Abstract
Salp Swarm Algorithm (SSA) is a new type of metaheuristic and has shown superiority over other well-known algorithms such as Particle Swarm Optimization and Grey Wolf Optimizer in solving challenging optimization problems. Despite its superior performance, SSA still has problems such as insufficient convergence speed. Moreover, its local optima avoidance ability is not as good as those evolutionary algorithms using crossover operators. In this paper, we propose a modified Salp Swarm Algorithm (m-SSA) which improves the exploitation and exploration of SSA by integrating random walk strategy and especially enhances exploration by adding a new controlling parameter. In addition, a simulated annealing-type acceptance criterion is adopted to accept the fittest follower position as the new best leader position. The performance of the proposed algorithm is benchmarked on a set of classical functions and CEC2014 test suite. The proposed algorithm (m-SSA) outperforms SSA significantly on most test functions. When compared with other state-of-the-art metaheuristics, it also presents very competitive results. Besides, we apply the proposed algorithm on training feedforward neural networks (FNNs) and the results prove the effectiveness and efficiency of m-SSA.
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References
Aljarah I, Faris H, Mirjalili S (2018a) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 22(1):1–15
Aljarah I, Mafarja M, Heidari AA, Faris H, Zhang Y, Mirjalili S (2018b) Asynchronous accelerating multi-leader salp chains for feature selection. Appl Soft Comput 71:964–979
Assad A, Deep K (2018) A hybrid harmony search and simulated annealing algorithm for continuous optimization. Inf Sci 450:246–266
Chen T, Wang M, Huang X, Xie Q (2018) Tdoa-aoa localization based on improved salp swarm algorithm. In: 2018 14th IEEE international conference on signal processing (ICSP), IEEE, pp 108–112
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
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
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68
Glover F (1989) Tabu search-part i. ORSA J Comput 1(3):190–206
Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99
Guo SM, Yang CC, Hsu PH, Tsai JSH (2014) Improving differential evolution with a successful-parent-selecting framework. IEEE Trans Evolut Comput 19(5):717–730
Gupta S, Deep K (2019) A novel random walk grey wolf optimizer. Swarm Evolut Comput 44:101–112
Hegazy AE, Makhlouf M, El-Tawel GS (2018) Improved salp swarm algorithm for feature selection. J King Saud Univ Comput Inf Sci. https://doi.org/10.1016/j.jksuci.2018.06.003
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
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680
Liang J, Qu B, Suganthan P (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore, p 635
Liu Q, Wu L, Xiao W, Wang F, Zhang L (2018) A novel hybrid bat algorithm for solving continuous optimization problems. Appl Soft Comput 73:67–82
Lourenço H, Martin O, Stutzle T (2001) Iterated local search. arXiv preprint arXiv: math/0102188
Lourenço HR, Martin OC, Stützle T (2019) Iterated local search: framework and applications. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. Springer, Berlin, pp 129–168
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
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
Storn R, Price K (1996) Minimizing the real functions of the ICEC’96 contest by differential evolution. In: Proceedings of IEEE international conference on evolutionary computation, IEEE, pp 842–844
Tu Q, Chen X, Liu X (2019a) Hierarchy strengthened grey wolf optimizer for numerical optimization and feature selection. IEEE Access 7:78012–78028
Tu Q, Chen X, Liu X (2019b) Multi-strategy ensemble grey wolf optimizer and its application to feature selection. Appl Soft Comput 76:16–30
Xinchao Z (2011) Simulated annealing algorithm with adaptive neighborhood. Appl Soft Comput 11(2):1827–1836
Xing Z, Jia H (2019) Multilevel color image segmentation based on glcm and improved salp swarm algorithm. IEEE Access 7:37672–37690
Yaghini M, Khoshraftar MM, Fallahi M (2013) A hybrid algorithm for artificial neural network training. Eng Appl Artif Intell 26(1):293–301
Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: González JR, Pelta DA, Cruz C, Terrazas G, Krasnogor N (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74
Yang XS (2014) Nature-inspired optimization algorithms. Elsevier, Amsterdam
Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. arXiv preprint arXiv:1005.2908
Yashesh D, Deb K, Bandaru S (2014) Non-uniform mapping in real-coded genetic algorithms. In: 2014 IEEE congress on evolutionary computation (CEC), IEEE, pp 2237–2244
Yılmaz S, Küçüksille EU (2015) A new modification approach on bat algorithm for solving optimization problems. Appl Soft Comput 28:259–275
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
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The work was supported by the National Natural Science Foundation of China (Grant No. U1530120).
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Yin, Y., Tu, Q. & Chen, X. Enhanced Salp Swarm Algorithm based on random walk and its application to training feedforward neural networks. Soft Comput 24, 14791–14807 (2020). https://doi.org/10.1007/s00500-020-04832-9
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DOI: https://doi.org/10.1007/s00500-020-04832-9