Abstract
As an optimization paradigm, Salp Swarm Algorithm (SSA) outperforms various population-based optimizers in the perspective of the accuracy of obtained solutions and convergence rate. However, SSA gets stuck into sub-optimal solutions and degrades accuracy while solving the complex optimization problems. To relieve these shortcomings, a modified version of the SSA is proposed in the present work, which tries to establish a more stable equilibrium between the exploration and exploitation cores. This method utilizes two different strategies called opposition-based learning and levy-flight (LVF) search. The algorithm is named m-SSA, and its validation is performed on a well-known set of 23 classical benchmark problems. To observe the strength of the proposed method on the scalability of the test problems, the dimension of these problems is varied from 50 to 1000. Furthermore, the proposed m-SSA is also used to solve some real engineering optimization problems. The analysis of results through various statistical measures, convergence rate, and statistical analysis ensures the effectiveness of the proposed strategies integrated with the m-SSA. The comparison of the m-SSA with the conventional SSA, variants of SSA and some other state-of-the-art algorithms illustrate its enhanced search efficiency.



Similar content being viewed by others
References
Mohapatra P, Das KN, Roy S (2017) A modified competitive swarm optimizer for large scale optimization problems. Appl Soft Comput 59:340–362
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In MHS’95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE, pp 39–43
Dorigo M, Birattari M (2010) Ant colony optimization. Springer, Berlin, pp 36–39
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471
Bansal JC, Sharma H, Jadon SS, Clerc M (2014) Spider monkey optimization algorithm for numerical optimization. Memet Comput 6(1):31–47
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
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
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
Abbassi R, Abbassi A, Heidari AA, Mirjalili S (2019) An efficient salp swarm-inspired algorithm for parameters identification of photovoltaic cell models. Energy Convers Manag 179:362–372
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: Algorithm and applications. Future Gener Comput Syst 97:849–872
Zhang Q, Chen H, Heidari AA, Zhao X, Xu Y, Wang P, Li Y, Li C (2019) Chaos-induced and mutation-driven schemes boosting salp chains-inspired optimizers. IEEE Access 7:31243–31261
Faris H, Heidari AA, Al-Zoubi AM, Mafarja M, Aljarah I, Eshtay M, Mirjalili S (2020) Time-varying hierarchical chains of salps with random weight networks for feature selection. Expert Syst Appl 140:112898
Faris H, Mirjalili S, Aljarah I, Mafarja M, Heidari AA (2020) Salp Swarm algorithm: theory, literature review, and application in extreme learning machines, Nature-Inspired Optimizers. Springer, pp 185–199
Aksoy HS, Gor M, Inal E (2016) A new design chart for estimating friction angle between soil and pile materials. Geomech Eng 10(3):315–324
Bui DT, Moayedi H, Gör M, Jaafari A, Foong LK (2019) Predicting slope stability failure through machine learning paradigms. ISPRS Int J Geo Inf 8(9):395. https://doi.org/10.3390/ijgi8090395
Moayedi H, Bui DT, Gör M, Pradhan B, Jaafari A (2019) The feasibility of three prediction techniques of the artificial neural network, adaptive neuro-fuzzy inference system, and hybrid particle swarm optimization for assessing the safety factor of cohesive slopes. ISPRS Int J Geo Inf 8(9):391. https://doi.org/10.3390/ijgi8090391
Tolba M, Rezk H, Diab A, Al-Dhaifallah M (2018) A novel robust methodology based salp swarm algorithm for allocation and capacity of renewable distributed generators on distribution grids. Energies 11(10):2556
Baygi SMH, Karsaz A (2018) A hybrid optimal PID-LQR control of structural system: a case study of salp swarm optimization. In 2018 3rd Conference on Swarm Intelligence and Evolutionary Computation (CSIEC). IEEE, pp 1–6
Ibrahim A, Ahmed A, Hussein S, Hassanien AE (2018) Fish image segmentation using salp swarm algorithm. In International Conference on advanced machine learning technologies and applications. Springer, Cham, pp 42–51
Ekinci S, Hekimoğlu B, Kaya S (2018) Tuning of PID controller for AVR system using salp swarm algorithm. In 2018 International Conference on artificial intelligence and data processing (IDAP). IEEE, pp. 1–6
Ekinci S, Hekimoglu B (2018) Parameter optimization of power system stabilizer via salp swarm algorithm. In 2018 5th International Conference on electrical and electronic engineering (ICEEE). IEEE, pp 143–147
Hussien AG, Hassanien AE, Houssein EH (2017) Swarming behaviour of salps algorithm for predicting chemical compound activities. In Intelligent Computing and Information Systems (ICICIS), 2017 Eighth International Conference on. IEEE, pp 315–320
Liu X, Xu H (2018) Application on target localization based on salp swarm algorithm. In 2018 37th Chinese Control Conference (CCC). IEEE, pp 4542–4545
Sun ZX, Hu R, Qian B, Liu B, Che GL (2018) Salp swarm algorithm based on blocks on critical path for reentrant job shop scheduling problems. In International Conference on Intelligent Computing. Springer, Cham, pp 638–648
Bairathi D, Gopalani D (2019) Salp swarm algorithm (SSA) for training feed-forward neural networks. In Soft computing for problem solving. Springer, Singapore, pp 521–534
El-Fergany AA, Hasanien HM (2019) Salp swarm optimizer to solve optimal power flow comprising voltage stability analysis. Neural Comput Appl, pp 1–17
El-Fergany AA (2018) Extracting optimal parameters of PEM fuel cells using salp swarm optimizer. Renew Energy 119:641–648
Ahmed S, Mafarja M, Faris H, Aljarah I (2018) Feature selection using salp swarm algorithm with chaos. In Proceedings of the 2nd International Conference on Intelligent Systems, Metaheuristics & Swarm Intelligence. ACM, pp 65–69
Sayed GI, Khoriba G, Haggag MH (2018) A novel chaotic salp swarm algorithm for global optimization and feature selection. Appl Intell, pp 1–20
Yang, B., Zhong, L., Zhang, X., Shu, H., Yu, T., Li, H., & Sun, L. (2019). Novel bio-inspired memetic salp swarm algorithm and application to MPPT for PV systems considering partial shading condition. Journal of Cleaner Production
Aljarah I, Mafarja M, Heidari AA, Faris H, Zhang Y, Mirjalili S (2018) Asynchronous accelerating multi-leader salp chains for feature selection. Appl Soft Comput 71:964–979
Hegazy AE, Makhlouf MA, El-Tawel GS (2018) Improved salp swarm algorithm for feature selection. J King Saud Univ-Comput Inf Sci
Singh N, Chiclana F, Magnot JP (2019) A new fusion of salp swarm with sine cosine for optimization of non-linear functions. Eng Comput, pp 1–28
Ibrahim RA, Ewees AA, Oliva D, Elaziz MA, Lu S (2018) Improved salp swarm algorithm based on particle swarm optimization for feature selection. J Ambient Intell Humaniz Comput, pp 1–15
Faris H, Mafarja MM, Heidari AA, Aljarah I, Ala’M AZ, Mirjalili S, Fujita H (2018) An efficient binary salp swarm algorithm with crossover scheme for feature selection problems. Knowl-Based Syst 154:43–67
Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In International Conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC’06). IEEE, 1:695–701
Mahdavi S, Rahnamayan S, Deb K (2018) Opposition based learning: a literature review. Swarm Evol Comput 39:1–23
Gao W, Dimitrov D, Abdo H (2018a) Tight independent set neighborhood union condition for fractional critical deleted graphs and ID deleted graphs. Disc Cont Dyn Syst 12:711–721
Gao W, Guirao JLG, Basavanagoud B, Wu J (2018b) Partial multi-dividing ontology learning algorithm. Inform Sci 467:35–58
Gao W, Wang W, Dimitrov D, Wang Y (2018c) Nano properties analysis via fourth multiplicative ABC indicator calculating. Arab J Chem 11(6):793–801
Gao W, Wu H, Siddiqui MK, Baig AQ (2018d) Study of biological networks using graph theory. Saudi J Biolog Sci 25(6):1212–1219
Gao W, Guirao JLG, Abdel-Aty M, Xi W (2019) An independent set degree condition for fractional critical deleted graphs. Disc Cont Dyn Syst 12:877–886
Jensi R, Jiji GW (2016) An enhanced particle swarm optimization with levy flight for global optimization. Appl Soft Comput 43:248–261
Li Z, Zhou Y, Zhang S, Song J (2016) Lévy-flight moth-flame algorithm for function optimization and engineering design problems. Math Probl Eng, 2016
Salgotra R, Singh U, Saha S (2018) New cuckoo search algorithms with enhanced exploration and exploitation properties. Expert Syst Appl 95:384–420
Yang XS (2010) Nature-inspired metaheuristic algorithms. Luniver Press
Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133
Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338
Sandgren E (1988) Nonlinear integer and discrete programming in mechanical design. In Proceeding of the ASME design technology conference, pp 95–105
Das S, Suganthan PN (2010) Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on real world optimization problems. Jadavpur University, Nanyang Technological University, Kolkata, pp 341–359
Nowcki H (1974) Optimization in pre-contract ship design. In: Fujita Y, Lind K, Williams TJ (eds) Computer applications in the automation of shipyard operation and ship design, vol 2. NorthHolland. Elsevier, New York, pp 327–338
Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35
Belegundu AD, Arora JS (1985) A study of mathematical programming methods for structural optimization Part I: theory. Int J Numer Methods Eng 21(9):1583–1599
Arora JS (2004) Introduction to optimum design. Academic Press, Cambridge
Gandomi AH, Yang XS (2011) Benchmark problems in structural optimization. Chapter 12 in computational optimization, methods and algorithms, (S Koziel, XS Yang eds) Springer-Verlag, Berlin, 267–291
Acknowledgements
The first author gratefully acknowledges to the Ministry of Human Resource and Development (MHRD), Government of India, for their financial support. Grant No. MHR-02-41-113-429.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Corresponding author at: Ton Duc Thang University, Ho Chi Minh City, Vietnam
About this article
Cite this article
Gupta, S., Deep, K., Heidari, A.A. et al. Harmonized salp chain-built optimization. Engineering with Computers 37, 1049–1079 (2021). https://doi.org/10.1007/s00366-019-00871-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-019-00871-5