Evolutionary Multi-objective Whale Optimization Algorithm

  • Faisal Ahmed SiddiqiEmail author
  • Chowdhury Mofizur Rahman
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 941)


Whale Optimization Algorithm (WOA) is a recently proposed metaheuristic algorithm and achieved much attention of the researchers worldwide for its competitive performance over other popular metaheuristic algorithms. As a metaheuristic algorithm, it mimics the hunting behavior of humpback whale which uses its unique spiral bubble-net feeding maneuver to search and hunt prey. The WOA has been designed to solve mono-objective problems and it shows great performance and even surplus other state of the art metaheuristics in terms of fast convergence and other performance criteria. But this such a distinctive and successful metaheuristic’s performance in dealing multi-objective problems especially in dealing with multi-objective benchmark problems has not been studied that much extent. In this paper, we developed a multi-objective version of WOA which incorporates both whale search and evolutionary search strategy. The obtained results are also compared with NSGA-II, NSGA-III, MOEA/D, MOEA/D-DE, MOPSO and d-MOPSO state of art multi-objective evolutionary algorithms.


Multi-objective Whale Optimization Algorithm (MOWOA) Non-dominated sorting genetic algorithm (NSGA) Pareto-optimal set (PS) Pareto-optimal front (PF) 


  1. 1.
    Mirjalili, S., Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016)CrossRefGoogle Scholar
  2. 2.
    Prakash, D.B., Lakshminarayana, C.: Optimal siting of capacitors in radial distribution network using whale optimization algorithm. Alex. Eng. J. 56, 499–509 (2016)CrossRefGoogle Scholar
  3. 3.
    Reddy, P.D.P., Reddy, V.C.V., Manohar, T.G.: Whale optimization algorithm for optimal sizing of renewable resources for loss reduction in distribution systems. Renew. Wind Water Sol. 4(1), 3 (2017)CrossRefGoogle Scholar
  4. 4.
    Mafarja, M., Mirjalili, S.: Whale optimization approaches for wrapper feature selection. Appl. Soft Comput. J. 62(November), 441–453 (2018)CrossRefGoogle Scholar
  5. 5.
    Mostafa, A., Hassanien, A.E., Houseni, M., Hefny, H.: Liver segmentation in MRI images based on whale optimization algorithm. Multimed. Tools Appl. 76(April), 1–24 (2017)Google Scholar
  6. 6.
    Dao, T.K., Pan, T.S., Pan, J.S.: A multi-objective optimal mobile robot path planning based on whale optimization algorithm. In: 2016 IEEE 13th International Conference on Signal Processing, pp. 337–342 (2016)Google Scholar
  7. 7.
    Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Parallel Problem Solving from Nature PPSN VI, pp. 849–858 (2000)Google Scholar
  8. 8.
    Yagyasen, D., Darbari, M., Shukla, P.K., Singh, V.K.: Diversity and convergence issues in evolutionary multiobjective optimization: application to agriculture science. IERI Procedia 5, 81–86 (2013)CrossRefGoogle Scholar
  9. 9.
    Bosman, P.A.N., Thierens, D.: The balance between proximity and diversity in multi – objective evolutionary algorithms. IEEE Trans. Evol. Comput. 7(2), 174–188 (2003)CrossRefGoogle Scholar
  10. 10.
    Lin, Q., Li, J., Du, Z., Chen, J., Ming, Z.: A novel multi-objective particle swarm optimization with multiple search strategies. Eur. J. Oper. Res. 247(3), 732–744 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Sierra, M.R., Coello, C.A.C.: Improving PSO-based multi-objective optimization using crowding, mutation and ∈-dominance. In: International Conference on Evolutionary Multi-criterion Optimization, pp. 505–519. Springer, Heidelberg, March 2005Google Scholar
  12. 12.
    Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9, 1–34 (1994)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Jiang, S., Yang, S.: Convergence versus diversity in multiobjective optimization. In: International Conference on Parallel Problem Solving from Nature, pp. 984–993. Springer, Cham, September 2016Google Scholar
  14. 14.
    Khare, V.: Performance Scaling Multi-objective Evolutionary Algorithms. School of Computer Science, The University of Birmingham, Birmingham (2002)Google Scholar
  15. 15.
    Ngatchou, P., Zarei, A., El-Sharkawi, A.: Pareto multi objective optimization. In: Proceedings of the 13th International Conference on Intelligent Systems Application to Power Systems 2005, pp. 84–91. IEEE, November 2005Google Scholar
  16. 16.
    Zhou, A., Jin, Y., Zhang, Q., Sendhoff, B., Tsang, E.: Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion. In: 2006 IEEE International Conference on Evolutionary Computation, pp. 892–899 (2006)Google Scholar
  17. 17.
    Tian, Y., Cheng, R., Zhang, X., Jin, Y.: PlatEMO: a MATLAB platform for evolutionary multi-objective optimization. IEEE Comput. Intell. Mag. 12, 73–87 (2017)CrossRefGoogle Scholar
  18. 18.
    Jangir, P., Jangir, N.: Non-dominated sorting whale optimization algorithm (NSWOA): a multi-objective optimization algorithm for solving engineering design problems. Glob. J. Res. Eng.: F Electr. Electron. Eng. 17(4) (2017). Version 1.0Google Scholar
  19. 19.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8, 173–195 (2000)CrossRefGoogle Scholar
  20. 20.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. In: Evolutionary Multiobjective Optimization, Advanced Information and Knowledge Processing, pp. 105–145. Springer, London (2005)Google Scholar
  21. 21.
    Li, H., Zhang, Q., Deng, J.: Biased multiobjective optimization and decomposition algorithm. IEEE Trans. Cybern. 47, 52–66 (2016)CrossRefGoogle Scholar
  22. 22.
    Deb, K., Jain, H.: An evolutionary many- objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577–601 (2014)CrossRefGoogle Scholar
  23. 23.
    Kumawat, I.R., Nanda, S.J., Maddila, R.K.: Multi-objective whale optimization. TENCON - IEEE Region 10 Conference, November-2017Google Scholar
  24. 24.
    Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar
  25. 25.
    Li, H., Zhang, Q.: Comparison between NSGA-II and MOEA/D on a set of multiobjective optimization problems with complicated pareto sets. IEEE Trans. Evol. Comput. 13(2), 284–302 (2009)CrossRefGoogle Scholar
  26. 26.
    Parsopoulos, K., Vrahatis, M.N.: Particle swarm optimization method in multiobjective problems. In: SAC 2002, Madrid, Spain (2002)Google Scholar
  27. 27.
    Zapotecas Martínez, S., Coello Coello, C.A.: A multi-objective particle swarm optimizer based on decomposition. In: Proceeding of the 13th Annual Conference on Genetic and Evolutionary Computation - GECCO ’11, p. 69 (2011)Google Scholar
  28. 28.
    Zhang, Q., Zhou, A., Zhao, S., Suganthan, P.N., Liu, W., Tiwari, S.: Multiobjective optimization test instances for the CEC 2009 special session and competition. University of Essex, Colchester, UK and Nanyang Technological University, Technical report. CES-487, Technical report (2008)Google Scholar
  29. 29.
    Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science 1995. MHS’95, pp. 39–43. IEEE, October 1995Google Scholar
  30. 30.
    El Aziz, M.A., Ewees, A.A., Hassanien, A.E.: Multi-objective whale optimization algorithm for content-based image retrieval. Multimed. Tools Appl. 77, 1–38 (2018)CrossRefGoogle Scholar
  31. 31.
    Wang, J., Du, P., Niu, T., Yang, W.: A novel hybrid system based on a new proposed algorithm—multi-objective whale optimization algorithm for wind speed forecasting. Appl. Energy 208(October), 344–360 (2017)CrossRefGoogle Scholar
  32. 32.
    Cheng, R., et al.: Benchmark functions for the CEC 2017 competition on evolutionary many-objective optimization (2017)Google Scholar
  33. 33.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Faisal Ahmed Siddiqi
    • 1
    Email author
  • Chowdhury Mofizur Rahman
    • 1
  1. 1.United International UniversityDhakaBangladesh

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