Abstract
Trapping in local solutions is the main issue in several metaheuristic techniques. To solve such drawbacks by enhancing the search agents, a modified search strategy becomes a more attractive tactic. In this paper, an innovative version of Manta Ray Foraging Optimization (MRFO) is proposed to solve its crucial drawbacks while handling global and engineering optimization problems. The proposed version presents an integrated variant of MRFO with the triangular mutation operator and orthogonal learning strategy, called MRTMO. The two approaches are considered to achieve a robust equipoise between algorithm cores and provide a reliable mechanism to guide the search agents during the optimization process. The proposed MRTMO was tested with challenging CEC2005 and CEC2017 functions and six engineering problems to show its performance. Additionally, several evaluation metrics were employed to ensure the efficiency and robustness of the proposed MRTMO. Furthermore, extensive comparisons with existing optimization algorithms were carried out to ensure the superiority of MRTMO. The numerical experiments proved the competitive performance of the proposed MRTMO in solving all tested CEC optimization and engineering problems.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig12_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-03899-1/MediaObjects/10489_2022_3899_Fig13_HTML.png)
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Mousavirad SJ, Schaefer G, Ebrahimpour-Komleh H (2021) The human mental search algorithm for solving optimisation problems. In: Enabling AI applications in data science. Springer, pp 27–47
Goldfeld SM, Quandt RE, Trotter HF (1966) Maximization by quadratic hill-climbing. Econometrica: J Econometric Society:541–551
Abbasbandy S (2003) Improving newton–raphson method for nonlinear equations by modified adomian decomposition method. Appl Math Comput 145(2-3):887–893
Abualigah L, Diabat A, Geem ZW (2020) A comprehensive survey of the harmony search algorithm in clustering applications. Appl Sci 10(11):3827
White DR, Fowler B, Banzhaf W, Barr ET (2020) Modelling genetic programming as a simple sampling algorithm. In: Genetic programming theory and practice XVII. Springer, pp 367–381
Abualigah L, Abd Elaziz M, Sumari P, Geem ZW, Gandomi AH (2022) Reptile search algorithm (rsa): a nature-inspired meta-heuristic optimizer. Expert Syst Appl 191:116158
Adam SP, Alexandropoulos S-AN, Pardalos PM, Vrahatis MN (2019) No free lunch theorem: a review. Approx Optim:57–82
Pelusi D, Mascella R, Tallini L, Nayak J, Naik B, Deng Y (2020) An improved moth-flame optimization algorithm with hybrid search phase. Knowl-Based Syst 191:105277
Ewees AA, Abd Elaziz M (2020) Performance analysis of chaotic multi-verse harris hawks optimization: a case study on solving engineering problems. Eng Appl Artif Intell 88:103370
Abd Elaziz M, Mirjalili S (2019) A hyper-heuristic for improving the initial population of whale optimization algorithm. Knowl-Based Syst 172:42–63
Zhao W, Zhang Z, Wang L (2020) Manta ray foraging optimization: an effective bio-inspired optimizer for engineering applications. Eng Appl Artif Intell 87:103300
Hemeida MG, Ibrahim AA, Mohamed A-AA, Alkhalaf S, El-Dine AMB (2021) Optimal allocation of distributed generators dg based manta ray foraging optimization algorithm (mrfo). Ain Shams Eng‘J
Hemeida MG, alkhalaf S, mohamed A-AA, Ibrahim AA, Senjyu T (2020) Distributed generators optimization based on multi-objective functions using manta rays foraging optimization algorithm (mrfo). Energies 13(15):3847
Ghosh KK, Ahmed S, Singh PK, Geem ZW, Sarkar R (2020) Improved binary sailfish optimizer based on adaptive β-hill climbing for feature selection. IEEE Access 8:83548–83560
Micev M, Ćalasan M, Ali ZM, Hasanien HM, Aleem SHA (2021) Optimal design of automatic voltage regulation controller using hybrid simulated annealing–manta ray foraging optimization algorithm. Ain Shams Eng J
Abd Elaziz M, Yousri D, Al-qaness MA, AbdelAty AM, Radwan AG, Ewees AA (2021) A grunwald–letnikov based manta ray foraging optimizer for global optimization and image segmentation. Eng Appl Artif Intell 98:104105
Qin Q, Cheng S, Zhang Q, Wei Y, Shi Y (2015) Multiple strategies based orthogonal design particle swarm optimizer for numerical optimization. Comput Oper Res 60:91–110
Ma L, Cheng S, Shi Y (2020) Enhancing learning efficiency of brain storm optimization via orthogonal learning design. IEEE Trans Syst Man Cybern Syst 51(11):6723–6742
Zhang H, Li R, Cai Z, Gu Z, Heidari AA, Wang M, Chen H, Chen M (2020) Advanced orthogonal moth flame optimization with broyden–fletcher–goldfarb–shanno algorithm: framework and real-world problems. Expert Syst Appl 159:113617
Mirjalili S (2016) Sca: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133
Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191
Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Hashim FA, Houssein EH, Mabrouk MS, Al-Atabany W, Mirjalili S (2019) Henry gas solubility optimization: a novel physics-based algorithm. Futur Gener Comput Syst 101:646–667
Salgotra R, Singh U, Saha S, Nagar A (2019) New improved salshade-cnepsin algorithm with adaptive parameters. In: 2019 IEEE congress on evolutionary computation (CEC). IEEE, pp 3150–3156
Mohamed AW, Hadi AA, Fattouh AM, Jambi KM (2017) Lshade with semi-parameter adaptation hybrid with cma-es for solving cec 2017 benchmark problems
Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609
Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Applic 27(2):495–513
Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294
Deb K (1991) Optimal design of a welded beam via genetic algorithms. AIAA J 29(11):2013–2015
Ragsdell K, Phillips D (1976) Optimal design of a class of welded structures using geometric programming. J Manuf Sci Eng 38(3):1021–1025
Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36):3902–3933
Krohling RA, Dos Santos Coelho L (2006) Coevolutionary particle swarm optimization using gaussian distribution for solving constrained optimization problems. IEEE Trans Syst Man Cybern B Cybern 36(6):1407–1416
Ewees AA, Abd Elaziz M, Houssein EH (2018) Improved grasshopper optimization algorithm using opposition-based learning. Expert Syst Appl 112:156–172
Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) Gsa: a gravitational search algorithm. Inf Sci 179(13):2232–2248
Huang F-Z, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356
Mezura-Montes E, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473
Ray T, Saini P (2001) Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng Optim 33(6):735–748
Belegundu AD, Arora JS (1985) A study of mathematical programmingmethods for structural optimization. Part ii: Numer Results Int J Numer Methods Eng 21(9):1601–1623
He Q, Wang L (2007) A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Appl Math Comput 186(2):1407–1422
Liu H, Cai Z, Wang Y (2010) Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Appl Soft Comput 10(2):629–640
Kaveh A, Talatahari S (2010) An improved ant colony optimization for constrained engineering design problems. Eng Comput
Savsani P, Savsani V (2016) Passing vehicle search (pvs): a novel metaheuristic algorithm. Appl Math Model 40(5-6):3951–3978
Ewees AA, Abd Elaziz M (2020) Performance analysis of chaotic multi-verse harris hawks optimization: a case study on solving engineering problems. Eng Appl Artif Intell 88:103370
Rao RV, Savsani VJ, Vakharia D (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43(3):303–315
Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35
Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13(5):2592–2612
Zhang M, Luo W, Wang X (2008) Differential evolution with dynamic stochastic selection for constrained optimization. Inf Sci 178(15):3043–3074
Tsai J-F (2005) Global optimization of nonlinear fractional programming problems in engineering design. Eng Optim 37(4):399–409
Baykasoğlu A, Ozsoydan FB (2015) Adaptive firefly algorithm with chaos for mechanical design optimization problems. Appl soft Comput 36:152–164
Baykasoğlu A, Akpinar Ş (2015) Weighted superposition attraction (wsa): a swarm intelligence algorithm for optimization problems–part 2: constrained optimization. Appl Soft Comput 37:396–415
Guedria NB (2016) Improved accelerated pso algorithm for mechanical engineering optimization problems. Appl Soft Comput 40:455–467
Brancato V, Calabrese L, Palomba V, Frazzica A, Fullana-Puig M, Solé A, Cabeza LF (2018) Mgso4· 7h2o filled macro cellular foams: an innovative composite sorbent for thermo-chemical energy storage applications for solar buildings. Sol Energy 173:1278–1286
Czerniak JM, Zarzycki H, Ewald D (2017) Aao as a new strategy in modeling and simulation of constructional problems optimization. Simul Model Pract Theory 76:22–33
Shehab M, Alshawabkah H, Abualigah L, Nagham A. -M. (2020) Enhanced a hybrid moth-flame optimization algorithm using new selection schemes. Eng Comput:1–26
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Software 69:46–61
Acknowledgments
This work was supported by National Natural Science Foundation of China (Grant No. 62150410434).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interests
The authors declare that they have no conflict of interest.
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
About this article
Cite this article
Elaziz, M.A., Abualigah, L., Ewees, A.A. et al. Triangular mutation-based manta-ray foraging optimization and orthogonal learning for global optimization and engineering problems. Appl Intell 53, 7788–7817 (2023). https://doi.org/10.1007/s10489-022-03899-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-022-03899-1