Harmony Search Algorithm with Dynamic Adjustment of PAR Values for Asymmetric Traveling Salesman Problem

  • Krzysztof SzwarcEmail author
  • Urszula Boryczka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12033)


This paper describes an improvement to the Harmony Search algorithm, which has been adjusted to effectively solve a problem with indisputable practical significance, i.e. Asymmetric Traveling Salesman Problem (ATSP). We modify the technique structure, enabling the value of PAR parameter to be changed dynamically, which has an impact on the frequency of greedy movements during the construction of another harmony. The article demonstrates the effectiveness of the described approach and presents a comparative study of three sets of characteristic PAR values used during the method execution. The research was conducted on a ‘test bed’ consisting of nineteen instances of the ATSP.


Dynamic adjustable parameters Harmony Search Asymmetric Traveling Salesman Problem 


  1. 1.
    Boryczka, U., Szwarc, K.: The adaptation of the harmony search algorithm to the ATSP. In: Nguyen, N.T., Hoang, D.H., Hong, T.-P., Pham, H., Trawiński, B. (eds.) ACIIDS 2018. LNCS (LNAI), vol. 10751, pp. 341–351. Springer, Cham (2018). Scholar
  2. 2.
    Boryczka, U., Szwarc, K.: The adaptation of the harmony search algorithm to the atsp with the evaluation of the influence of the pitch adjustment place on the quality of results. J. Inf. Telecommun. 3(1), 2–18 (2019)Google Scholar
  3. 3.
    Chang, Y., Li, Z., Kou, Y., Sun, Q., Yang, H., Zhao, Z.: A new approach to weapon-target assignment in cooperative air combat. Math. Probl. Eng. 2017 (2017). 17 pages
  4. 4.
    Daham, B.F., Mohammed, M.N., Mohammed, K.S.: Parameter controlled harmony search algorithm for solving the Four-Color Mapping Problem. Int. J. Comput. Inf. Technol. 3(6), 1398–1402 (2014)Google Scholar
  5. 5.
    Gaham, M., Bouzouia, B., Achour, N.: An effective operations permutation-based discrete harmony search approach for the flexible job shop scheduling problem with makespan criterion. Appl. Intell. 48(6), 1423–1441 (2018)CrossRefGoogle Scholar
  6. 6.
    Geem, Z.W.: Optimal design of water distribution networks using harmony search. Ph.D. thesis, Korea University (2000)Google Scholar
  7. 7.
    Geem, Z.W.: Multiobjective optimization of time-cost trade-off using harmony search. J. Constr. Eng. Manag. 136(6), 711–716 (2010)CrossRefGoogle Scholar
  8. 8.
    Kim, J.H.: Harmony search algorithm: a unique music-inspired algorithm. Procedia Eng. 154, 1401–1405 (2016). 12th International Conference on Hydroinformatics (HIC 2016) - Smart Water for the FutureCrossRefGoogle Scholar
  9. 9.
    Komaki, M., Sheikh, S., Teymourian, E.: A hybrid harmony search algorithm to minimize total weighted tardiness in the permutation flow shop. In: 2014 IEEE Symposium on Computational Intelligence in Production and Logistics Systems (CIPLS), pp. 1–8 (2014)Google Scholar
  10. 10.
    Li, X., Qin, K., Zeng, B., Gao, L., Wang, L.: A dynamic parameter controlled harmony search algorithm for assembly sequence planning. Int. J. Adv. Manuf. Technol. 92(9), 3399–3411 (2017)CrossRefGoogle Scholar
  11. 11.
    Mikaeil, R., Ozcelik, Y., Ataei, M., Shaffiee Haghshenas, S.: Application of harmony search algorithm to evaluate performance of diamond wire saw. J. Mining Environ. 10(1), 27–36 (2019)Google Scholar
  12. 12.
    Nowakowski, P., Szwarc, K., Boryczka, U.: Vehicle route planning in e-waste mobile collection on demand supported by artificial intelligence algorithms. Transp. Res. Part D Transp. Environ. 63, 1–22 (2018)CrossRefGoogle Scholar
  13. 13.
    Osaba, E., Diaz, F., Onieva, E., Carballedo, R., Perallos, A.: A population metaheuristic with adaptive crossover probability and multi-crossover mechanism for solving combinatorial optimization problems. IJAI 12, 1–23 (2014)Google Scholar
  14. 14.
    Rojas-Morales, N., Rojas, M.C.R.: Improving harmony search algorithms by using tonal variation: the case of Sudoku and MKP. Connection Sci. 30(3), 245–271 (2018)CrossRefGoogle Scholar
  15. 15.
    Syberfeldt, A., Rogström, J., Geertsen, A.: Simulation-based optimization of a real-world travelling salesman problem using an evolutionary algorithm with a repair function. Int. J. Artif. Intell. Expert Syst. (IJAE) 6(3), 27–39 (2015)Google Scholar
  16. 16.
    Wang, L., Pan, Q.K., Tasgetiren, M.F.: Minimizing the total flow time in a flow shop with blocking by using hybrid harmony search algorithms. Expert Syst. Appl. 37(12), 7929–7936 (2010)CrossRefGoogle Scholar
  17. 17.
    Weyland, D.: A rigorous analysis of the harmony search algorithm: how the research community can be misled by a “novel” methodology. Int. J. Appl. Metaheuristic Comput. 1(2), 50–60 (2010)CrossRefGoogle Scholar
  18. 18.
    Weyland, D.: A critical analysis of the harmony search algorithm—how not to solve sudoku. Oper. Res. Perspect. 2, 97–105 (2015)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Öncan, T., Altınel, I.K., Laporte, G.: A comparative analysis of several asymmetric traveling salesman problem formulations. Comput. Oper. Res. 36(3), 637–654 (2009)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of Silesia in KatowiceSosnowiecPoland

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