Abstract
Metaheuristics are one of the most promising techniques for solving optimization problems. Salp swarm algorithm (SSA) is a new swarm intelligence based metaheuristic. To improve the performance of SSA, this paper introduces multiple leader salp swarm algorithm (MLSSA), which has more exploratory power than SSA. The algorithm is tested on several mathematical optimization benchmark functions. Results are compared with some well known metaheuristics. The results represents the capability of MLSSA to converge towards the optimum. In recent studies many metaheuristic techniques are applied to train feed-forward neural networks. In this paper MLSSA is also applied for neural network training and is analysed for thirteen different datasets. Performance is compared with SSA, particle swarm optimization, differential evolution, genetic algorithm, ant colony optimization and evolution strategy.
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Rao SS (2009) Engineering optimization: theory and practice. Wiley, Hoboken
Glover FW, Kochenberger GA (eds) (2006) Handbook of metaheuristics, vol 57. Springer, Berlin
Hertz J (1991) Introduction to the theory of neural computation. Basic Books, New York, p 1
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
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, 1995. MHS’95. IEEE, pp 39–43
Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization, vol 200. Technical report-tr06, Erciyes university, engineering faculty, computer engineering department
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Proceedings of the workshop on nature inspired cooperative strategies for optimization (NICSO 2010). Springer, pp 65–74
Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio Inspired Comput 2:78–84
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Bansal JC, Sharma H, Jadon SS, Clerc M (2014) Spider monkey optimization algorithm for numerical optimization. Memet Comput 6(1):31–47
Bairathi D, Gopalani D (2018) A novel swarm intelligence based optimization method: harris hawk optimization. In International conference on intelligent systems design and applications. Springer, Cham, pp 832–842
Shadravan S, Naji HR, Bardsiri VK (2019) The sailfish optimizer: a novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems. Eng Appl Artif Intell 80:20–34
Yapici H, Cetinkaya N (2019) A new meta-heuristic optimizer: pathfinder algorithm. Appl Soft Comput 78:545–568
Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evolut Comput 44:148–175
Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–72
Rechenberg I (1989) Evolution strategy: natures way of optimization. In: Optimization: methods and applications. Possibilities and limitations. Springer, Berlin, pp 106–126
Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection, Vol 1. MIT press, Cambridge
Dasgupta D, Zbigniew M (eds) (2013) Evolutionary algorithms in engineering applications. Springer, Berlin
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
Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680
Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248
Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213:267–289
Erol OK, Eksin I (2006) A new optimization method: big bangbig crunch. Adv Eng Softw 37:106–111
Webster B, Bernhard PJ (2003) A local search optimization algorithm based on natural principles of gravitation. In: Proceedings of the 2003 international conference on information and knowledge engineering (IKE03). pp 255–261
Formato RA (2007) Central force optimization: a new metaheuristic with applica- tions in applied electromagnetics. Prog Electromag Res 77:425–491
Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clus- tering. Inf Sci 222:175–184
Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513
Yadav A (2019) AEFA: Artificial electric field algorithm for global optimization. Swarm Evolut Comput 48:93–108
Rao RV, Savsani VJ, Vakharia DP (2012) Teachinglearning-based optimization: an optimization method for continuous non-linear large scale problems. Inf Sci 183:1–15
Rao RV, Savsani VJ, Vakharia DP (2011) Teachinglearning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43:303–315
Glover F (1989) Tabu search part I. ORSA J Comput 1(3):190–206
Glover F (1990) Tabu search part II. ORSA J Comput 2:4–32
Eita MA, Fahmy MM (2014) Group counseling optimization. Appl Soft Comput 22:585–604
Eita MA, Fahmy MM (2010) Group counseling optimization: a novel approach. In: Bramer M, Ellis R, Petridis M (eds) Research and development in intelligent systems XXVI. Springer, London, pp 195–208
He S, Wu Q, Saunders J (2006) A novel group search optimizer inspired by animal behavioural ecology. In: Proceedings of the 2006 IEEE congress on evolutionary computation. CEC, pp 1272–1278
He S, Wu QH, Saunders J (2009) Group search optimizer: an optimization algorithm inspired by animal searching behavior. IEEE Trans Evolut Comput 13:973–90
Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: Proceedings of the 2007 IEEE congress on evolutionary computation. CEC, pp 4661–4667
Dai C, Zhu Y, Chen W (2007) Seeker optimization algorithm. Computational intelligence and security. Springer, Berlin, pp 167–176
Tan Y, Zhu Y (2010) Fireworks algorithm for optimization. Advances in swarm intelligence. Springer, Berlin, pp 355–364
Gandomi AH (2014) Interior search algorithm (ISA): a novel approach for global optimization. ISA Trans 53(4):1168–1183
Zhang J, Xiao M, Gao L, Pan Q (2018) Queuing search algorithm: a novel metaheuristic algorithm for solving engineering optimization problems. Appl Math Model 63:464–490
Zhang K, Huang Q, Zhang Y, Song J, Shi J (2019) Hybrid Lagrange interpolation differential evolution algorithm for path synthesis. Mech Mach Theory 134:512–540
Zhao W, Wang L, Zhang Z (2019) A novel atom search optimization for dispersion coefficient estimation in groundwater. Future Gener Comput Syst 91:601–610
Zhao W, Wang L, Zhang Z (2019) Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl Based Syst 163:283–304
Sharma N, Sharma H, Sharma A (2018) Beer froth artificial bee colony algorithm for job-shop scheduling problem. Appl Soft Comput 68:507–524
Lyu Z, Wei Z, Pan J, Chen H, Xia C, Han J, Shi L (2019) Periodic charging planning for a mobile WCE in wireless rechargeable sensor networks based on hybrid PSO and GA algorithm. Appl Soft Comput 75:388–403
Mokarram MJ, Niknam T, Aghaei J, Shafie-khah M, Catalo JP (2019) Hybrid optimization algorithm to solve the nonconvex multiarea economic dispatch problem. IEEE Syst J PP(99):1–10
Al-Tashi Q, Kadir SJA, Rais HM, Mirjalili S, Alhussian H (2019) Binary optimization using hybrid grey wolf optimization for feature selection. IEEE Access 7:39496–39508
Wahid F, Ghazali R, Ismail LH (2019) An enhanced approach of artificial bee colony for energy management in energy efficient residential building. Wirel Pers Commun 104(1):235–257
Wahid F, Kim DH (2016) An efficient approach for energy consumption optimization and management in residential building using artificial bee colony and fuzzy logic. Math Probl Eng 2016:9104735. https://doi.org/10.1155/2016/9104735
Wahid F, Ghazali R (2019) Hybrid of firefly algorithm and pattern search for solving optimization problems. Evolut Intell 12(1):1–10
Mohammadpour T, Bidgoli AM, Enayatifar R, Javadi HHS (2019) Efficient clustering in collaborative filtering recommender system: hybrid method based on genetic algorithm and gravitational emulation local search algorithm. Genomics. https://doi.org/10.1016/j.ygeno.2019.01.001
Rumelhart DE, Williams RJ, Hinton GE (1986) Learning internal representations by error propagation. Parallel Distrib Process Explor Microstruct Cogn 1:318–362
Mendes R, Cortez P, Rocha M, Neves J (2002) Particle swarm for feedforward neural network training. In: Proceedings of the international joint conference on neural networks, vol 2. pp 1895–1899
Meissner M, Schmuker M, Schneider G (2006) Optimized particle swarm optimization (OPSO) and its application to artificial neural network training. BMC Bioinform 7:125
Fan H, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Glob Optim 27:105–129
Slowik A, Bialko M (2008) Training of artificial neural networks using differential evolution algorithm. Hum Syst Interact. https://doi.org/10.1109/HSI.2008.4581409
Gao Q, Lei KQY, He Z (2005) An improved genetic algorithm and its application in artificial neural network, information, communications and signal processing, 2005. In: Fifth international conference on, December 06–09, 2005, pp 357–360
Tsai JT, Chou JH, Liu TK (2006) Tuning the structure and parameters of a neural network by using hybrid Taguchi-genetic algorithm. IEEE Trans Neural Netw 17(1):69–80
Blum C, Socha K (2005) Training feed-forward neural networks with ant colony optimization: an application to pattern classification. In: 5th international conference on, hybrid intelligent systems, 2005. HIS05, p 6
Socha K, Blum C (2007) An ant colony optimization algorithm for continuous optimization: application to feed-forward neural network training. Neural Comput Appl 16:235–247
Pavlidis NG, Tasoulis DK, Plagianakos VP, Nikiforidis G, Vrahatis MN (2005) Spiking neural network training using evolutionary algorithms, neural networks, 2005. In: IJCNN 05. Proceedings 2005 IEEE international joint conference, vol 4. pp 2190–2194
Ozturk C, Karaboga D (2011) Hybrid artificial bee colony algorithm for neural network training. In: 2011 IEEE congress on evolutionary computation (CEC). pp 84–88
Bairathi D, Gopalani D (2017) Opposition-based sine cosine algorithm (OSCA) for training feed-forward neural networks. In: 13th International conference on signal-image technology and internet-based systems (SITIS). IEEE, pp 438–444
Bairathi D, Gopalani D (2017) Salp swarm algorithm (SSA) for training feed-forward neural networks. In: 7th International conference soft computing for problem solving, Bhubaneswar
Mirjalili S (2015) How effective is the Grey Wolf optimizer in training multi-layer perceptrons. Appl Intell 43(1):150–161
Aljarah I, Faris H, Mirjalili S (2016) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 22:1–15
Olorunda O, Engelbrecht AP (2008) Measuring exploration/exploitation in particle swarms using swarm diversity. In: IEEE congress on evolutionary computation, 2008. CEC 2008. (IEEE world congress on computational intelligence). IEEE, pp 1128–1134
Alba E, Dorronsoro B (2005) The exploration/exploitation tradeoff in dynamic cellular genetic algorithms. IEEE Trans Evolut Comput 9(2):126–142
Crepinsek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv (CSUR) 45(3):35
Ali MM, Khompatraporn C, Zabinsky ZB (2005) A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. J Glob Optim 31(4):635–672
Bansal JC, Sharma H, Nagar A, Arya KV (2013) Balanced artificial bee colony algorithm. Int J Artif Intell Soft Comput 3(3):222–243
Liang J, Qu B, Suganthan P, Chen Q (2014) Problem definitions and evaluation criteria for the Cec 2015 competition on learning-based real-parameter single objective optimization, technical report 201411A, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore
Blake CL, Merz CJ (1998) UCI repository of machine learning databases, 1998
Mirjalili S, Mirjalili SM, Lewis A (2014) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188–209
Demar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7(Jan):1–30
Garca S, Fernndez A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180(10):2044–2064
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Bairathi, D., Gopalani, D. Numerical optimization and feed-forward neural networks training using an improved optimization algorithm: multiple leader salp swarm algorithm. Evol. Intel. 14, 1233–1249 (2021). https://doi.org/10.1007/s12065-019-00269-8
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DOI: https://doi.org/10.1007/s12065-019-00269-8