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A water cycle algorithm based on quadratic interpolation for high-dimensional global optimization problems

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Abstract

The water cycle algorithm (WCA) is easily trapped in local optimal solutions when dealing with high-dimensional optimization problems and has low precision and slow convergence. A WCA based on quadratic interpolation (QIWCA) is proposed in this study to address these drawbacks. First, a new nonlinear adjustment strategy for distance control parameters is designed to balance the exploration and exploitation capabilities of the algorithm. Second, during the search process of the algorithm, mutation operations are probabilistically performed to enhance the global exploration capability of the algorithm. Lastly, the quadratic interpolation operator is introduced to improve the local exploitation capability of the algorithm. QIWCA is also compared with several of the most advanced meta-heuristic algorithms on 46 benchmark functions. Experimental results show that QIWCA outperforms the compared algorithms in terms of convergence speed, global exploration capability, solution accuracy, and reliability.

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References

  1. Zhao F, He X, Zhang Y, Lei W, Ma W, Zhang C, Song H (2020) A jigsaw puzzle inspired algorithm for solving large-scale no-wait flow shop scheduling problems. Appl Intell 50(1):87–100

    Article  Google Scholar 

  2. Dong Y, Zhang H, Wang C, Zhou X (2021) A novel hybrid model based on Bernstein polynomial with mixture of Gaussians for wind power forecasting. Appl Energy 286:116545

    Article  Google Scholar 

  3. Han X, Dong Y, Yue L, Xu Q, Xie G, Xu X (2021) State-transition simulated annealing algorithm for constrained and unconstrained multi-objective optimization problems. Appl Intell 51(2):775–787

    Article  Google Scholar 

  4. Zhu S, Wu Q, Jiang Y, Xing W (2021) A novel multi-objective group teaching optimization algorithm and its application to engineering design. Computers & Industrial Engineering: 107198

  5. Chen H, Wang M, Zhao X (2020) A multi-strategy enhanced sine cosine algorithm for global optimization and constrained practical engineering problems. Appl Math Comput 369:124872

    MathSciNet  MATH  Google Scholar 

  6. Radaideh MI, Shirvan K (2021) Rule-based reinforcement learning methodology to inform evolutionary algorithms for constrained optimization of engineering applications. Knowl-Based Syst 217:106836

    Article  Google Scholar 

  7. Kalananda VKRA, Komanapalli VLN (2021) A combinatorial social group whale optimization algorithm for numerical and engineering optimization problems. Appl Soft Comput 99:106903

    Article  Google Scholar 

  8. Chen Y, Pi D (2020) An innovative flower pollination algorithm for continuous optimization problem. Appl Math Model 83:237–265

    Article  MathSciNet  MATH  Google Scholar 

  9. Sun Y, Yang T, Liu Z (2019) A whale optimization algorithm based on quadratic interpolation for highdimensional global optimization problems. Appl Soft Comput 85:105744

    Article  Google Scholar 

  10. Maučec MS, Brest J (2019) A review of the recent use of differential evolution for large-scale global optimization: an analysis of selected algorithms on the CEC 2013 LSGO benchmark suite. Swarm and Evolutionary Computation 50:100428

    Article  Google Scholar 

  11. Liu K, Bellet A (2019) Escaping the curse of dimensionality in similarity learning: efficient Frank-Wolfe algorithm and generalization bounds. Neurocomputing 333:185–199

    Article  Google Scholar 

  12. Chow YT, Darbon J, Osher S, Yin W (2019) Algorithm for overcoming the curse of dimensionality for state-dependent Hamilton-Jacobi equations. J Comput Phys 387:376–409

    Article  MathSciNet  MATH  Google Scholar 

  13. Song Y, Wu D, Deng W, Gao XZ, Li T, Zhang B, Li Y (2021) MPPCEDE: multi-population parallel co-evolutionary differential evolution for parameter optimization. Energy Convers Manag 228:113661

    Article  Google Scholar 

  14. Dat NT, Van Kien C, Anh HPH, Son NN (2020) Parallel multi-population technique for meta-heuristic algorithms on multi core processor. In: 2020 5th international conference on green technology and sustainable development (GTSD). IEEE, pp 489–494

  15. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks, vol 4. IEEE, pp 1942–1948

  16. Price KV (2013) Differential evolution. In: Handbook of optimization. Springer, pp 187–214

  17. Federici L, Benedikter B, Zavoli A (2020) EOS: a parallel, self-adaptive, multi-population evolutionary algorithm for constrained global optimization. In: 2020 IEEE Congress on Evolutionary Computation (CEC). IEEE, pp 1–10

  18. Guo C, Yang Z, Wu X, Tan T, Zhao K (2019) Application of an adaptive multi-population parallel genetic algorithm with constraints in electromagnetic tomography with incomplete projections. Appl Sci 9(13):2611

    Article  Google Scholar 

  19. Long W, Wu T, Liang X, Xu S (2019) Solving high-dimensional global optimization problems using an improved sine cosine algorithm. Expert Syst Appl 123:108–126

    Article  Google Scholar 

  20. Mohapatra P, Das KN, Roy S (2017) A modified competitive swarm optimizer for large scale optimization problems. Appl Soft Comput 59:340–362

    Article  Google Scholar 

  21. Hussain K, Neggaz N, Zhu W, Houssein EH (2021) An efficient hybrid sine-cosine Harris hawks optimization for low and high-dimensional feature selection. Expert Syst Appl pp 114778

  22. Dong H, Dong Z (2020) Surrogate-assisted grey wolf optimization for high-dimensional, computationally expensive black-box problems. Swarm and Evolutionary Computation 57:100713

    Article  Google Scholar 

  23. Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water cycle algorithm–a novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures 110:151–166

    Article  Google Scholar 

  24. Chen C, Wang P, Dong H, Wang X (2020) Hierarchical learning water cycle algorithm. Appl Soft Comput 86:105935

    Article  Google Scholar 

  25. Bahreininejad A (2019) Improving the performance of water cycle algorithm using augmented Lagrangian method. Adv Eng Softw 132:55–64

    Article  Google Scholar 

  26. Korashy A, Kamel S, Youssef AR, Jurado F (2019) Modified water cycle algorithm for optimal direction over current relays coordination. Appl Soft Comput 74:10–25

    Article  Google Scholar 

  27. Ghosh PK, Sadhu PK, Basak R, Sanyal A (2020) Energy efficient design of three phase induction motor by water cycle algorithm. Ain Shams Engineering Journal 11(4):1139–1147

    Article  Google Scholar 

  28. Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation 1(1):3–18

    Article  Google Scholar 

  29. Sadollah A, Eskandar H, Bahreininejad A, Kim JH (2015) Water cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems. Appl Soft Comput 30:58–71

    Article  Google Scholar 

  30. Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872

    Article  Google Scholar 

  31. Li S, Chen H, Wang M, Heidari AA, Mirjalili S (2020) Slime mould algorithm: a new method for stochastic optimization. Futur Gener Comput Syst 111:300–323

    Article  Google Scholar 

  32. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  33. Tran TD (2010) Real-coded genetic algorithm benchmarked on noiseless black-box optimization testbed. In: Proceedings of the 12th annual conference companion on Genetic and evolutionary computation, pp 1731–1738

  34. Awad NH, Ali MZ, Suganthan PN, Reynolds RG (2016) An ensemble sinusoidal parameter adaptation incorporated with L-SHADE for solving CEC2014 benchmark problems. In: 2016 IEEE congress on evolutionary computation (CEC). IEEE, pp 2958–2965

  35. Chen L, Zheng Z, Liu HL, Xie S (2014) An evolutionary algorithm based on covariance matrix leaning and searching preference for solving CEC 2014 benchmark problems. IEEE, pp 2672–2677

  36. Wang L, Li L. p. (2010) An effective differential evolution with level comparison for constrained engineering design. Struct Multidiscip Optim 41(6):947–963

    Article  Google Scholar 

  37. dos Santos Coelho L (2010) Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst Appl 37(2):1676–1683

    Article  Google Scholar 

  38. Deb K (1991) Optimal design of a welded beam via genetic algorithms. AIAA journal 29 (11):2013–2015

    Article  Google Scholar 

  39. Coello CAC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203

    Article  Google Scholar 

  40. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  41. Mezura-Montes E, Coello Coello C, Velázquez-Reyes J., Muñoz-dávila L (2007) Multiple trial vectors in differential evolution for engineering design. Eng Optim 39(5):567–589

    Article  MathSciNet  Google Scholar 

  42. Ma L, Wang C, xie NG, Shi M, Ye Y, Wang L (2021) Moth-flame optimization algorithm based on diversity and mutation strategy. Appl Intell: 1–37

  43. Salimi H (2015) Stochastic fractal search: a powerful metaheuristic algorithm. Knowl-Based Syst 75:1–18

    Article  Google Scholar 

  44. Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization

  45. Chegini SN, Bagheri A, Najafi F (2018) PSOSCALF: a new hybrid PSO based on sine cosine algorithm and levy flight for solving optimization problems. Appl Soft Comput 73:697–726

    Article  Google Scholar 

  46. Hashim FA, Hussain K, Houssein EH, Mabrouk MS, Al-Atabany W (2021) Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl Intell 51(3):1531–1551

    Article  MATH  Google Scholar 

  47. Krohling RA, dos Santos Coelho L (2006) Coevolutionary particle swarm optimization using Gaussian distribution for solving constrained optimization problems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 36(6):1407–1416

    Article  Google Scholar 

  48. Zahara E, Kao YT (2009) Hybrid Nelder–Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36(2):3880–3886

    Article  Google Scholar 

  49. Yuan Q, Qian F (2010) A hybrid genetic algorithm for twice continuously differentiable NLP problems. Computers & Chemical Engineering 34(1):36–41

    Article  Google Scholar 

  50. Ragsdell K, Phillips D (1976) Optimal design of a class of welded structures using geometric programming

  51. Mezura-Montes E, Coello CAC (2005) A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Trans Evol Comput 9(1):1–17

    Article  MATH  Google Scholar 

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Acknowledgements

This work has been supported by a grant from the National Natural Science Foundation of China (62163034) and Xinjiang Urumqi Autonomous Region Natural Science Key Project of University Research Program (XJEDU2020I004).

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Authors and Affiliations

  1. Xinjiang University, School of Electrical Engineering, Urumqi, Xinjiang, 830047, China

    Jiahao Ye, Lirong Xie & Hongwei Wang

  2. Dalian University of Technology, School of Control Science and Engineering, Dalian, Liaoning, 116024, China

    Hongwei Wang

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  1. Jiahao Ye
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  2. Lirong Xie
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Correspondence to Lirong Xie.

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Ye, J., Xie, L. & Wang, H. A water cycle algorithm based on quadratic interpolation for high-dimensional global optimization problems. Appl Intell 53, 2825–2849 (2023). https://doi.org/10.1007/s10489-022-03428-0

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