Application of Hill Climbing Algorithm in Determining the Characteristic Objects Preferences Based on the Reference Set of Alternatives

  • Jakub WięckowskiEmail author
  • Bartłomiej Kizielewicz
  • Joanna Kołodziejczyk
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 193)


Random processes are a frequent issue when trying to solve problems in various areas. The randomness factor makes it difficult to clearly define the input parameters of a system in maximizing its effects. The solution to this problem may be the usage of stochastic optimization methods. In the following article, the Hill Climbing method has been used to solve the problem of optimization, which in combination with the COMET method gave satisfactory results by determining the relationship between the preference assessment of already existing alternatives to the newly determined alternatives. The motivation to conduct the study was the desire to systematize knowledge on the effective selection of input parameters for stochastic optimization methods. The proposed solution indicates how to select the grid size in an unknown problem and the step size in the Hill Climbing method.


Multi-criteria decision-making Hill climbing COMET 



The work was supported by the National Science Centre, Decision No. DEC-2016/23/N/HS4/01931.


  1. 1.
    Alajmi, B.N., Ahmed, K.H., Finney, S.J., Williams, B.W.: Fuzzy-logic-control approach of a modified hill-climbing method for maximum power point in microgrid standalone photovoltaic system. IEEE Trans. Power Electron. 26(4), 1022–1030 (2010)CrossRefGoogle Scholar
  2. 2.
    Bashir, Z., Wa̧tróbski, J., Rashid, T., Sałabun, W., Ali, J.: Intuitionistic-fuzzy goals in zero-sum multi criteria matrix games. Symmetry 9(8), 158 (2017)Google Scholar
  3. 3.
    Boender, C.G.E., De Graan, J.G., Lootsma, F.A.: Multi-criteria decision analysis with fuzzy pairwise comparisons. Fuzzy Sets Syst. 29(2), 133–143 (1989)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Deschrijver, G., Kerre, E.E.: On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst. 133(2), 227–235 (2003)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Faizi, S., Sałabun, W., Rashid, T., Wa̧tróbski, J., Zafar, S.: Group decision-making for hesitant fuzzy sets based on characteristic objects method. Symmetry 9(8), 136 (2017)Google Scholar
  6. 6.
    Guitouni, A., Martel, J.M.: Tentative guidelines to help choosing an appropriate MCDA method. Eur. J. Oper. Res. 109(2), 501–521 (1998)CrossRefGoogle Scholar
  7. 7.
    Goldfeld, S.M., Quandt, R.E., Trotter, H.F.: Maximization by quadratic hill-climbing. Econometrica: J. Econom. Soc. 541–551 (1966)Google Scholar
  8. 8.
    Gupta, M.M., Qi, J.: Theory of T-norms and fuzzy inference methods. Fuzzy Sets Syst. 40(3), 431–450 (1991)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lim, A., Rodrigues, B., Zhang, X.: A simulated annealing and hill-climbing algorithm for the traveling tournament problem. Eur. J. Oper. Res. 174(3), 1459–1478 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Łokietek, T., Jaszczak, S., Nikończuk, P.: Optimization of control system for modified configuration of a refrigeration unit. Procedia Comput. Sci. 159, 2522–2532 (2019)CrossRefGoogle Scholar
  11. 11.
    Nikończuk, P.: Preliminary modeling of overspray particles sedimentation at heat recovery unit in spray booth. Eksploatacja i Niezawodność 20, 387–393 (2018)CrossRefGoogle Scholar
  12. 12.
    Piegat, A.: Fuzzy modeling and control (Studies in Fuzziness and Soft Computing). Physica 742, (2001)Google Scholar
  13. 13.
    Piegat, A., Sałabun, W.: Nonlinearity of human multi-criteria in decision-making. J. Theor. Appl. Comput. Sci. 6(3), 36–49 (2012)Google Scholar
  14. 14.
    Prügel-Bennett, A.: When a genetic algorithm outperforms hill-climbing. Theor. Comput. Sci. 320(1), 135–153 (2004)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Roubens, M.: Fuzzy sets and decision analysis. Fuzzy Sets Syst. 90(2), 199–206 (1997)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Sałabun, W.: The Characteristic Objects Method: A New Distance-based Approach to Multicriteria Decision-making Problems. J. Multi-Criteria Decis. Anal. 22(1–2), 37–50 (2015)CrossRefGoogle Scholar
  17. 17.
    Sałabun, W., Palczewski, K., Wa̧tróbski, J.: Multicriteria approach to sustainable transport evaluation under incomplete knowledge: electric bikes case study. Sustainability 11(12), 3314 (2019)Google Scholar
  18. 18.
    Sałabun, W., Piegat, A.: Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome. Artif. Intell. Rev. 48(4), 557–571 (2017)CrossRefGoogle Scholar
  19. 19.
    Sałabun, W., Ziemba, P., Wa̧tróbski, J.: The rank reversals paradox in management decisions: the comparison of the AHP and comet methods. In: International Conference on Intelligent Decision Technologies, pp. 181-191. Springer, Cham (2016)Google Scholar
  20. 20.
    Tsamardinos, I., Brown, L.E., Aliferis, C.F.: The max-min hill-climbing Bayesian network structure learning algorithm. Mach. Learn. 65(1), 31–78 (2006)CrossRefGoogle Scholar
  21. 21.
    Wa̧tróbski, J., Sałabun, W.: Green supplier selection framework based on multi-criteria decision-analysis approach. In: International Conference on Sustainable Design and Manufacturing, pp. 361–371. Springer, Cham (2016)Google Scholar
  22. 22.
    Wa̧tróbski, J., Sałabun, W.: The characteristic objects method: a new intelligent decision support tool for sustainable manufacturing. In: International Conference on Sustainable Design and Manufacturing, pp. 349–359. Springer, Cham (2016)Google Scholar
  23. 23.
    Wa̧tróbski, J., Sałabun, W., Karczmarczyk, A., Wolski, W.: Sustainable decision-making using the COMET method: An empirical study of the ammonium nitrate transport management. In: 2017 Federated Conference on Computer Science and Information Systems (FedCSIS), pp. 949–958. IEEE (2017)Google Scholar
  24. 24.
    Xi, B., Liu, Z., Raghavachari, M., Xia, C. H., Zhang, L.: A smart hill-climbing algorithm for application server configuration. In: Proceedings of the 13th International Conference on World Wide Web, pp. 287–296 (2004)Google Scholar
  25. 25.
    Xiao, W., Dunford, W.G.: A modified adaptive hill climbing MPPT method for photovoltaic power systems. In 2004 IEEE 35th Annual Power Electronics Specialists Conference (IEEE Cat. No. 04CH37551), vol. 3, pp. 1957-1963. IEEE (2004)Google Scholar
  26. 26.
    Yao, K.: Spherically invariant random processes: theory and applications. Communications. Information and Network Security, pp. 315–331. Springer, Boston, MA (2003)Google Scholar
  27. 27.
    Yildiz, A.R.: An effective hybrid immune-hill climbing optimization approach for solving design and manufacturing optimization problems in industry. J. Mater. Process. Technol. 209(6), 2773–2780 (2009)CrossRefGoogle Scholar
  28. 28.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  29. 29.
    Zimmermann, H.J.: Fuzzy Set Theory and Its Applications. Springer Science & Business Media (2011)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Jakub Więckowski
    • 1
    Email author
  • Bartłomiej Kizielewicz
    • 1
  • Joanna Kołodziejczyk
    • 1
  1. 1.Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information TechnologyWest Pomeranian University of Technology in SzczecinSzczecinPoland

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