Abstract
Meta-heuristic algorithms are often leveraged to solve complicated engineering optimization and scientific problems. Salp swarm algorithm is one of the most useful meta-heuristic algorithms in recent years. To alleviate the slow convergence speed of the salp swarm algorithm, as well as the tendency to fall into local minima, we have proposed an efficient salp swarm algorithm called E-SSA, which combines the effective evolutionary strategies of basic salp swarm algorithm and two efficient mechanisms named self-adaption weight and scale-free network. These two mechanisms have been integrated into the follower evolution process of the algorithm to achieve the balance of exploration and exploitation. The performance of the E-SSA is benchmarked against a suit of CEC’2019 series functions and 23 commonly used international benchmarks. The algorithm is further validated via three engineering application problems. The experimental results indicate that the improved algorithm has clear advantages in optimization performance compared with other existing heuristic algorithms.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abdel-Basset M, Abdel-Fatah L, Sangaiah AK (2018) Metaheuristic algorithms: A comprehensive review. Comput Intell Multimed Big Data Cloud With Eng Appl:185–231
Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: Overview and conceptual comparison. Acm Comput Surv 35(3):268–308
Wang C, Yu T, Shao G, Nguyen T-T, Bui TQ (2019) Shape optimization of structures with cutouts by an efficient approach based on xiga and chaotic particle swarm optimization. Eur J Mech-A/Solids 74:176–187
deOliveira MC, Delgado MR, Britto A (2021) A hybrid greedy indicator-and pareto-based many-objective evolutionary algorithm. Appl Intell:1–23
Cheong KH, Koh JM (2019) A hybrid genetic-levenberg marquardt algorithm for automated spectrometer design optimization. Ultramicroscopy 202:100–106
Wilde H, Knight V, Gillard J (2020) Evolutionary dataset optimisation: learning algorithm quality through evolution. Appl Intell 50(4):1172–1191
Tayyebi S, Hajjar Z, Soltanali S (2021) A metaheuristic approach of hybrid bee colony and simulated annealing combined with fuzzy model: Prediction of conversion and selectivity in c8h16 dimerization. Chemometr Intell Lab Syst:104368
Mathlouthi I, Gendreau M, Potvin J-Y (2021) A metaheuristic based on tabu search for solving a technician routing and scheduling problem. Comput Oper Res 125:105079
Skackauskas J, Kalganova T, Dear I, Janakiram M (2021) Dynamic impact for ant colony optimization algorithm. Swarm Evol Comput:100993
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks, vol 4. IEEE, pp 1942–1948
Abdollahzadeh B, Gharehchopogh FS, Mirjalili S (2021) African vultures optimization algorithm: A new nature-inspired metaheuristic algorithm for global optimization problems. Comput Ind Eng 158:107408
Das S, Suganthan PN (2010) Differential evolution: A survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31
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
Ma L, Wang C, Xie N-, Shi M, Ye Y, Wang L (2021) Moth-flame optimization algorithm based on diversity and mutation strategy. Appl Intell 51:5836–5872
Wang L, Ma L, Wang C, Xie N-g, Koh JM, Cheong KH (2021) Identifying influential spreaders in social networks through discrete moth-flame optimization. IEEE Trans Evol Comput 25(6):1091–1102
Emary E, Zawbaa HM, Hassanien AE (2016) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172:371–381
Wang B, Wang C, Wang L, Xie N, Wei W (2019) Recognition of semg hand actions based on cloud adaptive quantum chaos ions motion algorithm optimized svm. J Mech Med Biol 19(06):1950047
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Chu D, Ma W, Yang Z, Li J, Deng Y, Cheong KH (2021) A physarum-inspired algorithm for logistics optimization: From the perspective of effective distance. Swarm Evol Comput 64:100890
Shi M, Wang C, Li X-Z, Li M-Q, Wang L, Xie N-G (2021) Eeg signal classification based on svm with improved squirrel search algorithm. Biomed Eng/Biomed Tech 66(2):137–152
Qais MH, Hasanien HM, Alghuwainem S (2019) Enhanced salp swarm algorithm: Application to variable speed wind generators. Eng Appl Artif Intell 80:82–96
Thanh PD, Binh H TT, Trung TB (2020) An efficient strategy for using multifactorial optimization to solve the clustered shortest path tree problem. Appl Intell 50(4):1233–1258
Nematollahi AF, Rahiminejad A, Vahidi B (2017) A novel physical based meta-heuristic optimization method known as lightning attachment procedure optimization. Appl Soft Comput 59:596–621
Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: Squirrel search algorithm. Swarm Evol Comput 44:148–175
Kumar M, Kulkarni AJ, Satapathy SC (2018) Socio evolution & learning optimization algorithm: A socio-inspired optimization methodology. Futur Gener Comput Syst 81:252–272
Moghdani R, Salimifard K (2018) Volleyball premier league algorithm. Appl Soft Comput 64:161–185
Arora S, Singh S (2019) Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23(3):715–734
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: Algorithm and applications. Fut Gener Comput Syst 97:849–872
Nematollahi AF, Rahiminejad A, Vahidi B (2020) A novel meta-heuristic optimization method based on golden ratio in nature. Soft Comput 24(2):1117–1151
Ong KM, Ong P, Sia CK (2021) A carnivorous plant algorithm for solving global optimization problems. Appl Soft Comput 98:106833
Mohammadi-Balani A, Nayeri MD, Azar A, Taghizadeh-Yazdi M (2021) Golden eagle optimizer: A nature-inspired metaheuristic algorithm. Comput Ind Eng 152:107050
Azizi M (2021) Atomic orbital search: A novel metaheuristic algorithm. Appl Math Model 93:657–683
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
Hashim FA, Houssein EH, Hussain K, Mabrouk MS, WalidAl-Atabany (2022) Honey badger algorithm: New metaheuristic algorithm for solving optimization problems. Math Comput Simul 192:84–110
Balakrishnan K, Dhanalakshmi R, Khaire UM (2021) Improved salp swarm algorithm based on the levy flight for feature selection. J Supercomput 77:12399–12419
Xing Z, Jia H (2019) Multilevel color image segmentation based on glcm and improved salp swarm algorithm. IEEE Access 7:37672–37690
Mallikarjuna B, Reddy YVS, Kiranmayi R (2018) Salp swarm algorithm to combined economic and emission dispatch problems. Int J Eng Technol 7(3.29):311–315
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
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
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
Sayed GI, Khoriba G, Haggag MH (2018) A novel chaotic salp swarm algorithm for global optimization and feature selection. Appl Intell 48(10):3462–3481
Zhao X, Yang F, Han Y, Cui Y (2020) An opposition-based chaotic salp swarm algorithm for global optimization. IEEE Access 8:36485–36501
Wu J, Nan R, Chen L (2019) Improved salp swarm algorithm based on weight factor and adaptive mutation. J Exper Theor Artif Intell 31(3):493–515
Nautiyal B, Prakash R, Vimal V, Liang G, Chen H (2021) Improved salp swarm algorithm with mutation schemes for solving global optimization and engineering problems. Eng Comput:1–23
Gupta S, Deep K, Heidari AA, Moayedi H, Chen H (2019) Harmonized salp chain-built optimization. Eng Comput:1–31
Fan Y, Shao J, Sun G, Shao X (2020) A modified salp swarm algorithm based on the perturbation weight for global optimization problems. Complexity
Salgotra R, Singh U, Singh S, Singh G, Mittal N Self-adaptive salp swarm algorithm for engineering optimization problems
Panda N, Majhi SK (2020) Improved salp swarm algorithm with space transformation search for training neural network. Arab J Sci Eng 45(4):2743–2761
Zhang H, Cai Z, Ye X, Wang M, Kuang F, Chen H, Li C, Li Y (2020) A multi-strategy enhanced salp swarm algorithm for global optimization. Eng Comput:1–27
Ibrahim RA, Ewees AA, Oliva D, Elaziz MA, Lu S (2019) Improved salp swarm algorithm based on particle swarm optimization for feature selection. J Ambient Intell Human Comput 10(8):3155–3169
Zhang J, Wang J-S (2020) Improved salp swarm algorithm based on levy flight and sine cosine operator. IEEE Acess 8:99740–99771
Yue C, Qu B, Liang J (2017) A multiobjective particle swarm optimizer using ring topology for solving multimodal multiobjective problems. IEEE Trans Evol Comput 22(5):805–817
Zhang C, Yi Z (2011) Scale-free fully informed particle swarm optimization algorithm. Inf Sci 181(20):4550–4568
Wu D, Jiang N, Du W, Tang K, Cao X (2018) Particle swarm optimization with moving particles on scale-free networks. IEEE Trans Netw Sci Eng 7(1):497–506
Wang C, Liu Y, Zhao Y, Chen Y (2014) A hybrid topology scale-free gaussian-dynamic particle swarm optimization algorithm applied to real power loss minimization. Eng Appl Artif Intell 32:63–75
Ji J, Song S, Tang C, Gao S, Tang Z, Todo Y (2019) An artificial bee colony algorithm search guided by scale-free networks. Inf Sci 473:142–165
Riget J, Vesterstrøm JS (2002) A diversity-guided particle swarm optimizer-the ARPSO. Dept Comput Sci Univ Aarhus, Aarhus, Denmark, Tech Rep 2:2002
Cheng S, Shi Y, Qin Q, Ting TO (2012) Population diversity based inertia weight adaptation in particle swarm optimization. In: 2012 IEEE Fifth International Conference on Advanced Computational Intelligence (ICACI). IEEE, pp 395–403
Wang C, Wang B, Cen Y, Xie N- (2020) Ions motion optimization algorithm based on diversity optimal guidance and opposition-based learning. Control Decis 35(7):1584–1596
Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286 (5439):509–512
Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214(1):108–132
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Price KV, Awad NH, Ali MZ, Suganthan PN (2018) Problem definitions and evaluation criteria for the 100-digit challenge special session and competition on single objective numerical optimization. In: Technical Report. Nanyang Technological University
Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294
Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98
Nowacki H (1973) Optimization in pre-contract ship design
Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Wu J, Nan R, Chen L (2019) Improved salp swarm algorithm based on weight factor and adaptive mutation. J Exper Theor Artif Intell 31(3):493–515
Zhang D, Cheng Z, Xin Z, Zhang H, Yan W (2020) Salp swarm algorithm based on craziness and adaptive. Control Decis 35(9):2112–2120
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 Evol Comput 1(1):3–18
Huang F-, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356
Coello C AC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203
Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47
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
Cheng M-Y, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112
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
Mirjalili S (2015) Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowl-based Syst 89:228–249
Acknowledgments
This work was supported by the Program for Synergy Innovation in the Anhui Higher Education Institutions of China (Grant No. GXXT-2021-044), Scientific Research Foundation of Education Department of Anhui Province, China (Grant No. KJ2021A0506), Natural Science Foundation of Anhui Province, China(Grant No. 2108085MG237), Open Fund of Key Laboratory of Anhui Higher Education Institutes, China(Grant No.CS2021-02), Science and Technology Planning Project of Wuhu City, Anhui Province, China(Grant No. 2021jc1-2) and Research Start-Up Fund for Introducing Talents from Anhui Polytechnic University(Grant No. 2021YQQ066).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Competing Interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix A
Appendix B
I-The tension/compression spring design problem
The optimization objective is
The corresponding constraints are
The range of variables is as follows
II-The cantilever beam design problem
The optimization objective is
The corresponding constraint is
III-The three-bar truss design problem
The optimization objective is
The corresponding constraint is
The range of variables is as follows
Rights and permissions
About this article
Cite this article
Wang, C., Xu, Rq., Ma, L. et al. An efficient salp swarm algorithm based on scale-free informed followers with self-adaption weight. Appl Intell 53, 1759–1791 (2023). https://doi.org/10.1007/s10489-022-03438-y
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-022-03438-y