Laplacian whale optimization algorithm

  • Amarjeet SinghEmail author
Original Article


Whale optimization algorithm is a new member of nature inspired optimization algorithm which is inspired from foraging behaviour of humpback whales. Similar to other heuristic algorithms, Whale optimization algorithm suffers with immature convergence and stagnation problems while solving optimization problems. In this paper, Whale optimization algorithm is hybridized with Laplace Crossover operator and a new algorithm, Laplacian whale optimization algorithm (LXWOA), has been proposed. It has been used to solve a set of 23 classical benchmark functions which consists of scalable unimodal functions, scalable multimodal functions and low dimensional multimodal functions and the results are compared with original whale optimization algorithm, particle swarm optimization, differential evolution, gravitational search algorithm and Laplacian gravitational search algorithm. In this paper, LXWOA and WOA have also been used to solve the problem of extraction of compounds from gardenia.


Whale optimization algorithm Laplace crossover Numerical optimization Heuristic algorithm Gardenia problem 



  1. Abbass HA (2001) MBO: marriage in honey bees optimization-a haplometrosis polygynous swarming approach. In: Proceedings of the 2001 congress on evolutionary computation, pp 207–214Google Scholar
  2. Abdel-Basset M, El-Shahat D, El-Henawy I, Sangaiah AK, Ahmed SH (2018) A novel whale optimization algorithm for cryptanalysis in Merkle-Hellman cryptosystem. Mobile Netw Appl 1–11Google Scholar
  3. Abdel-Basset M, El-Shahat D, Sangaiah AK (2019) A modified nature inspired meta-heuristic whale optimization algorithm for solving 0–1 knapsack problem. Int J Mach Learn Cybern 1–20Google Scholar
  4. Ala’m AZ, Faris H, Hassonah MA (2018) Evolving support vector machines using whale optimization algorithm for spam profiles detection on online social networks in different lingual contexts. Knowl Based Syst 153:91–104Google Scholar
  5. Algabalawy MA, Abdelaziz AY, Mekhamer SF, Aleem SHA (2018) Considerations on optimal design of hybrid power generation systems using whale and sine cosine optimization algorithms. J Electr Syst Inf Technol 5(3):312–325Google Scholar
  6. Aljarah I, Faris H, Mirjalili S (2018) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 1–15Google Scholar
  7. Basturk B, Karaboga D (2006) An artificial bee colony (ABC) algorithm for numeric function optimization. In: Proceedings of the IEEE swarm intelligence symposium, pp 12–14Google Scholar
  8. Bui QT, Pham MV, Nguyen QH, Nguyen LX, Pham HM (2019) Whale optimization algorithm and adaptive neuro-fuzzy inference system: a hybrid method for feature selection and land pattern classification. Int J Remote Sens 1–16Google Scholar
  9. Dasgupta D, Zbigniew M (2013) Evolutionary algorithms in engineering applications. SpringerGoogle Scholar
  10. Deep K, Bansal JC (2009) Optimization of directional over current relay times using Laplace Crossover Particle Swarm Optimization (LXPSO). In: 2009 World congress on nature & biologically inspired computing (NaBIC), pp 288–293Google Scholar
  11. Deep K, Thakur M (2007) A new crossover operator for real coded genetic algorithms. Appl Math Comput 188(1):895–911MathSciNetzbMATHGoogle Scholar
  12. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39Google Scholar
  13. Du H, Wu X, Zhuang J (2006) Small-world optimization algorithm for function optimization. In: Jiao L, Wang L, Gao X, Liu J, Wu F (eds) Advances in natural computation. ICNC 2006. Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, vol 4222, pp 264–273Google Scholar
  14. Eid HF (2018) Binary whale optimisation: an effective swarm algorithm for feature selection. Int J Metaheuristics 7(1):67–79Google Scholar
  15. El Aziz MA, Ahmed Ewees AA, Hassanien AE (2017) Whale Optimization Algorithm and Moth-Flame Optimization for multilevel thresholding image segmentation. Expert Syst Appl 83:242–256Google Scholar
  16. El Aziz MA, Ewees AA, Hassanien AE, Mudhsh M, Xiong S (2018) Multi-objective whale optimization algorithm for multilevel thresholding segmentation. In: Advances in soft computing and machine learning in image processing. Springer, Cham, pp 23–39Google Scholar
  17. El Aziz MA, Ewees AA, Hassanien AE (2018b) Multi-objective whale optimization algorithm for content-based image retrieval. Multimed Tools Appl 77(19):26135–26172Google Scholar
  18. Elaziz MA, Oliva D (2018) Parameter estimation of solar cells diode models by an improved opposition-based whale optimization algorithm. Energy Convers Manag 171:1843–1859Google Scholar
  19. Elhosseini MA, Haikal AY, Badawy M, Khashan N (2019) Biped robot stability based on an A-C parametric Whale Optimization Algorithm. J Comput Sci 31:17–32MathSciNetGoogle Scholar
  20. Erol OK, Eksin I (2006) A new optimization method: big bang-big crunch. Adv Eng Softw 37(2):106–111Google Scholar
  21. Formato RA (2007) Central force optimization: a new metaheuristic with applications in applied electromagnetics. Prog Electromagn Res 77:425–491Google Scholar
  22. Garg V, Deep K (2016) Optimal extraction of bioactive compounds from Gardenia using Laplacian biogeography based optimization. In: Kim J, Jim Z (eds) Harmony search algorithm advances in intelligent systems and computing, vol 382. Springer, Berlin, pp 251–258Google Scholar
  23. Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68Google Scholar
  24. Ghahremani-Nahr J, Kian R, Sabet E (2019) A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm. Expert Syst Appl 116:454–471Google Scholar
  25. Glover F (1989) Tabu search—Part I. ORSA J Comput 1(3):190–206MathSciNetzbMATHGoogle Scholar
  26. Glover F (1990) Tabu search—Part II. ORSA J Comput 2(1):4–32MathSciNetzbMATHGoogle Scholar
  27. Goldbogen JA, Friedlaender AS, Calambokidis J, Mckenna MF, Simon M, Nowacek DP (2013) Integrative approaches to the study of baleen whale diving behavior, feeding performance, and foraging ecology. Bioscience 63(2):90–100Google Scholar
  28. Hasanien HM (2018) Performance improvement of photovoltaic power systems using an optimal control strategy based on whale optimization algorithm. Electr Power Syst Res 157:168–176Google Scholar
  29. Hassan G, Hassanien AE (2018) Retinal fundus vasculature multilevel segmentation using whale optimization algorithm. Signal Image Video Process 12(2):263–270Google Scholar
  30. Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–72Google Scholar
  31. Horng MF, Dao TK, Shieh CS (2017) A multi-objective optimal vehicle fuel consumption based on whale optimization algorithm. In: Advances in intelligent information hiding and multimedia signal processing. Springer, Cham, pp 371–380Google Scholar
  32. Hussien AG, Hassanien AE, Houssein EH, Bhattacharyya S, Amin M (2019) S-shaped binary whale optimization algorithm for feature selection. In: Recent trends in signal and image processing. Springer, Singapore, pp 79–87Google Scholar
  33. Jadhav AN, Gomathi N (2018) WGC: hybridization of exponential grey wolf optimizer with whale optimization for data clustering. Alex Eng J 57(3):1569–1584Google Scholar
  34. Kaur G, Arora S (2018) Chaotic whale optimization algorithm. J Comput Des Eng 5(3):275–284Google Scholar
  35. Kaveh A, Ghazaan MI (2017) Enhanced whale optimization algorithm for sizing optimization of skeletal structures. Mech Based Des Struct Mach 45(3):345–362Google Scholar
  36. Kennedy J (2011) Particle swarm optimization. In: Encyclopedia of machine learning. Springer US, pp 760–766Google Scholar
  37. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680MathSciNetzbMATHGoogle Scholar
  38. Koza JR (1992) Genetic programmingGoogle Scholar
  39. Laskar NM, Guha K, Chatterjee I, Chanda S, Baishnab KL, Paul PK (2019) HWPSO: a new hybrid whale-particle swarm optimization algorithm and its application in electronic design optimization problems. Appl Intell 49(1):265–291Google Scholar
  40. Luo J, Shi B (2018) A hybrid whale optimization algorithm based on modified differential evolution for global optimization problems. Appl Intell 1–19Google Scholar
  41. Mafarja MM, Mirjalili S (2017) Hybrid Whale Optimization Algorithm with simulated annealing for feature selection. Neurocomputing 260:302–312Google Scholar
  42. Mehne HH, Mirjalili S (2018) A parallel numerical method for solving optimal control problems based on whale optimization algorithm. Knowl Based Syst 151:114–123Google Scholar
  43. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67Google Scholar
  44. Mirjalili S, Mirjalili SM, Saremi S, Mirjalili S (2020) Whale Optimization Algorithm: theory, literature review, and application in designing photonic crystal filters. In: Nature-inspired optimizers. Springer, Cham, pp 219–238Google Scholar
  45. Moghaddam FF, Moghaddam RF, Cheriet M (2012) Curved space optimization: a random search based on general relativity theory. arXiv: 1208.2214Google Scholar
  46. Mostafa A, Hassanien AE, Houseni M, Hefny H (2017) Liver segmentation in MRI images based on whale optimization algorithm. Multimed Tools Appl 76(23):24931–24954Google Scholar
  47. Mucherino A, Seref O (2007) Monkey search: a novel metaheuristic search for global optimization. In: AIP conference proceedings, pp 162–173Google Scholar
  48. Nasiri J, Khiyabani FM (2018) A whale optimization algorithm (WOA) approach for clustering. Cogent Math Stat 5(1):1–13MathSciNetGoogle Scholar
  49. Nazari-Heris M, Mehdinejad M, Mohammadi-Ivatloo B, Babamalek-Gharehpetian G (2017) Combined heat and power economic dispatch problem solution by implementation of whale optimization method. Neural Comput Appl 1–16Google Scholar
  50. Oliva D, El Aziz MA, Hassanien AE (2017) Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm. Appl Energy 200:141–154Google Scholar
  51. Rao RV, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43(3):303–315Google Scholar
  52. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248zbMATHGoogle Scholar
  53. Rechenberg I (1978) Evolutionsstrategien. Springer, Berlin, pp 83–114Google Scholar
  54. Reddy PDP, Reddy VCV, Manohar TG (2017) Optimal renewable resources placement in distribution networks by combined power loss index and whale optimization algorithms. J Electr Syst Inf Technol 175–191Google Scholar
  55. Saidala RK, Devarakonda N (2018) Improved whale optimization algorithm case study: clinical data of anaemic pregnant woman. In: Data engineering and intelligent computing. Springer, Singapore, pp 271–281Google Scholar
  56. Shashi DK, Katiyar VK (2010) Multi-objective extraction optimization of bioactive compounds from Gardenia using real coded genetic algorithm. In: 6th World congress of biomaconics, vol 31, pp 1436–1466Google Scholar
  57. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713Google Scholar
  58. Singh A, Deep K (2015) Real coded genetic algorithm operators embedded in gravitational search algorithm for continuous optimization. Int J Intell Syst Appl 7(12):1–22Google Scholar
  59. Singh A, Deep K (2017a) Novel hybridized variants of gravitational search algorithm for constraint optimization. Int J Swarm Intell 3(1):1–22MathSciNetGoogle Scholar
  60. Singh A, Deep K (2017b) Hybridized gravitational search algorithms with real coded genetic algorithms for integer and mixed integer optimization problems. In: Proceedings of sixth international conference on soft computing for problem solving. Springer, Singapore, pp 84–112Google Scholar
  61. Sreenu K, Sreelatha M (2017) W-scheduler: whale optimization for task scheduling in cloud computing. Cluster Comput 1–12Google Scholar
  62. Sun Y, Wang X, Chen Y, Liu Z (2018) A modified whale optimization algorithm for large-scale global optimization problems. Expert Syst Appl 114:563–577Google Scholar
  63. Tan Y, Zhu Y (2010) Fireworks algorithm for optimization. In: Advances in swarm intelligence. Springer, pp 355–364Google Scholar
  64. Tharwat A, Moemen YS, Hassanien AE (2017) Classication of toxicity effects of biotransformed hepatic drugs using whale optimized support vector machines. J Biomed Inform 68:132–149Google Scholar
  65. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82Google Scholar
  66. Xiong G, Zhang J, Shi D, He Y (2018) Parameter extraction of solar photovoltaic models using an improved whale optimization algorithm. Energy Convers Manag 174:388–405Google Scholar
  67. Yan Z, Sha J, Liu B, Tian W, Lu J (2018) An ameliorative whale optimization algorithm for multi-objective optimal allocation of water resources in Handan, China. Water 10(1):87–116Google Scholar
  68. Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Proceedings of the workshop on nature inspired cooperative strategies for optimization (NICSO 2010). Springer, pp 65–74Google Scholar
  69. Yang X-S (2010b) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspired Comput 2(2):78–84Google Scholar
  70. Yang X-S, Deb S (2009) Cuckoo search via Lévy flights. In: Proceedings of the world congress on nature & biologically inspired computing, NaBIC 2009, pp 210–214Google Scholar
  71. Yang B, Liu X, Gao Y (2009) Extraction optimization of bioactive compounds (crocin, geniposide and total phenolic compounds) from Gardenia (Gardenia jasminoides Ellis) fruits with response surface methodology. Innov Food Sci Emerg Technol 10:610–615Google Scholar
  72. Yousri D, Allam D, Eteiba MB (2019) Chaotic whale optimizer variants for parameters estimation of the chaotic behavior in permanent magnet synchronous motor. Appl Soft Comput 74:479–503Google Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019

Authors and Affiliations

  1. 1.Department of MathematicsJanki Devi Memorial College, University of Delhi, Sir Ganga Ram Hospital MargNew DelhiIndia

Personalised recommendations