Human-Whale cooperation optimization (HWO) algorithm: A metaheuristic algorithm for solve optimization problems

Document Type : Research Paper


1 Department of Computer Engineering, Kerman Branch, Islamic Azad University, Kerman, Iran

2 Department of Computer Engineering, Bardsir Branch, Islamic Azad University, Bardsir, Iran


Metaheuristic algorithms are one of the most effective methods for solving optimization problems and are modeled on the behavior of living things or biological phenomena. The swarm behavior of animals in nature to survive is a good way to create metaheuristic algorithms with a group intelligence approach. The swarm hunting mechanism is one of the most interesting meta-behavioral behaviors observed in a large number of organisms, and the chances of success in prey hunting by swarm behaviors will increase. In this paper, a new metaheuristic algorithm with a swarm intelligence approach is presented by using the human hunting mechanism and whale. In this type of behavior, whales and humans participate in hunting in such a way that whales and humans benefit from each other. Implementation and analysis of the proposed method provided less error than 82.60% of the experiments of other algorithms such as particle swarm optimization(PSO), firefly algorithm(FA), grasshopper optimization algorithm(GOA), and butterfly optimization algorithm(BOA). Experiments show that the proposed method converges in complex functions with a probability of 4.36% in local optimizations, which is less than the comparable algorithms. Experiments show that the proposed method can be implemented on a wide range of functional optimization problems and reduces the optimization error due to the simultaneous local and global search of the intelligent algorithm.


[1] H. Abedinpourshotorban, S.M. Shamsuddin, Z. Beheshti and D.N. Jawawi, Electromagnetic field optimization: A physics-inspired metaheuristic optimization algorithm, Swarm Evolut. Comput. 26 (2016), 8–22.
[2] A.A. Asif, Evolution of ant colony optimization algorithm: A brief literature review, arXiv preprint arXiv:1908.08007, 2019.
[3] M.R. Bonyadi, A theoretical guideline for designing an effective adaptive particle swarm, IEEE Trans. Evolut. Comput. 24 (2019), no. 1, 57–68.
[4] M. Bordbar, A. Neshat, S. Javadi, B. Pradhan and H. Aghamohammadi, Meta-heuristic algorithms in optimizing GALDIT framework: a comparative study for coastal aquifer vulnerability assessment, J. Hydrology 585 (2020), 124768.
[5] M.C. Catalbas and A. Gulten, Circular structures of puffer fish: A new metaheuristic optimization algorithm, Third Int. Conf. Electric. Biomed. Engin. Clean Energy Green Comput. (EBECEGC), 2018, pp. 1–5.
[6] C. Chen, RWFOA: a random walk-based fruit fly optimization algorithm, Soft Comput. 24 (2020), no. 16, 12681– 12690.
[7] S. Chowdhury, M. Marufuzzaman, H. Tunc, L. Bian and W. Bullington, A modified ant colony optimization algorithm to solve a dynamic traveling salesman problem: a case study with drones for wildlife surveillance, J. Comput. Design Engin. 6 (2019), no. 3, 368–386.
[8] E. Cuevas, F. Fausto and A. Gonzjlez, The swarm method of the social-spider, New Advancements in Swarm Algorithms: Operators and Applications. Springer, Cham, 2020. 111-137.
[9] G. Dhiman and V. Kumar, Emperor penguin optimizer: A bio-inspired algorithm for engineering problems, Knowledge-Based Syst. 159 (2018), 20–50.
[10] G. Dhiman and V. Kumar, Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications, Adv. Engin. Software 114 (2017), 48–70.
[11] G. Dhiman and V. Kumar, Spotted hyena optimizer for solving complex and non-linear constrained engineering problems, Harmony search and nature inspired optimization algorithms. Springer, Singapore, 2019. 857-867.
[12] E. Fadakar and M. Ebrahimi, A new metaheuristic football game inspired algorithm, 1st Conf. Swarm Intell. Evolut. Comput. (CSIEC), 2016, pp. 6–11.
[13] A. Faramarzi, M. Heidarinejad, S. Mirjalili and A.H. Gandomi, Marine predators algorithm: A nature-inspired metaheuristic, Expert Syst. Appl. 152 (2020), 113377.
[14] V. Hayyolalam and A.A.P. Kazem, Black Widow Optimization Algorithm: A novel meta-heuristic approach for solving engineering optimization problems, Engin. Appl. Artific. Intell. 87 (2020), 103–249.
[15] A.A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja and H. Chen, Harris hawks optimization: Algorithm and applications, Future Gen. Comput. Syst. 97 (2019), 849–872.
[16] A.A. Heidari, H. Faris, S. Mirjalili, I. Aljarah and M. Mafarja, Ant lion optimizer: theory, literature review, and application in multi-layer perceptron neural networks, Nature-Inspired Optim. (2020), 23–46.
[17] M.M. Islam, H. Shareef, A. Mohamed and A. Wahyudie, A binary variant of lightning search algorithm: BLSA, Soft Comput. 21 (2017), no. 11, 2971–2990.
[18] C.B. Kalayci, O. Polat and M.A. Akbay, An efficient hybrid metaheuristic algorithm for cardinality constrained portfolio optimization, Swarm Evolution. Comput. 54 (2020), 100–662.
[19] A. Kaveh and T. Bakhshpoori, Water evaporation optimization: a novel physically inspired optimization algorithm, Comput. Structures 167 (2016), 69–85.
[20] T. Khurshaid, A. Wadood, S.G. Farkoush, C.H. Kim, J. Yu and S.B. Rhee, Improved firefly algorithm for the optimal coordination of directional overcurrent relays, IEEE Access 7 (2019), 78503–78514.
[21] Z. Lei, S. Gao, S. Gupta, J. Cheng and G. Yang, An aggregative learning gravitational search algorithm with self-adaptive gravitational constants, Expert Syst. Appl. 152 (2020), 113396.
[22] Q. Liu, J. Li, L. Wu, F. Wang and W. Xiao, A novel bat algorithm with double mutation operators and its application to low-velocity impact localization problem, Engin. Appl. Artific. Intell. 90 (2020), 103–505.
[23] S. Mirjalili, Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems, Neural Comput. Appl. 27 (2016), no. 4, 1053-1073.
[24] S. Mirjalili, I. Aljarah, M. Mafarja, A.A. Heidari and H. Faris, Grey Wolf optimizer: theory, literature review, and application in computational fluid dynamics problems, Nature-Inspired Optim. (2020), 87–105.
[25] S. Mirjalili and A. Lewis, The whale optimization algorithm, Adv. Engin. Software 95 (2016), 51–67.
[26] S. Mirjalili, S. M. Mirjalili, S. Saremi and S. Mirjalili, Whale optimization algorithm: theory, literature review, and application in designing photonic crystal filters, Nature-Inspired Optim. (2020), 219-238.
[27] S.H.S. Moosavi and V.K. Bardsiri, Poor and rich optimization algorithm: A new human-based and multi populations algorithm, Engin. Appl. Artific. Intell. 86 (2019), 165–181.
[28] A. Mukherjee and D. De, Octopus algorithm for wireless personal communications, Wireless Person. Commun. 101 (2018), no. 1, 531-565.
[29] M.G. Omran and S. Al-Sharhan, Improved continuous Ant Colony Optimization algorithms for real-world engineering optimization problems, Engin. Appl. Artific. Intell. 85 (2019), 818–829.
[30] M. Orujpour, M. R. Feizi-Derakhshi and T. Rahkar-Farshi, Multi-modal forest optimization algorithm, Neural Comput. Appl. 32 (2020), no. 10, 6159–6173.
[31] C.M. Rahman and T. A. Rashid, A survey on dragonfly algorithm and its applications in engineering, arXiv preprint arXiv: (2020), 12-126.
[32] M.A. Shaheen, H.M. Hasanien, S.F. Mekhamer and H.E. Talaat, Optimal power flow of power systems including distributed generation units using sunflower optimization algorithm, IEEE Access 7 (2019), 109289–109300.
[33] A.K. Shukla, P. Singh and M. Vardhan, An adaptive inertia weight teaching-learning-based optimization algorithm and its applications, Appl. Math. Modell. 77 (2020), 309–326.
[34] H. Whitehead and R. Reeves, Killer whales and whaling: the scavenging hypothesis, Bio. Lett. 1 (2005), no. 4, 415–418.
[35] C. Yang, J. Ji and S. Li, Stability analysis of chemotaxis dynamics in bacterial foraging optimization over multidimensional objective function, Soft Comput. 24 (2020), no. 5, 3711–3725.
Volume 14, Issue 1
January 2023
Pages 2279-2300
  • Receive Date: 17 November 2021
  • Revise Date: 18 January 2022
  • Accept Date: 20 February 2022