Abstract
The whale optimization algorithm (WOA), a biologically inspired optimization technique, is known for its straightforward design and effectiveness. Despite many advantages, it has certain disadvantages, such as a limited exploration capacity and early convergence as a result of the minimal exploration of the search process. The WOA cannot bypass the local solution; consequently, the search is unbalanced. This study introduces a new variant of WOA, namely elite-based WOA (EBWOA), to address the inherent shortcomings of traditional WOA. Unlike the three phases used in the traditional WOA, only the encircling prey and bubble-net attack phases are applied in the new variant. Using the local elite method, exploration will be conducted with an encircling prey phase to ensure some exploitation during exploration. The choice between exploration and exploitation is achieved by introducing a new choice parameter. An inertia weight \({(\omega }_{i})\) is used in both phases to scour the region. The EBWOA is used to evaluate twenty-five benchmark functions, IEEE CEC 2019 functions, and two design problems and compared to several fundamental techniques and WOA variants. In addition, the EBWOA is used to solve the practical cloud scheduling problem. Performance is compared against a variety of metaheuristics using real cloud workloads by running experiments on the standard CloudSim simulator. Comparing the numerical results of benchmark functions, IEEE CEC 2019 functions, statistical verification, and the solution generation speed of EBWOA confirmed the effectiveness of the proposed EBWOA approach. It has also shown a great improvement over baseline algorithms in creating efficient scheduling solutions by significantly reducing makespan time and energy consumption targets.
Similar content being viewed by others
Data Availability
All data generated or analyzed during this study are included in the article.
References
Chakraborty S, Saha AK, Sharma S, Chakraborty R, Debnath S. A hybrid whale optimization algorithm for global optimization. J Ambient Intell Human Comput. 2021;1–37.
Angeline PJ. Genetic programming: on the programming of computers by means of natural selection. Biosystems. 1994;33(1):69–73. https://doi.org/10.1016/0303-2647(94)90062-0.
Storn R, Price K. Differential evolution – a simple and Efficient heuristic for global optimization over continuous spaces. J Global Optim. 1997;11(4):341–59. https://doi.org/10.1023/a:1008202821328.
Tian X, Yang HD, Deng FQ. A novel artificial immune network algorithm. IEEE 2006 international conference on machine learning and cybernetics; 2006. p. 2159–65.
Anandita S, Rosmansyah Y, Dabarsyah B, Choi JU. Implementation of dendritic cell algorithm as an anomaly detection method for port scanning attack. International Conference on Information Technology Systems and Innovation (ICITSI); 2015. https://doi.org/10.1109/icitsi.2015.7437688.
Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S. Equilibrium optimizer: a novel optimization algorithm. Knowl Based Syst. 2019;191:105190. https://doi.org/10.1016/j.knosys.2019.105190.
Hashim FA, Houssein EH, Mabrouk MS, Al-Atabany W, Mirjalili S. Henry gas solubility optimization: a novel physics-based algorithm. Futur Gener Comput Syst. 2019;101:646–67. https://doi.org/10.1016/j.future.2019.07.015.
Cheng MY, Prayogo D. Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct. 2014;139:98–112. https://doi.org/10.1016/j.compstruc.2014.03.007.
Mirjalili S, Lewis A. The whale optimization algorithm. Adv Eng Softw. 2016;95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008.
Rao RV, Savsani VJ, Vakharia DP. Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des. 2011;43(3):303–15. https://doi.org/10.1016/j.cad.2010.12.015.
Abdollahzadeh B, Soleimanian Gharehchopogh F, Mirjalili S. Artificial gorilla troops optimizer: a new nature-inspired metaheuristic algorithm for global optimization problems. Int J Intell Syst. 2021;36(10):5887–958.
Azizi M. Atomic orbital search: a novel metaheuristic algorithm. Appl Math Model. 2021;93:657–83.
Hashim FA, Houssein EH, Hussain K, Mabrouk MS, Al-Atabany W. Honey Badger Algorithm: new metaheuristic algorithm for solving optimization problems. Math Comput Simul. 2022;192:84–110.
Mohammad Hasani Zade B, Mansouri N. PPO: a new nature-inspired metaheuristic algorithm based on predation for optimization. Soft Comput. 2022;26(3):1331–402.
Nama S, Saha AK, Ghosh S. Improved backtracking search algorithm for pseudo-dynamic active earth pressure on retaining wall supporting c-Ф backfill. Appl Soft Comput. 2017;52:885–97. https://doi.org/10.1016/j.asoc.2016.09.037.
Wolpert DH, Macready WG. No free lunch theorems for optimization. IEEE Trans Evol Comput. 1997;1(1):67–82. https://doi.org/10.1109/4235.585893.
Kaur G, Arora S. Chaotic whale optimization algorithm. J Comput Des Eng. 2018;5(3):275–84. https://doi.org/10.1016/j.jcde.2017.12.006.
Sun Y, Wang X, Chen Y, Liu Z. A modified whale optimization algorithm for large-scale global optimization problems. Expert Syst Appl. 2018;114:563–77. https://doi.org/10.1016/j.eswa.2018.08.027.
Chen H, Xu Y, Wang M, Zhao X. A balanced whale optimization algorithm for constrained engineering design problems. Appl Math Model. 2019;71:45–59.
Laskar NM, Guha K, Chatterjee I, et al. HWPSO: A new hybrid whale-particle swarm optimization algorithm and its application in electronic design optimization problems. Appl Intell. 2019;49:265–91. https://doi.org/10.1007/s10489-018-1247-6.
Mostafa Bozorgi S, Yazdani S. IWOA: An improved whale optimization algorithm for optimization problems. J Comput Des Eng. 2019;6(3):243–59.
Abd Elaziz M, Mirjalili S. A hyper-heuristic for improving the initial population of whale optimization algorithm. Knowl Based Syst. 2019;172:42–63.
Yildiz AR. A novel hybrid whale–Nelder–Mead algorithm for optimization of design and manufacturing problems. Int J Adv Manuf Technol. 2019;105(12):5091–104. https://doi.org/10.1007/s00170-019-04532-1.
Chakraborty S, Saha AK, Sharma S, Mirjalili S, Chakraborty R. A novel enhanced whale optimization algorithm for global optimization. Comput Ind Eng. 2021;153:107086. https://doi.org/10.1016/j.cie.2020.107086.
Khadanga RK, Kumar A, Panda S. A novel modified whale optimization algorithm for load frequency controller design of a two-area power system composed of PV grid and thermal generator. Neural Comput Appl. 2020;32:8205–16. https://doi.org/10.1007/s00521-019-04321-7.
Chen H, Yang C, Heidari AA, Zhao X. An efficient double adaptive random spare reinforced whale optimization algorithm. Expert Syst Appl. 2020;154:113018. https://doi.org/10.1016/j.eswa.2019.113018.
Chakraborty S, Sharma S, Saha AK, Chakraborty S. SHADE-WOA: A metaheuristic algorithm for global optimization. Appl Soft Comput. 2021;113:107866. https://doi.org/10.1016/j.asoc.2021.107866.
Yan Z, Zhang J, Tang J. Modified whale optimization algorithm for underwater image matching in a UUV vision system. Multimed Tools Appl. 2021;80:187–213. https://doi.org/10.1007/s11042-020-09736-2.
Kushwah R, Kaushik M, Chugh K. A modified whale optimization algorithm to overcome delayed convergence in artificial neural networks. Soft Comput. 2021;25:10275–86. https://doi.org/10.1007/s00500-021-05983-z.
Fuqiang L, Tongren Y, Hualing B, Ming F, Suxin W, Min H. A bilevel whale optimization algorithm for risk management scheduling of information technology projects considering outsourcing. Knowl Based Syst. 2022;235:107600. https://doi.org/10.1016/j.knosys.2021.107600.
Anitha J, Pandian SIA, Agnes SA. An efficient multilevel color image thresholding based on modified whale optimization algorithm. Expert Syst Appl. 2021;178:115003. https://doi.org/10.1016/j.eswa.2021.115003.
Chakraborty S, Saha AK, Chakraborty R, Saha M, Nama S. HSWOA: An ensemble of hunger games search and whale optimization algorithm for global optimization. Int J Intell Syst. 2021. https://doi.org/10.1002/INT.22617.
Chakraborty S, Sharma S, Saha AK, Saha A. A novel improved whale optimization algorithm to solve numerical optimization and real-world applications. Artif Intell Rev. 2022;1–112.
Lin X, Yu X, Li W. A heuristic whale optimization algorithm with the niching strategy for global multi-dimensional engineering optimization. Comput Ind Eng. 2022;171:108361.
Cao D, Xu Y, Yang Z, Dong H, Li X. An enhanced whale optimization algorithm with improved dynamic opposite learning and adaptive inertia weight strategy. Complex Intell Syst. 2022;1–29.
Chakraborty S, Saha AK, Chakraborty R, Saha M. An enhanced whale optimization algorithm for large-scale optimization problems. Knowl Based Syst. 2021;233:107543. https://doi.org/10.1016/j.knosys.2021.107543.
Kaur S, Awasthi LK, Sangal AL, Dhiman G. Tunicate Swarm Algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng Appl Artif Intell. 2020;90:103541.
Alsattar HA, Zaidan AA, Zaidan BB. Novel meta-heuristic bald eagle search optimisation algorithm. Artif Intell Rev. 2020;53(3):2237–64.
Fan Q, Chen Z, Zhang W, Fang X. ESSAWOA: enhanced whale optimization algorithm integrated with salp swarm algorithm for global optimization. Eng Comput. 2020;1–18.
Chakraborty S, Saha AK, Nama S, Debnath S. COVID-19 X-ray image segmentation by modified whale optimization algorithm with population reduction. Comput Biol Med. 2021;139:104984. https://doi.org/10.1016/j.compbiomed.2021.104984.
Fan Y, Shao J, Sun G, Shao X. A self-adaption butterfly optimization algorithm for numerical optimization problems. IEEE Access. 2020;8:88026–41.
Gupta S, Deep K, Moayedi H, Foong LK, Assad A. Sine cosine grey wolf optimizer to solve engineering design problems. Eng Comput. 2021;37(4):3123–49.
Long W, Wu T, Liang X, Xu S. Solving high-dimensional global optimization problems using an improved sine cosine algorithm. Expert Syst Appl. 2019;123:108–26.
Sandgren E. Nonlinear Integer and Discrete Programming in Mechanical Design Optimization. J Mech Des. 1990;112(2):223. https://doi.org/10.1115/1.2912596.
Moghaddam SK, Buyya R, Ramamohanarao K. Performance-aware management of cloud resources: a taxonomy and future directions. ACM Comput Surv. 2019;52(4):1–37. https://doi.org/10.1145/3337956.
Amini Motlagh A, Movaghar A, Rahmani AM. Task scheduling mechanisms in cloud computing: a systematic review. Int J Commun Syst. 2020;33(6):e4302. https://doi.org/10.1002/dac.4302.
Chhabra A, Singh G, Singh Kahlon K. QoS-aware energy-efficient task scheduling on HPC cloud infrastructures using swarm-intelligence meta-heuristics. Comput Mater Cont. 2020;64(2):813–34. https://doi.org/10.32604/cmc.2020.010934.
Chhabra A, Singh G, Kahlon KS. Multi-criteria HPC task scheduling on IaaS cloud infrastructures using meta-heuristics. Clust Comput. 2021;24(2):885–918. https://doi.org/10.1007/s10586-020-03168-1.
Mohammad Hasani Zade B, Mansouri N, Javidi MM. SAEA: A security-aware and energy-aware task scheduling strategy by Parallel Squirrel Search Algorithm in cloud environment. Expert Syst Appl. 2021;176:114915. https://doi.org/10.1016/j.eswa.2021.114915.
Wei X. Task scheduling optimization strategy using improved ant colony optimization algorithm in cloud computing. J Ambient Intell Humaniz Comput. 2020. https://doi.org/10.1007/s12652-020-02614-7.
Fu X, Sun Y, Wang H, Li H. Task scheduling of cloud computing based on hybrid particle swarm algorithm and genetic algorithm. Clust Comput. 2021. https://doi.org/10.1007/s10586-020-03221-z.
Belgacem A, Beghdad-Bey K. Multi-objective workflow scheduling in cloud computing: trade-off between makespan and cost. Clust Comput. 2022;25(1):579–95. https://doi.org/10.1007/s10586-021-03432-y.
Mohammad Hasani Zade B, Mansouri N, Javidi MM. A two-stage scheduler based on New Caledonian Crow Learning Algorithm and reinforcement learning strategy for cloud environment. J Netw Comput Appl. 2022;202:103385. https://doi.org/10.1016/j.jnca.2022.103385.
Zhou Z, Li F, Zhu H, Xie H, Abawajy JH, Chowdhury MU. An improved genetic algorithm using greedy strategy toward task scheduling optimization in cloud environments. Neural Comput Appl. 2020;32(6):1531–41. https://doi.org/10.1007/s00521-019-04119-7.
Mohammad Hasani Zade B, Mansouri N, Javidi MM. Multi-objective scheduling technique based on hybrid hitchcock bird algorithm and fuzzy signature in cloud computing. Eng Appl Artif Intell. 2021;104:104372. https://doi.org/10.1016/j.engappai.2021.104372.
Abualigah L, Alkhrabsheh M. Amended hybrid multi-verse optimizer with genetic algorithm for solving task scheduling problem in cloud computing. J Supercomput. 2022;78(1):740–65. https://doi.org/10.1007/s11227-021-03915-0.
Abd Elaziz M, Attiya I. An improved Henry gas solubility optimization algorithm for task scheduling in cloud computing. Artif Intell Rev. 2021;54(5):3599–637. https://doi.org/10.1007/s10462-020-09933-3.
Shukri SE, Al-Sayyed R, Hudaib A, Mirjalili S. Enhanced multi-verse optimizer for task scheduling in cloud computing environments. Expert Syst Appl. 2021;168:114230. https://doi.org/10.1016/j.eswa.2020.114230.
Vila S, Guirado F, Lerida JL, Cores F. Energy-saving scheduling on IaaS HPC cloud environments based on a multi-objective genetic algorithm. J Supercomput. 2019;75(3):1483–95. https://doi.org/10.1007/s11227-018-2668-z.
Ni L, Sun X, Li X, Zhang J. GCWOAS2: Multiobjective task scheduling strategy based on gaussian cloud-whale optimization in cloud computing. Comput Intell Neurosci. 2021. https://doi.org/10.1155/2021/5546758.
Nadimi-Shahraki MH, Zamani H, Mirjalili S. Enhanced whale optimization algorithm for medical feature selection: a COVID-19 case study. Comput Biol Med. 2022;148:105858. https://doi.org/10.1016/j.compbiomed.2022.105858.
Zhou Z, Li F, Abawajy JH, Gao C. Improved PSO algorithm integrated with opposition-based learning and tentative perception in networked data centers. IEEE Access. 2020;8:55872–80. https://doi.org/10.1109/ACCESS.2020.2981972.
Assiri AS. On the performance improvement of butterfly optimization approaches for global optimization and Feature Selection. PLoS ONE. 2021;16(1):e0242612. https://doi.org/10.1371/journal.pone.0242612.
Hussien AG, Amin M, Abd El Aziz M. A comprehensive review of moth-flame optimisation: variants, hybrids, and applications. J Exp Theor Artif Intell. 2020;32(4):705–25. https://doi.org/10.1080/0952813X.2020.1737246.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Ethical Approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Conflict of Interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Chakraborty, S., Saha, A.K. & Chhabra, A. Improving Whale Optimization Algorithm with Elite Strategy and Its Application to Engineering-Design and Cloud Task Scheduling Problems. Cogn Comput 15, 1497–1525 (2023). https://doi.org/10.1007/s12559-022-10099-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12559-022-10099-z