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Puma optimizer (PO): a novel metaheuristic optimization algorithm and its application in machine learning

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Abstract

Optimization techniques, particularly meta-heuristic algorithms, are highly effective in optimizing and enhancing efficiency across diverse models and systems, renowned for their ability to attain optimal or near-optimal solutions within a reasonable timeframe. In this work, the Puma Optimizer (PO) is proposed as a new optimization algorithm inspired from the intelligence and life of Pumas in. In this algorithm, unique and powerful mechanisms have been proposed in each phase of exploration and exploitation, which has increased the algorithm’s performance against all kinds of optimization problems. In addition, a new type of intelligent mechanism, which is a type of hyper-heuristic for phase change, is presented. Using this mechanism, the PO algorithm can perform a phase change operation during the optimization operation and balance both phases. Each phase is automatically adjusted to the nature of the problem. To evaluate the proposed algorithm, 23 standard functions and CEC2019 functions were used and compared with different types of optimization algorithms. Moreover, using the statistical test T-test and the execution time to solve the problem have been discussed. Finally, it has been tested using four machine learning and data mining problems, and the results obtained from all the analysis signifies the excellent performance of this algorithm against all kinds of problems compared to other optimizers. This algorithm has performed better than the compared algorithms in 27 benchmarks out of 33 benchmarks and has obtained better results in solving the clustering problem in 7 data sets out of 10 data sets. Furthermore, the results obtained in the problems of community detection and feature selection and MLP were superior. The source codes of the PO algorithm are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/157231-puma-optimizer-po.

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Data availability

Enquiries about data availability should be directed to the authors.

Abbreviations

PO:

Puma optimizer

rand :

A random number between [0,1]

UM:

Unimodal

randn :

Random numbers in the normal interval

MM:

Multimodal

mean :

Mean function

CM:

Composition

Iter :

Current number of iterations

SM:

Scalable Multimodal function

FM:

Fixed-dimension multimodal function

Puma male :

Best search agent

MaxIter :

Max number of iterations

Npop :

Total number of search agent

cos :

Function of cosine

X i :

Current search agent

Ub :

The Upper bound of search spaces

Cost :

The cost of the solution

Lb :

The lower bound of search spaces

exp :

Exponential function

EB:

Evolutionary based

SB:

Swarm-based

HP:

Human-based

iterations:

Max number of iterations

PB:

Physic-based

Best:

The best result

population:

Number of pumas

Worst:

The worst result

Mean:

Average results

MLP:

Multi-layer perceptron

STD:

Standard deviation

FS:

Feature selection

CD:

Community detection

FCCD:

The face-centered central composite design

DC:

Data clustering

SCA:

Sine cosine algorithm

FHO:

Fire hawk optimizer

SAO:

Smell agent optimization

TSA:

Tunicate swarm algorithm

GWO:

Gray wolf algorithm

MFO:

Moth-flame optimization algorithm

WOA:

Whale optimization algorithm

DMOA:

Dwarf mongoose optimization algorithm

PSO:

Particle swarm optimization

BAT:

Bat algorithm

GA:

Genetic algorithm

ABC:

Artificial bee colony

FFA:

Farmland fertility algorithm

BBO:

Biogeography-Based optimizer

SMA:

Slime mould algorithm

CSO:

Cuckoo search optimization

References

  1. Floudas, C.A., Gounaris, C.E.: A review of recent advances in global optimization. J. Global Optim. 45, 3–38 (2009)

    MathSciNet  Google Scholar 

  2. Törn, A., Zilinskas, A.: Global optimization. Springer, Berlin (1989)

    Google Scholar 

  3. Parsopoulos, K.E., Vrahatis, M.N.: Recent approaches to global optimization problems through particle swarm optimization. Nat. Comput. 1, 235–306 (2002)

    MathSciNet  Google Scholar 

  4. Beyer, H.-G., Sendhoff, B.: Robust optimization—a comprehensive survey. Comput. Methods Appl. Mech. Eng. 196(33–34), 3190–3218 (2007)

    MathSciNet  Google Scholar 

  5. Gharehchopogh, F.S., Gholizadeh, H.: A comprehensive survey: whale optimization algorithm and its applications. Swarm Evol. Comput. 48, 1–24 (2019)

    Google Scholar 

  6. Talbi, E.-G.: Metaheuristics: from design to implementation. John Wiley & Sons, Hoboken (2009)

    Google Scholar 

  7. Khodadadi, N., et al.: Chaotic stochastic paint optimizer (CSPO). In: Proceedings of 7th International Conference on Harmony Search Soft Computing and Applications: ICHSA 2022. Springer, Singapore (2022)

    Google Scholar 

  8. Deb, K., Deb, K.: Multi-objective optimization. In: Search methodologies: introductory tutorials in optimization and decision support techniques, pp. 403–449. Springer, Boston (2013)

    Google Scholar 

  9. Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341 (1997)

    MathSciNet  Google Scholar 

  10. Kennedy, J. Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks. IEEE (1995)

  11. Trojovský, P., Dehghani, M.: Pelican optimization algorithm: a novel nature-inspired algorithm for engineering applications. Sensors 22(3), 855 (2022)

    Google Scholar 

  12. Rashedi, E., Nezamabadi-Pour, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179(13), 2232–2248 (2009)

    Google Scholar 

  13. El-kenawy, E.-S.M., et al.: Al-Biruni Earth Radius (BER) metaheuristic search optimization algorithm. Comput. Syst. Sci. Eng. 45, 1917–1934 (2023)

    Google Scholar 

  14. Rao, R.V., Savsani, V.J., Vakharia, D.: Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43(3), 303–315 (2011)

    Google Scholar 

  15. Shayanfar, H., Gharehchopogh, F.S.: Farmland fertility: a new metaheuristic algorithm for solving continuous optimization problems. Appl. Soft Comput. 71, 728–746 (2018)

    Google Scholar 

  16. Rardin, R.L., Rardin, R.L.: Optimization in operations research. Prentice Hall Upper Saddle River, NJ (1998)

    Google Scholar 

  17. Rao, S.S.: Engineering optimization: theory and practice. John Wiley & Sons, Hoboken (2019)

    Google Scholar 

  18. Khodadadi, N., Talatahari, S., Gandomi, A.H.: ANNA advanced neural network algorithm for optimisation of structures. Proc. Inst. Civil Eng. Struct. Build. (2023). https://doi.org/10.1680/jstbu.22.00083

    Article  Google Scholar 

  19. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)

    Google Scholar 

  20. Mirjalili, S.: The ant lion optimizer. Adv. Eng. Softw. 83, 80–98 (2015)

    Google Scholar 

  21. Yapici, H., Cetinkaya, N.: A new meta-heuristic optimizer: Pathfinder algorithm. Appl. Soft Comput. 78, 545–568 (2019)

    Google Scholar 

  22. Faramarzi, A., et al.: Equilibrium optimizer: a novel optimization algorithm. Knowl. Based Syst. 191, 105190 (2020)

    Google Scholar 

  23. Trojovský, P., Dehghani, M.: A new optimization algorithm based on mimicking the voting process for leader selection. PeerJ Comput. Sci. 8, e976 (2022)

    Google Scholar 

  24. Yang, X.-S.: Firefly algorithms for multimodal optimization. In: Stochastic Algorithms: Foundations and Applications: 5th International Symposium, SAGA 2009, Sapporo, Japan, pp. 26–28. Springer, Berlin (2009)

    Google Scholar 

  25. Dorigo, M., Birattari, M., Stutzle, T.: Ant colony optimization. IEEE Comput. Intell. Mag. 1(4), 28–39 (2006)

    Google Scholar 

  26. Mirjalili, S., Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016)

    Google Scholar 

  27. Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Global Optim. 39, 459–471 (2007)

    MathSciNet  Google Scholar 

  28. Mirjalili, S., et al.: Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114, 163–191 (2017)

    Google Scholar 

  29. Abdollahzadeh, B., et al.: Mountain gazelle optimizer: a new nature-inspired metaheuristic algorithm for global optimization problems. Adv. Eng. Softw. 174, 103282 (2022)

    Google Scholar 

  30. Yazdani, M., Jolai, F.: Lion optimization algorithm (LOA): a nature-inspired metaheuristic algorithm. J. Comput. Design Eng. 3(1), 24–36 (2016)

    Google Scholar 

  31. Abdollahzadeh, B., Gharehchopogh, F.S., Mirjalili, S.: Artificial gorilla troops optimizer: a new nature-inspired metaheuristic algorithm for global optimization problems. Int. J. Intell. Syst. 36(10), 5887–5958 (2021)

    Google Scholar 

  32. Kaveh, A., Talatahari, S., & Khodadadi, N. (2020). Stochastic paint optimizer: theory and application in civil engineering. Engineering with Computers, 1–32

  33. Kumar, N., Singh, N., Vidyarthi, D.P.: Artificial lizard search optimization (ALSO): a novel nature-inspired meta-heuristic algorithm. Soft. Comput. 25(8), 6179–6201 (2021)

    Google Scholar 

  34. Abdollahzadeh, B., Gharehchopogh, F.S., Mirjalili, S.: African vultures optimization algorithm: a new nature-inspired metaheuristic algorithm for global optimization problems. Comput. Ind. Eng. 158, 107408 (2021)

    Google Scholar 

  35. Faramarzi, A., et al.: Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst. Appl. 152, 113377 (2020)

    Google Scholar 

  36. Holland, J.H.: Genetic algorithms. Sci. Am. 267(1), 66–73 (1992)

    Google Scholar 

  37. Cheraghalipour, A., Hajiaghaei-Keshteli, M., Paydar, M.M.: Tree growth algorithm (TGA): a novel approach for solving optimization problems. Eng. Appl. Artif. Intell. 72, 393–414 (2018)

    Google Scholar 

  38. Tang, D., et al.: ITGO: invasive tumor growth optimization algorithm. Appl. Soft Comput. 36, 670–698 (2015)

    Google Scholar 

  39. Dehghani, M., et al.: Coati optimization algorithm: a new bio-inspired metaheuristic algorithm for solving optimization problems. Knowl. Based Syst. 259, 110011 (2023)

    Google Scholar 

  40. Simon, D.: Biogeography-based optimization. IEEE Trans. Evol. Comput. 12(6), 702–713 (2008)

    Google Scholar 

  41. Kirkpatrick, S., Gelatt, C.D., Jr., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    MathSciNet  Google Scholar 

  42. Erol, O.K., Eksin, I.: A new optimization method: big bang–big crunch. Adv. Eng. Softw. 37(2), 106–111 (2006)

    Google Scholar 

  43. Formato, R.A.: Central force optimization. Prog. Electromagn. Res. 77(1), 425–491 (2007)

    Google Scholar 

  44. Abedinpourshotorban, H., et al.: Electromagnetic field optimization: a physics-inspired metaheuristic optimization algorithm. Swarm Evol. Comput. 26, 8–22 (2016)

    Google Scholar 

  45. Dehghani, M., Trojovská, E., Trojovský, P.: A new human-based metaheuristic algorithm for solving optimization problems on the base of simulation of driving training process. Sci. Rep. 12(1), 9924 (2022)

    Google Scholar 

  46. Hashim, F.A., et al.: Henry gas solubility optimization: a novel physics-based algorithm. Futur. Gener. Comput. Syst. 101, 646–667 (2019)

    Google Scholar 

  47. Mirjalili, S., Mirjalili, S.M., Hatamlou, A.: Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput. Appl. 27, 495–513 (2016)

    Google Scholar 

  48. Kumar, M., Kulkarni, A.J., Satapathy, S.C.: Socio evolution & learning optimization algorithm: a socio-inspired optimization methodology. Futur. Gener. Comput. Syst. 81, 252–272 (2018)

    Google Scholar 

  49. Zhang, Q., et al.: Collective decision optimization algorithm: a new heuristic optimization method. Neurocomputing 221, 123–137 (2017)

    Google Scholar 

  50. Ackerman, B.B., Lindzey, F.G., Hemker, T.P.: Cougar food habits in southern Utah. J. Wildl. Manag. 48, 147–155 (1984)

    Google Scholar 

  51. Robinette, W.L., Gashwiler, J.S., Morris, O.W.: Food habits of the cougar in Utah and Nevada. J. Wildl. Manag. 23(3), 261–273 (1959)

    Google Scholar 

  52. Knopff, K.H., et al.: Cougar kill rate and prey composition in a multiprey system. J. Wildl. Manag. 74(7), 1435–1447 (2010)

    Google Scholar 

  53. Bartnick, T.D., et al.: Variation in cougar (Puma concolor) predation habits during wolf (Canis lupus) recovery in the southern greater yellowstone ecosystem. Can. J. Zool. 91(2), 82–93 (2013)

    Google Scholar 

  54. Kunkel, K.E., et al.: Winter prey selection by wolves and cougars in and near Glacier National Park Montana. J. Wildl. Manag. 63, 901–910 (1999)

    Google Scholar 

  55. Murphy, K.M., et al.: Encounter competition between bears and cougars: some ecological implications. Ursus 10, 55–60 (1998)

    Google Scholar 

  56. Monroy-Vilchis, O., et al.: Cougar and jaguar habitat use and activity patterns in central Mexico. Anim. Biol. 59(2), 145–157 (2009)

    Google Scholar 

  57. Lambert, C.M., et al.: Cougar population dynamics and viability in the Pacific Northwest. J. Wildl. Manag. 70(1), 246–254 (2006)

    Google Scholar 

  58. LaRue, M.A., et al.: Cougars are recolonizing the midwest: analysis of cougar confirmations during 1990–2008. J. Wildl. Manag. 76(7), 1364–1369 (2012)

    Google Scholar 

  59. Demers, A., et al.: The cougar project: a work-in-progress report. ACM SIGMOD Rec. 32(4), 53–59 (2003)

    Google Scholar 

  60. Anderson, C.R., Jr., Lindzey, F.G.: Estimating cougar predation rates from GPS location clusters. J. Wildl. Manag. 67, 307–316 (2003)

    Google Scholar 

  61. Drake, J.H., Özcan, E., Burke, E.K.: An improved choice function heuristic selection for cross domain heuristic search. In: Parallel Problem Solving from Nature-PPSN XII: 12th International Conference, Taormina, Italy. Springer, Berlin (2012)

    Google Scholar 

  62. Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3(2), 82–102 (1999)

    Google Scholar 

  63. Digalakis, J.G., Margaritis, K.G.: On benchmarking functions for genetic algorithms. Int. J. Comput. Math. 77(4), 481–506 (2001)

    MathSciNet  Google Scholar 

  64. Mirjalili, S., Mirjalili, S.M., Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014)

    Google Scholar 

  65. Mirjalili, S.: SCA: a sine cosine algorithm for solving optimization problems. Knowl.-Based Syst. 96, 120–133 (2016)

    Google Scholar 

  66. Agushaka, J.O., Ezugwu, A.E., Abualigah, L.: Dwarf mongoose optimization algorithm. Comput. Methods Appl. Mech. Eng. 391, 114570 (2022)

    MathSciNet  Google Scholar 

  67. Kaur, S., et al.: Tunicate swarm algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng. Appl. Artif. Intell. 90, 103541 (2020)

    Google Scholar 

  68. Mirjalili, S.: Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl. Based Syst. 89, 228–249 (2015)

    Google Scholar 

  69. Azizi, M., Talatahari, S., Gandomi, A.H.: Fire hawk optimizer: a novel metaheuristic algorithm. Artif. Intell. Rev. 56(1), 287–363 (2023)

    Google Scholar 

  70. Salawudeen, A.T., et al.: A novel smell agent optimization (SAO): an extensive CEC study and engineering application. Knowl. Based Syst. 232, 107486 (2021)

    Google Scholar 

  71. Balachandran, M., et al.: Optimizing properties of nanoclay–nitrile rubber (NBR) composites using face centred central composite design. Mater. Des. 35, 854–862 (2012)

    Google Scholar 

  72. Gambella, C., Ghaddar, B., Naoum-Sawaya, J.: Optimization problems for machine learning: a survey. Eur. J. Oper. Res. 290(3), 807–828 (2021)

    MathSciNet  Google Scholar 

  73. Nanda, S.J., Panda, G.: A survey on nature inspired metaheuristic algorithms for partitional clustering. Swarm Evol. Comput. 16, 1–18 (2014)

    Google Scholar 

  74. José-García, A., Gómez-Flores, W.: Automatic clustering using nature-inspired metaheuristics: a survey. Appl. Soft Comput. 41, 192–213 (2016)

    Google Scholar 

  75. Zhou, H., Zhang, Y., Li, J.: An overlapping community detection algorithm in complex networks based on information theory. Data Knowl. Eng. 117, 183–194 (2018)

    Google Scholar 

  76. Jiang, J.Q., McQuay, L.J.: Modularity functions maximization with nonnegative relaxation facilitates community detection in networks. Phys. A 391(3), 854–865 (2012)

    Google Scholar 

  77. Kim, P., Kim, S.: Detecting community structure in complex networks using an interaction optimization process. Phys. A 465, 525–542 (2017)

    Google Scholar 

  78. Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)

    Google Scholar 

  79. Lusseau, D.: Evidence for social role in a dolphin social network. Evol. Ecol. 21, 357–366 (2007)

    Google Scholar 

  80. Porter, M.A., Onnela, J.-P., Mucha, P.J.: Communities in networks. Notices of the AMS 56(9), 1082–1097 (2009)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03, Hradec Králové, Czech Republic

    Benyamin Abdollahzadeh & Pavel Trojovský

  2. Department of Civil and Architectural Engineering, University of Miami, Coral Gables, FL, USA

    Nima Khodadadi

  3. Department of Computer Science, School of Engineering, Afagh Higher Education Institute, Urmia, Iran

    Saeid Barshandeh

  4. Department of Computer Engineering, Urmia Branch, Islamic Azad University, Urmia, Iran

    Farhad Soleimanian Gharehchopogh

  5. Department of Communications and Electronics, Delta Higher Institute of Engineering and Technology, Mansoura, 35111, Egypt

    El-Sayed M. El-kenawy

  6. Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, 19328, Jordan

    Laith Abualigah

  7. Computer Sciences Department, University of Tabuk, Tabuk 47913, Saudi Arabia

    Laith Abualigah

  8. Computer Science Department, Al al-Bayt University, Mafraq, 25113, Jordan

    Laith Abualigah

  9. Centre for Artificial Intelligence Research and Optimization, Torrens University Australia, Adelaide, Australia

    Seyedali Mirjalili

  10. Research and Innovation Center, Obuda University, Budapest, 1034, Hungary

    Seyedali Mirjalili

Authors
  1. Benyamin Abdollahzadeh
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  2. Nima Khodadadi
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  3. Saeid Barshandeh
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  4. Pavel Trojovský
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  6. El-Sayed M. El-kenawy
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  8. Seyedali Mirjalili
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Contributions

Methodology, BA, NK; Software, BA, NK; Investigation, SB and SK and LA; Writing–original draft, BA and NA; Writing–review & editing, SK, PT and FS; Supervision, SM; Project administration, SM All authors have read and agreed to the published version of the manuscript.

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Correspondence to Nima Khodadadi.

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Appendix 1

Appendix 1

See Tables 25, 26, 27, 28.

Table 25 Details of unimodal benchmark functions
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Table 26 Details of multimodal benchmark functions
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Table 27 Details of fixed-dimension multimodal benchmark functions
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Table 28 The 100-digit challenge basic test functions
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Abdollahzadeh, B., Khodadadi, N., Barshandeh, S. et al. Puma optimizer (PO): a novel metaheuristic optimization algorithm and its application in machine learning. Cluster Comput 27, 5235–5283 (2024). https://doi.org/10.1007/s10586-023-04221-5

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