaw, P.T.; et al.: Coverage path planning for decomposition reconfigurable grid-maps using deep reinforcement learning based travelling salesman problem. IEEE Access 8, 225945–225956 (2020)

    Article  Google Scholar 

  6. Yang, X.; Ostermeier, M.; Hübner, A.: Winning the race to customers with micro-fulfillment centers: an approach for network planning in quick commerce. Central Eur. J. Oper. Res. 18, 1–40 (2024)

    Google Scholar 

  7. Nałkecz-Charkiewicz, K.; Nowak, R.M.: Algorithm for DNA sequence assembly by quantum annealing. BMC Bioinformatics 23, 122 (2022)

    Article  Google Scholar 

  8. Pyrkov, A.; et al.: Complexity of life sciences in quantum and AI era. Wiley Interdiscip. Rev. Comput. Mol. Sci. 14, e1701 (2024)

    Article  Google Scholar 

  9. Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem (1976)

  10. Holland, J.H.: Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence (MIT press, 1992).

  11. Kirkpatrick, S.; Gelatt, C.D., Jr.; Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  12. Tan, C.; Yang, K.: Privacy-preserving adaptive traffic signal control in a connected vehicle environment. Trans. Res. Part C Emerg. Technol. 158, 104453 (2024)

    Article  Google Scholar 

  13. Budak, G., Chen, X.: A hybrid mathematical model for flying sidekick travelling salesman problem with time windows, 4, 96 (2023)

  14. Zhao, F.; Si, B.; Wei, Z.; Lu, T.: Time-dependent vehicle routing problem of perishable product delivery considering the differences among paths on the congested road. Oper. Res. Int. J. 23, 5 (2023)

    Article  Google Scholar 

  15. Kanda, J.; De Carvalho, A.; Hruschka, E.; Soares, C.; Brazdil, P.: Meta-learning to select the best meta-heuristic for the traveling salesman problem: a comparison of meta-features. Neurocomputing 205, 393–406 (2016)

    Article  Google Scholar 

  16. Fan, M., & Li, J.: Surrogate-assisted genetic algorithms for the travelling salesman problem and vehicle routing problem (2020)

  17. Golabi, M., Essaid, M., Sulaman, M., & Idoumghar, L.: Extreme learning machine-based genetic algorithm for the facility location problem with distributed demands on network edges (2023)

  18. Drori, I., et al.: Learning to solve combinatorial optimization problems on real-world graphs in linear time (2020)

  19. Khalil, E., Dai, H., Zhang, Y., Dilkina, B., & Song, L.: Learning combinatorial optimization algorithms over graphs. Adv. Neural Inform. Process. Syst. 30 (2017)

  20. Buzdalova, A., Kononov, V., & Buzdalov, M.: Initial explorations, Selecting evolutionary operators using reinforcement learning (2014)

  21. Wang, Y.; Han, Z.: Ant colony optimization for traveling salesman problem based on parameters optimization. Appl. Soft Comput. 107, 107439 (2021)

    Article  Google Scholar 

  22. Hartono, N., et al: Parameter tuning for combinatorial bees algorithm in travelling salesman problems (2023)

  23. Pukhkaiev, D., Semendiak, Y., Götz, S., & Aßmann, U.: Combined selection and parameter control of meta-heuristics (2020)

  24. Alipour, M.M.; Razavi, S.N.; Feizi Derakhshi, M.R.; Balafar, M.A.: A hybrid algorithm using a genetic algorithm and multiagent reinforcement learning heuristic to solve the traveling salesman problem. Neural Comput. Appl. 30, 2935–2951 (2018)

    Article  Google Scholar 

  25. Miki, S., Yamamoto, D., & Ebara, H.: Applying deep learning and reinforcement learning to traveling salesman problem (2018)

  26. Ali, I.M.; Essam, D.; Kasmarik, K.: A novel design of differential evolution for solving discrete traveling salesman problems. Swarm Evol. Comput. 52, 100607 (2020)

    Article  Google Scholar 

  27. Hartigan, J.A.; Wong, M.A.: Algorithm as 136: A k-means clustering algorithm. J. R. Stat. Soc. Series C Appl. Stat. 28, 100–108 (1979)

    Google Scholar 

  28. Frey, B.J.; Dueck, D.: Clustering by passing messages between data points. Science 315, 972–976 (2007)

    Article  MathSciNet  Google Scholar 

  29. Rodriguez, A.; Laio, A.: Clustering by fast search and find of density peaks. Science 344, 1492–1496 (2014)

    Article  Google Scholar 

  30. Davies, D.L.; Bouldin, D.W.: A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. 2, 224–7 (1979)

    Article  Google Scholar 

  31. Rendón, E.; Abundez, I.; Arizmendi, A.; Quiroz, E.M.: Internal versus external cluster validation indexes. Int. J. Comput. Commun. 5, 27–34 (2011)

    Google Scholar 

  32. Liu, Y., Li, Z., Xiong, H., Gao, X., & Wu, J.: Understanding of internal clustering validation measures (2010)

  33. Halkidi, M.; Batistakis, Y.; Vazirgiannis, M.: On clustering validation techniques. J. Intell. Inform. Syst. 17, 107–145 (2001)

    Article  Google Scholar 

  34. Dunn, J.C.: A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters (1973)

  35. Ceriani, L.; Verme, P.: The origins of the gini index: extracts from variabilità e mutabilità (1912) by corrado gini. J. Econ. Inequal. 10, 421–443 (2012)

  36. Šulc, Z., & Řezanková, H.: Evaluation of recent similarity measures for categorical data (2014)

  37. Dorigo, M.: Optimization, learning and natural algorithms. Ph. D. Thesis, Politecnico di Milano (1992)

  38. Flood, M.M.: The traveling-salesman problem. Oper. Res. 4, 61–75 (1956)

  39. Liao, E.; Liu, C.: A hierarchical algorithm based on density peaks clustering and ant colony optimization for traveling salesman problem. IEEE Access 6, 38921–38933 (2018)

    Article  Google Scholar 

  40. Gülcü, Ş; Mahi, M.; Baykan, Ö.K.; Kodaz, H.: A parallel cooperative hybrid method based on ant colony optimization and 3-opt algorithm for solving traveling salesman problem. Soft. Comput. 22, 1669–1685 (2018)

    Article  Google Scholar 

  41. Mahi, M.; Baykan, Ö.K.; Kodaz, H.: A new hybrid method based on particle swarm optimization, ant colony optimization and 3-opt algorithms for traveling salesman problem. Appl. Soft Comput. 30, 484–490 (2015)

    Article  Google Scholar 

  42. Chen, S.-M.; Chien, C.-Y.: Solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques. Expert Syst. Appl. 38, 14439–14450 (2011)

    Article  Google Scholar 

  43. Wang, Y.: The hybrid genetic algorithm with two local optimization strategies for traveling salesman problem. Comput. Ind. Eng. 70, 124–133 (2014)

    Article  Google Scholar 

  44. Sahin, M.: Solving tsp by using combinatorial bees algorithm with nearest neighbor method. Neural Comput. Appl. 35, 1863–1879 (2023)

    Article  Google Scholar 

  45. Wu, C.; Fu, X.; Pei, J.; Dong, Z.: A novel sparrow search algorithm for the traveling salesman problem. IEEE Access 9, 153456–153471 (2021)

    Article  Google Scholar 

  46. Toaza, B.; Esztergár-Kiss, D.: A review of metaheuristic algorithms for solving TSP-based scheduling optimization problems. Appl. Soft Comput. 11, 110908 (2023)

    Article  Google Scholar 

Download references

Acknowledgements

This publication is the result of the work carried out in the project within the framework of the Doctoral Program of the Ministry of Higher Education and Scientific Research, Government of Algeria, which is implemented by LESIA and RLP Laboratories of the University of Biskra. Source code available on GitHub: https://github.com/aymentaki/Euclidean-TSP-Solver.

Author information

Authors and Affiliations

  1. LESIA Laboratory, Mohamed Khider University of Biskra, 07000, Biskra, Algeria

    Aymen Takie Eddine Selmi

  2. RLP Laboratory, Mohamed Khider University of Biskra, 07000, Biskra, Algeria

    Mohamed Faouzi Zerarka & Abdelhakim Cheriet

  3. The National School of Artificial Intelligence, 16000, Algiers, Algeria

    Abdelhakim Cheriet

Authors
  1. Aymen Takie Eddine Selmi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed Faouzi Zerarka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdelhakim Cheriet
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aymen Takie Eddine Selmi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Selmi, A.T.E., Zerarka, M.F. & Cheriet, A. Innovative Clustering-Driven Techniques for Enhancing Initial Solutions in Euclidean Traveling Salesman Problems with Machine Learning Integration. Arab J Sci Eng (2024). https://doi.org/10.1007/s13369-024-09094-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13369-024-09094-3

Keywords

Search

Navigation