An Enhanced Beluga Whale Optimization Algorithm for Engineering Optimization Problems

Abstract

This paper presents an enhanced beluga whale optimization algorithm (EBWOA) for engineering optimization problems. To enhance the performance and address the challenges of poor convergence and suboptimal solution stagnation commonly faced by the original beluga whale optimization algorithm (BWOA), EBWOA employs a two-step approach. In the initial stage, a dynamic update factor is introduced to accelerate convergence during the exploitation phase of BWOA. Subsequently, the second stage incorporates the Cauchy mutation operator to inject diversity into the population, preventing it from becoming entrapped in local optima. The proposed enhancement is validated on 15 classical benchmark functions and CEC-19 functions in terms of solution quality and convergence speed. To assess the efficiency of EBWOA, the algorithm is applied to a real-world industrial problem, specifically, the spiral steel pipe manufacturing system (SSPM), serving as a case study and four classical engineering design optimization problems. The simulation results demonstrated the superiority of EBWOA in optimizing the fuzzy availability of the SSPM industrial system and successfully solving all four constrained engineering design problems when compared to other recent metaheuristics.

Keywords

Metaheuristic algorithm / beluga whale optimization algorithm / Cauchy mutation / industrial system / fuzzy availability / engineering optimization

References

[1] Ali A F, Tawhid M A. A hybrid PSO and DE algorithm for solving engineering optimization problems. Applied Mathematics and Information Sciences, 2016, 10(2): 431-449.

[2] Arora S, Singh S. Butterfly optimization algorithm: A novel approach for global opimization. Soft Computing, 2019, 23: 715-734.

[3] Cui Y, Hu W, Rahmani A. Improved artificial bee colony algorithm with dynamic population composition for optimization problems. Nonlinear Dynamics, 2022, 107(1): 743-760.

[4] El-Shorbagy M A, El-Refaey A M. A hybrid genetic-firefly algorithm for engineering design problems. Journal of Computational Design and Engineering, 2022, 9(2): 706-730.

[5] Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S. Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems, 2020, 191: 105190.

[6] Garg H. Solving structural engineering design optimization problems using an artificial bee colony algorithm. Journal of Industrial and Management Optimization, 2014, 10(3): 777-794.

[7] Garg H. A hybrid PSO-GA algorithm for constrained optimization problems. Applied Mathematics and Computation, 2016, 274: 292-305.

[8] Garg H. A hybrid GSA-GA algorithm for constrained optimization problems. Information Sciences, 2019, 478: 499-523.

[9] Goldberg D E. Genetic Algorithms, 2013, India: Pearson Education

[10] Gupta S, Abderazek H, Yildiz B S, Yildiz A R, Mirjalili S, Sait S M. Comparison of metaheuristic optimization algorithms for solving constrained mechanical design optimization problems. Expert Systems with Applications, 2021, 183: 115351.

[11] Hamza F, Abderazek H, Lakhdar S, Ferhat D, Yildiz A R. Optimum design of cam-roller follower mechanism using a new evolutionary algorithm. The International Journal of Advanced Manufacturing Technology, 2018, 99: 1267-1282.

[12] Hassan M H, Kamel S, Jurado F, Ebeed M, Elnaggar M F. Economic load dispatch solution of large-scale power systems using an enhanced beluga whale optimizer. Alexandria Engineering Journal, 2023, 72: 573-591.

[13] He Q, Wang L. An effective co-evolutionary particle swarm optimization for cnstrained engineering design problems. Engineering Applications of Artificial Intelligence, 2007, 20(1): 89-99.

[14] Ho-Huu V, Nguyen-Thoi T, Truong-Khac T, Le-Anh L, Vo-Duy T. An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints. Neural Computing and Applications, 2018, 29: 167-185.

[15] Horng S C, Lin S S. Improved beluga whale optimization for solving the simulation optimization problems with stochastic constraints. Mathematics, 2023, 11(8): 1854.

[16] Houssein E H, Sayed A. Dynamic candidate solution boosted beluga whale optimization algorithm for biomedical classification. Mathematics, 2023, 11(3): 707.

[17] Hussien A G, Khurma R A, Alzaqebah A, Amin M, Hashim F A. Novel memetic of beluga whale optimization with self-adaptive exploration - Exploitation balance for global optimization and engineering problems. Soft Computing, 2023, 27(19): 13951-13989.

[18] Jia H, Sun K, Zhang W, Leng X. An enhanced chimp optimization algorithm for continuous optimization domains. Complex & Intelligent Systems, 2021, 8: 65-82.

[19] Jiang Z Y, Cai Z X, Wang Y. Hybrid self-adaptive orthogonal genetic algorithm for solving global optimization problems. Journal of Software, 2010, 21(6): 1296-1307.

[20] Kaveh A, Talatahari S. Engineering optimization with hybrid particle swarm and ant colony optimization. Asian Journal of Civil Engineering (Building and Housing), 2009, 10(6): 611-628.

[21] Kaveh A, Talatahari S. An improved ant colony optimization for constrained engineering design problems. Engineering Computations, 2010, 27(1): 155-182.

[22] Kumar A, Pant S, Ram M. System reliability optimization using gray wolf optimizer algorithm. Quality and Reliability Engineering International, 2017, 33(7): 1327-1335.

[23] Kumar N, Mahato S K, Bhunia A K. Design of an efficient hybridized CS-PSO algorithm and its applications for solving constrained and bound constrained structural engineering design problems. Results in Control and Optimization, 2021, 5: 100064.

[24] Kumar A, Sinwar D, Dhaka V S, Maakar S K. Operational availability optimization of cooling tower of thermal power plants using swarm intelligence-based metaheuristic algorithms. ICT Analysis and Applications: Proceedings of ICT4SD:651–660, 2022, Singapore: Springer Nature Singapore

[25] Lamberti L. An efficient simulated annealing algorithm for design optimization of truss structures. Computers and Structures, 2008, 86(19–20): 1936-1953.

[26] Li Z, Lin X, Zhang Q, Liu H. Evolution strategies for continuous optimization: A survey of the state-of-the-art. Swarm and Evolutionary Computation, 2020, 56: 100694.

[27] Li K, Li S, Huang Z, Zhang M, Xu Z. Grey Wolf Optimization algorithm based on Cauchy-Gaussian mutation and improved search strategy. Scientific Reports, 2022, 12(1): 18961.

[28] Li Y, Chen Z, Hou M, Guo T. Multi-objective optimization design of anti-roll torsion bar using improved beluga whale optimization algorithm. Railway Sciences, 2024, 3(1): 32-46.

[29] Mirjalili S. Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems, 2015, 89: 228-249.

[30] Mirjalili S, Lewis A. The whale optimization algorithm. Advances in Engineering Software, 2016, 95: 51-67.

[31] Mirjalili S, Mirjalili S M, Hatamlou A. Multi-verse optimizer: A nature-inspired algorithm for global optimization. Neural Computing and Applications, 2016, 27: 495-513.

[32] Mohammed H, Rashid T. A novel hybrid GWO with WOA for global numerical optimization and solving pressure vessel design. Neural Computing and Applications, 2020, 32(18): 14701-14718.

[33] Nautiyal B, Prakash R, Vimal V, Liang G, Chen H. Improved salp swarm algorithm with mutation schemes for solving global optimization and engineering problems. Engineering with Computers, 2021, 38(4): 1-23.

[34] Negi G, Kumar A, Pant S, Ram M. Optimization of complex system reliability using hybrid grey wolf optimizer. Decision Making: Applications in Management and Engineering, 2021, 4(2): 241-256.

[35] Pena-Delgado A F, Peraza-Vázquez H, Almazán-Covarrubias J H, Torres Cruz N, Garcia-Vite P M, Morales-Cepeda A B, Ramirez-Arredondo J M. A novel bio-inspired algorithm applied to selective harmonic elimination in a three-phase eleven-level inverter. Mathematical Problems in Engineering, 2020, 2020: 1-10.

[36] Pham Q V, Mirjalili S, Kumar N, Alazab M, Hwang W J. Whale optimization algorithm with applications to resource allocation in wireless networks. IEEE Transactions on Vehicular Technology, 2020, 69(4): 4285-4297.

[37] Qin P, Hu H, Yang Z. The improved grasshopper optimization algorithm and its applications. Scientific Reports, 2021, 11(1): 23733.

[38] Rajabioun R. Cuckoo optimization algorithm. Applied Soft Computing, 2011, 11(8): 5508-5518.

[39] Rutenbar R A. Simulated annealing algorithms: An overview. IEEE Circuits and Devices Magazine, 1989, 5(1): 19-26.

[40] Saini M, Maan V S, Kumar A, Saini D K (2023). Cloud infrastructure availability optimization using Dragonfly and Grey Wolf optimization algorithms for health systems. Journal of Intelligent and Fuzzy Systems (Preprint):1–19.

[41] Sapre S, Mini S. Opposition-based moth flame optimization with Cauchy mutation and evolutionary boundary constraint handling for global optimization. Soft Computing, 2019, 23(15): 6023-6041.

[42] Sun P, Liu H, Zhang Y, Tu L, Meng Q. An intensify atom search optimization for engineering design problems. Applied Mathematical Modelling, 2021, 89: 837-859.

[43] Yang X S, Hossein Gandomi A. Bat algorithm: A novel approach for global engineering optimization. Engineering Computations, 2012, 29(5): 464-483.

[44] Yao L, Yuan P, Tsai C Y, Zhang T, Lu Y, Ding S. ESO: An enhanced snake optimizer for real-world engineering problems. Expert Systems with Applications, 2023, 230: 120594.

[45] Yildiz B S, Yildiz A R. The Harris hawks optimization algorithm, salp swarm algorithm, grasshopper optimization algorithm and dragonfly algorithm for structural design optimization of vehicle components. Materials Testing, 2019, 61(8): 744-748.

[46] Yokota T, Taguchi T, Gen M. A solution method for optimal weight design problem of the gear using genetic algorithms. Computers and Industrial Engineering, 1998, 35(3–4): 523-526.

[47] Yuan H, Chen Q, Li H, Zeng D, Wu T, Wang Y, Zhang W. Improved beluga whale optimization algorithm based cluster routing in wireless sensor networks. Mathematical Biosciences and Engineering, 2024, 21(3): 4587-4625.

[48] Zhang J, Xiao M, Gao L, Pan Q. Queuing search algorithm: A novel metaheuristic algorithm for solving engineering optimization problems. Applied Mathematical Modelling, 2018, 63: 464-490.

[49] Zheng Y J, Ling H F, Xue J Y. Ecogeography-based optimization: Enhancing biogeography-based optimization with ecogeographic barriers and differentiations. Computers and Operations Research, 2014, 50: 115-127.

[50] Zhong C, Li G, Meng Z. Beluga whale optimization: A novel nature-inspired metaheuristic algorithm. Knowledge-Based Systems, 2022, 251: 109215.

[51] Zhou Y, Ling Y, Luo Q. Lévy flight trajectory-based whale optimization algorithm for engineering optimization. Engineering Computations, 2018, 35(7): 2406-2428.