Multi-verse Optimizer: Theory, Literature Review, and Application in Data Clustering

  • Ibrahim Aljarah
  • Majdi Mafarja
  • Ali Asghar Heidari
  • Hossam Faris
  • Seyedali MirjaliliEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 811)


Multi-verse optimizer (MVO) is considered one of the recent metaheuristics. MVO algorithm is inspired from the theory of multi-verse in astrophysics. This chapter discusses the theoretical foundation, operations, and main strengths behind this algorithm. Moreover, a detailed literature review is conducted to discuss several variants of the MVO algorithm. In addition, the main applications of MVO are also thoroughly described. The chapter also investigates the application of the MVO algorithm in tackling data clustering tasks. The proposed algorithm is benchmarked by several datasets, qualitatively and quantitatively. The experimental results show that the proposed MVO-based clustering algorithm outperforms several similar algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Dragonfly Algorithm (DA) in terms of clustering purity, clustering homogeneity, and clustering completeness.


Optimization Meta-heuristics Multi-verse optimizer Swarm intelligence MVO Data clustering 


  1. 1.
    Abusnaina, A. A., Ahmed, S., Jarrar, R., & Mafarja, M. (2018). Training neural networks using salp swarm algorithm for pattern classification, 2.Google Scholar
  2. 2.
    Al-Madi, N., Aljarah, I., & Ludwig, S. A. (2014). Parallel glowworm swarm optimization clustering algorithm based on mapreduce. In 2014 IEEE Symposium on Swarm Intelligence (SIS) (pp. 1–8). IEEE.Google Scholar
  3. 3.
    Ali, E., El-Hameed, M., El-Fergany, A., & El-Arini, M. (2016). Parameter extraction of photovoltaic generating units using multi-verse optimizer. Sustainable Energy Technologies and Assessments, 17, 68–76.CrossRefGoogle Scholar
  4. 4.
    Aljarah, I., AlaM, A. Z., Faris, H., Hassonah, M. A., Mirjalili, S., & Saadeh, H. (2018). Simultaneous feature selection and support vector machine optimization using the grasshopper optimization algorithm. Cognitive Computation (pp. 1–18).CrossRefGoogle Scholar
  5. 5.
    Aljarah, I., Faris, H., & Mirjalili, S. (2018). Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Computing, 22(1), 1–15.CrossRefGoogle Scholar
  6. 6.
    Aljarah, I., Faris, H., Mirjalili, S., & Al-Madi, N. (2018). Training radial basis function networks using biogeography-based optimizer. Neural Computing and Applications, 29(7), 529–553.CrossRefGoogle Scholar
  7. 7.
    Aljarah, I., & Ludwig, S. A. (2012). Parallel particle swarm optimization clustering algorithm based on mapreduce methodology. In 2012 Fourth World Congress on Nature and Biologically Inspired Computing (NaBIC) (pp. 104–111). IEEE.Google Scholar
  8. 8.
    Aljarah, I., & Ludwig, S. A. (2013). Mapreduce intrusion detection system based on a particle swarm optimization clustering algorithm. In Evolutionary Computation (CEC), 2013 IEEE Congress on (pp. 955–962). IEEE.Google Scholar
  9. 9.
    Aljarah, I., & Ludwig, S. A. (2013). A new clustering approach based on glowworm swarm optimization. In 2013 IEEE Congress on Evolutionary Computation (CEC) (pp. 2642–2649). IEEE.Google Scholar
  10. 10.
    Aljarah, I., & Ludwig, S. A. (2013). Towards a scalable intrusion detection system based on parallel PSO clustering using mapreduce. In Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation (pp. 169–170). ACM.Google Scholar
  11. 11.
    Aljarah, I., & Ludwig, S. A. (2016). A scalable mapreduce-enabled glowworm swarm optimization approach for high dimensional multimodal functions. International Journal of Swarm Intelligence Research (IJSIR), 7(1), 32–54.CrossRefGoogle Scholar
  12. 12.
    Aljarah, I., Mafarja, M., Heidari, A. A., Faris, H., Zhang, Y., & Mirjalili, S. (2018). Asynchronous accelerating multi-leader salp chains for feature selection. Applied Soft Computing, 71, 964–979.CrossRefGoogle Scholar
  13. 13.
    Aminisharifabad, M., Yang, Q., & Wu, X. (2018). A penalized Autologistic regression with application for modeling the microstructure of dual-phase high strength steel. Journal of Quality Technology, in-press.Google Scholar
  14. 14.
    Barham, R., & Aljarah, I. (2017). Link prediction based on whale optimization algorithm. In 2017 International Conference on New Trends in Computing Sciences (ICTCS) (pp. 55–60). IEEE.Google Scholar
  15. 15.
    Benmessahel, I., Xie, K., & Chellal, M. (2017). A new evolutionary neural networks based on intrusion detection systems using multiverse optimization. Applied Intelligence, 1–13.Google Scholar
  16. 16.
    Boley, D., Gini, M., Gross, R., Han, E. H. S., Hastings, K., Karypis, G., et al. (1999). Partitioning-based clustering for web document categorization. Decision Support Systems, 27(3), 329–341.CrossRefGoogle Scholar
  17. 17.
    Celebi, M. E. (2014). Partitional clustering algorithms. Springer.Google Scholar
  18. 18.
    Chitsaz, H., & Aminisharifabad, M. (2015). Exact learning of rna energy parameters from structure. Journal of Computational Biology, 22(6), 463–473.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Das, S., Abraham, A., & Konar, A. (2008). Automatic clustering using an improved differential evolution algorithm. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 38(1), 218–237.CrossRefGoogle Scholar
  20. 20.
    Elfattah, M. A., Hassanien, A. E., Abuelenin, S., & Bhattacharyya, S. (2019). Multi-verse optimization clustering algorithm for binarization of handwritten documents. In Recent Trends in Signal and Image Processing (pp. 165–175). Springer (2019).Google Scholar
  21. 21.
    Ewees, A. A., El Aziz, M. A., & Hassanien, A. E. (2017). Chaotic multi-verse optimizer-based feature selection. Neural Computing and Applications, 1–16.Google Scholar
  22. 22.
    Faris, H., Aljarah, I., Al-Betar, M. A., & Mirjalili, S. Grey wolf optimizer: A review of recent variants and applications. Neural Computing and Applications, 1–23.Google Scholar
  23. 23.
    Faris, H., Aljarah, I., Al-Madi, N., & Mirjalili, S. (2016). Optimizing the learning process of feedforward neural networks using lightning search algorithm. International Journal on Artificial Intelligence Tools, 25(06), 1650033.CrossRefGoogle Scholar
  24. 24.
    Faris, H., Aljarah, I., & Al-Shboul, B. (2016). A hybrid approach based on particle swarm optimization and random forests for e-mail spam filtering. In International Conference on Computational Collective Intelligence (pp. 498–508). Springer.Google Scholar
  25. 25.
    Faris, H., Aljarah, I., & Mirjalili, S. (2016). Training feedforward neural networks using multi-verse optimizer for binary classification problems. Applied Intelligence, 45(2), 322–332.CrossRefGoogle Scholar
  26. 26.
    Faris, H., Aljarah, I., & Mirjalili, S. (2017). Evolving radial basis function networks using moth–flame optimizer. In Handbook of Neural Computation (pp. 537–550). Elsevier.Google Scholar
  27. 27.
    Faris, H., Aljarah, I., & Mirjalili, S. (2018). Improved monarch butterfly optimization for unconstrained global search and neural network training. Applied Intelligence, 48(2), 445–464.CrossRefGoogle Scholar
  28. 28.
    Faris, H., Aljarah, I., Mirjalili, S., Castillo, P. A., & Merelo, J. J. (2016). Evolopy: An open-source nature-inspired optimization framework in python. In IJCCI (ECTA) (pp. 171–177).Google Scholar
  29. 29.
    Faris, H., & Aljarah, I., et al. (2015). Optimizing feedforward neural networks using krill herd algorithm for e-mail spam detection. In 2015 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT) (pp. 1–5). IEEE.Google Scholar
  30. 30.
    Faris, H., Ala’M, A. Z., Heidari, A. A., Aljarah, I., Mafarja, M., Hassonah, M. A., & Fujita, H. (2019). An intelligent system for spam detection and identification of the most relevant features based on evolutionary random weight networks. Information Fusion, 48, 67–83.CrossRefGoogle Scholar
  31. 31.
    Faris, H., Hassonah, M. A., AlaM, A. Z., Mirjalili, S., & Aljarah, I. (2017). A multi-verse optimizer approach for feature selection and optimizing SVM parameters based on a robust system architecture. Neural Computing and Applications (pp. 1–15).CrossRefGoogle Scholar
  32. 32.
    Faris, H., Mafarja, M. M., Heidari, A. A., Aljarah, I., AlaM, A. Z., Mirjalili, S., et al. (2018). An efficient binary salp swarm algorithm with crossover scheme for feature selection problems. Knowledge-Based Systems, 154, 43–67.CrossRefGoogle Scholar
  33. 33.
    Fathy, A., & Rezk, H. (2018). Multi-verse optimizer for identifying the optimal parameters of pemfc model. Energy, 143, 634–644.CrossRefGoogle Scholar
  34. 34.
    Ghatasheh, N., Faris, H., Aljarah, I., & Al-Sayyed, R. M. (2015). Optimizing software effort estimation models using firefly algorithm. Journal of Software Engineering and Applications, 8(03), 133.CrossRefGoogle Scholar
  35. 35.
    Guan, Y., Ghorbani, A. A., & Belacel, N. (2003). Y-means: A clustering method for intrusion detection. In Canadian Conference on Electrical and Computer Engineering, IEEE CCECE 2003. vol. 2, (pp. 1083–1086). IEEE.Google Scholar
  36. 36.
    Guha, D., Roy, P. K., & Banerjee, S. (2017). Multi-verse optimisation: a novel method for solution of load frequency control problem in power system. IET Generation, Transmission & Distribution, 11(14), 3601–3611.CrossRefGoogle Scholar
  37. 37.
    Hassanin, M. F., Shoeb, A. M., & Hassanien, A. E. (2017). Designing multilayer feedforward neural networks using multi-verse optimizer. In Handbook of Research on Machine Learning Innovations and Trends (pp. 1076–1093). IGI Global.Google Scholar
  38. 38.
    Heidari, A. A., Faris, H., Aljarah, I., & Mirjalili, S. (2018). An efficient hybrid multilayer perceptron neural network with grasshopper optimization. Soft Computing, 1–18.Google Scholar
  39. 39.
    Heidari, A. A., & Abbaspour, R. A. (2018). Enhanced chaotic grey wolf optimizer for real-world optimization problems: A comparative study. In Handbook of Research on Emergent Applications of Optimization Algorithms (pp. 693–727). IGI Global.Google Scholar
  40. 40.
    Heidari, A. A., Abbaspour, R. A., & Jordehi, A. R. (2017). An efficient chaotic water cycle algorithm for optimization tasks. Neural Computing and Applications, 28(1), 57–85.CrossRefGoogle Scholar
  41. 41.
    Heidari, A. A., Abbaspour, R. A., & Jordehi, A. R. (2017). Gaussian bare-bones water cycle algorithm for optimal reactive power dispatch in electrical power systems. Applied Soft Computing, 57, 657–671.CrossRefGoogle Scholar
  42. 42.
    Heidari, A. A., & Delavar, M. R. (2016). A modified genetic algorithm for finding fuzzy shortest paths in uncertain networks. In ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B2 (299–304).CrossRefGoogle Scholar
  43. 43.
    Heidari, A. A., & Pahlavani, P. (2017). An efficient modified grey wolf optimizer with lévy flight for optimization tasks. Applied Soft Computing, 60, 115–134.CrossRefGoogle Scholar
  44. 44.
    Hu, C., Li, Z., Zhou, T., Zhu, A., & Xu, C. (2016). A multi-verse optimizer with levy flights for numerical optimization and its application in test scheduling for network-on-chip. PloS One, 11(12), e0167341.CrossRefGoogle Scholar
  45. 45.
    Jain, A. K., Murty, M. N., & Flynn, P. J. (1999). Data clustering: A review. ACM Computing Surveys (CSUR), 31(3), 264–323.CrossRefGoogle Scholar
  46. 46.
    Karthikeyan, K., & Dhal, P. (2017). Multi verse optimization (mvo) technique based voltage stability analysis through continuation power flow in ieee 57 bus. Energy Procedia, 117, 583–591.CrossRefGoogle Scholar
  47. 47.
    Kouba, N. E. Y., Menaa, M., Hasni, M., & Boudour, M. (2018). Application of multi-verse optimiser-based fuzzy-pid controller to improve power system frequency regulation in presence of hvdc link. International Journal of Intelligent Engineering Informatics, 6(1–2), 182–203.CrossRefGoogle Scholar
  48. 48.
    Kouba, N. E. Y., Menaa, M., Hasni, M., Tehrani, K., & Boudour, M. (2016). A novel optimized fuzzy-pid controller in two-area power system with hvdc link connection. In 2016 International Conference on Control, Decision and Information Technologies (CoDIT) (pp. 204–209). IEEE.Google Scholar
  49. 49.
    Kumar, A., & Suhag, S. (2017). Effect of tcps, smes, and dfig on load frequency control of a multi-area multi-source power system using multi-verse optimized fuzzy-pid controller with derivative filter. Journal of Vibration and Control, 1077546317724968.Google Scholar
  50. 50.
    Kumar, A., & Suhag, S. (2017). Multiverse optimized fuzzy-pid controller with a derivative filter for load frequency control of multisource hydrothermal power system. Turkish Journal of Electrical Engineering & Computer Sciences, 25(5), 4187–4199.CrossRefGoogle Scholar
  51. 51.
    Kwedlo, W. (2011). A clustering method combining differential evolution with the k-means algorithm. Pattern Recognition Letters, 32(12), 1613–1621.CrossRefGoogle Scholar
  52. 52.
    Lichman, M. (2013). UCI machine learning repository.
  53. 53.
    Mafarja, M., Aljarah, I., Heidari, A. A., Hammouri, A. I., Faris, H., & AlaM, A. Z., et al. (2017). Evolutionary population dynamics and grasshopper optimization approaches for feature selection problems. Knowledge-Based Systems.Google Scholar
  54. 54.
    Mafarja, M., Aljarah, I., Heidari, A. A., Faris, H., Fournier-Viger, P., Li, X., & Mirjalili, S. (2018). Binary dragonfly optimization for feature selection using time-varying transfer functions. Knowledge-Based Systems, 161, 185–204.CrossRefGoogle Scholar
  55. 55.
    Mafarja, M., & Mirjalili, S. (2017). Whale optimization approaches for wrapper feature selection. Applied Soft Computing, 62, 441–453.CrossRefGoogle Scholar
  56. 56.
    Mafarja, M. M., & Mirjalili, S. (2017). Hybrid whale optimization algorithm with simulated annealing for feature selection. Neurocomputing, 260, 302–312.CrossRefGoogle Scholar
  57. 57.
    Majdi, M., Abdullah, S., & Jaddi, N. S. (2015). Fuzzy population-based meta-heuristic approaches for attribute reduction in rough set theory. World Academy of Science, Engineering and Technology, International Journal of Computer, Electrical, Automation, Control and Information Engineering, 9(12), 2462–2470.Google Scholar
  58. 58.
    Van der Merwe, D., & Engelbrecht, A. P. (2003). Data clustering using particle swarm optimization. In Evolutionary Computation, 2003. CEC’03 The 2003 Congress on. vol. 1 (pp. 215–220). IEEE.Google Scholar
  59. 59.
    Meshkat, M., & Parhizgar, M. (2017). Stud multi-verse algorithm. In Swarm Intelligence and Evolutionary Computation (CSIEC), 2017 2nd Conference on (pp. 42–47). IEEE.Google Scholar
  60. 60.
    Mirjalili, S., Jangir, P., Mirjalili, S. Z., Saremi, S., & Trivedi, I. N. (2017). Optimization of problems with multiple objectives using the multi-verse optimization algorithm. Knowledge-Based Systems, 134, 50–71.CrossRefGoogle Scholar
  61. 61.
    Mirjalili, S., Mirjalili, S. M., & Hatamlou, A. (2016). Multi-verse optimizer: A nature-inspired algorithm for global optimization. Neural Computing and Applications, 27(2), 495–513.CrossRefGoogle Scholar
  62. 62.
    Ng, H., Ong, S., Foong, K., Goh, P., & Nowinski, W. (2006). Medical image segmentation using k-means clustering and improved watershed algorithm. In Image Analysis and Interpretation, 2006 IEEE Southwest Symposium on (pp. 61–65). IEEE.Google Scholar
  63. 63.
    Pan, W., Zhou, Y., & Li, Z. (2017). An exponential function inflation size of multi-verse optimisation algorithm for global optimisation. International Journal of Computing Science and Mathematics, 8(2), 115–128.MathSciNetCrossRefGoogle Scholar
  64. 64.
    Rokach, L., & Maimon, O. (2005). Clustering methods. In: Data mining and knowledge discovery handbook (pp. 321–352). Springer.Google Scholar
  65. 65.
    Rosenberg, A., & Hirschberg, J. (2007). V-measure: A conditional entropy-based external cluster evaluation measure. EMNLP-CoNLL, 7, 410–420.Google Scholar
  66. 66.
    Sayed, G. I., Darwish, A., & Hassanien, A. E. (2017). Quantum multiverse optimization algorithm for optimization problems. Neural Computing and Applications, 1–18.Google Scholar
  67. 67.
    Sayed, G. I., Darwish, A., & Hassanien, A. E. (2018). A new chaotic multi-verse optimization algorithm for solving engineering optimization problems. Journal of Experimental & Theoretical Artificial Intelligence, 30(2), 293–317.CrossRefGoogle Scholar
  68. 68.
    Shelokar, P., Jayaraman, V. K., & Kulkarni, B. D. (2004). An ant colony approach for clustering. Analytica Chimica Acta, 509(2), 187–195.CrossRefGoogle Scholar
  69. 69.
    Shukri, S., Faris, H., Aljarah, I., Mirjalili, S., & Abraham, A. (2018). Evolutionary static and dynamic clustering algorithms based on multi-verse optimizer. Engineering Applications of Artificial Intelligence, 72, 54–66.CrossRefGoogle Scholar
  70. 70.
    Strehl, A., Ghosh, J., & Mooney, R. (2000). Impact of similarity measures on web-page clustering. In Workshop on Artificial Intelligence for Web Search (AAAI 2000). vol. 58 (p. 64 ).Google Scholar
  71. 71.
    Sulaiman, M. H., Mohamed, M. R., Mustaffa, Z., & Aliman, O. (2016). An application of multi-verse optimizer for optimal reactive power dispatch problems. International Journal of Simulation-Systems, Science & Technology, 17, 41.Google Scholar
  72. 72.
    Trivedi, I. N., Jangir, P., Jangir, N., Parmar, S. A., Bhoye, M., & Kumar, A. (2016). Voltage stability enhancement and voltage deviation minimization using multi-verse optimizer algorithm. In Circuit, Power and Computing Technologies (ICCPCT), 2016 International Conference on (pp. 1–5). IEEE.Google Scholar
  73. 73.
    Valenzuela, M., Peña, A., Lopez, L., & Pinto, H. (2017). A binary multi-verse optimizer algorithm applied to the set covering problem. In Systems and Informatics (ICSAI), 2017 4th International Conference on (pp. 513–518). IEEE.Google Scholar
  74. 74.
    Vivek, K., Deepak, M., Mohit, J., Asha, R., & Vijander, S., et al. (2018). Development of multi-verse optimizer (mvo) for labview. In Intelligent Communication, Control and Devices (pp. 731–739). Springer.Google Scholar
  75. 75.
    Wang, X., Luo, D., Liu, J., Wang, W., & Jie, G. (2017). Prediction of natural gas consumption in different regions of china using a hybrid mvo-nngbm model. Mathematical Problems in Engineering, 2017.Google Scholar
  76. 76.
    Wang, X., Luo, D., Zhao, X., & Sun, Z. (2018). Estimates of energy consumption in china using a self-adaptive multi-verse optimizer-based support vector machine with rolling cross-validation. Energy, 152, 539–548.CrossRefGoogle Scholar
  77. 77.
    Zhao, H., Han, X., & Guo, S. (2016). Dgm (1, 1) model optimized by mvo (multi-verse optimizer) for annual peak load forecasting. Neural Computing and Applications, 1–15.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Ibrahim Aljarah
    • 1
  • Majdi Mafarja
    • 2
  • Ali Asghar Heidari
    • 3
  • Hossam Faris
    • 1
  • Seyedali Mirjalili
    • 4
    Email author
  1. 1.King Abdullah II School for Information TechnologyThe University of JordanAmmanJordan
  2. 2.Department of Computer Science, Faculty of Engineering and TechnologyBirzeit UniversityBirzeitPalestine
  3. 3.School of Surveying and Geospatial EngineeringUniversity of TehranTehranIran
  4. 4.Institute of Integrated and Intelligent Systems, Griffith University, NathanBrisbaneAustralia

Personalised recommendations