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Improved Salp Swarm Algorithm with Space Transformation Search for Training Neural Network

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Abstract

Swarm-based algorithm is best suitable when it can perform smooth balance between the exploration and exploitation as well as faster convergence by successfully avoiding local optima entrapment. At recent time, salp swarm algorithm (SSA) is developed as a nature-inspired swarm-based algorithm. It can solve continuous, nonlinear and complex in nature day-to-day life optimization problems. Like many other optimization algorithms, SSA suffers with the problem of local stagnation. This paper introduces an improved version of the SSA, which improves the performance of the existing SSA by using space transformation search (STS). The proposed algorithm is termed as STS-SSA. The STS-SSA enhances the exploration and exploitation capability in the search space and successfully avoids local optima entrapment. The STS-SSA is evaluated by considering the IEEE CEC 2017 standard benchmark function set. The efficiency and robustness of the proposed STS-SSA are measured using performance metrics, convergence analysis and statistical significance. A demonstration is given as an application of the proposed algorithm for solving a real-life problem. For this purpose, the multi-layer feed-forward network is trained using the proposed STS-SSA. The experimental results demonstrate that the developed STS-SSA can be used for solving optimization problems effectively.

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References

  1. Bhaskar, V.; Gupta, S.K.; Ray, A.K.: Applications of multiobjective optimization in chemical engineering. Rev. Chem. Eng. 16(1), 1–54 (2000)

    Google Scholar 

  2. Sobieszczanski-Sobieski, J.: Multidisciplinary design optimization: an emerging new engineering discipline. In: Herskovits, J. (ed.) Advances in Structural Optimization, pp. 483–496. Springer, Dordrecht (1995)

    MATH  Google Scholar 

  3. Kondratenko, Y.P.; Simon, D.: Structural and parametric optimization of fuzzy control and decision making systems. In: Zadeh, L.A., Yager, R.R., Shahbazova, S.N., Reformat, M.Z., Kreinovich, V. (eds.) Recent Developments and the New Direction in Soft-Computing Foundations and Applications, pp. 273–289. Springer, Cham (2018)

    Google Scholar 

  4. Hazen, B.T.; Skipper, J.B.; Boone, C.A.; Hill, R.R.: Back in business: operations research in support of big data analytics for operations and supply chain management. Ann. Oper. Res. 270(1–2), 201–211 (2018)

    Google Scholar 

  5. Tsamardinos, I.; Brown, L.E.; Aliferis, C.F.: The max-min hill-climbing Bayesian network structure learning algorithm. Mach. Learn. 65(1), 31–78 (2006)

    Google Scholar 

  6. Dengiz, B.; Alabas-Uslu, C.; Dengiz, O.: A tabu search algorithm for the training of neural networks. J. Oper. Res. Soc. 60(2), 282–291 (2009)

    MATH  Google Scholar 

  7. Lourenço, H.R.; Martin, O.C.; Stützle, T.: Iterated local search: framework and applications. In: Gendreau, M., Potvin, J.-Y. (eds.) Handbook of Metaheuristics, pp. 129–168. Springer, Boston (2019)

    Google Scholar 

  8. Aarts, E.; Korst, J.; Michiels, W.: Simulated annealing. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies, pp. 187–210. Springer, Boston (2005)

    Google Scholar 

  9. Yang, S.; Jat, S.N.: Genetic algorithms with guided and local search strategies for university course timetabling. IEEE Trans. Syst. Man Cybernet. C Appl. Rev. 41(1), 93–106 (2011)

    Google Scholar 

  10. Goldberg, D.E.; Holland, J.H.: Genetic algorithms and machine learning. Mach. Learn. 3(2), 95–99 (1988)

    Google Scholar 

  11. Espejo, P.G.; Ventura, S.; Herrera, F.: A survey on the application of genetic programming to classification. IEEE Trans. Syst. Man Cybernet. C Appl. Rev. 40(2), 121–144 (2010)

    Google Scholar 

  12. Wang, L.; Zeng, Y.; Chen, T.: Back propagation neural network with adaptive differential evolution algorithm for time series forecasting. Expert Syst. Appl. 42(2), 855–863 (2015)

    Google Scholar 

  13. Sánchez-Oro, J.; Martínez-Gavara, A.; Laguna, M.; Martí, R.; Duarte, A.: Variable neighborhood scatter search for the incremental graph drawing problem. Comput. Opt. Appl. 68(3), 775–797 (2017)

    MathSciNet  MATH  Google Scholar 

  14. Garza-Fabre, M.; Kandathil, S.M.; Handl, J.; Knowles, J.; Lovell, S.C.: Generating, maintaining, and exploiting diversity in a memetic algorithm for protein structure prediction. Evol. Comput. 24(4), 577–607 (2016)

    Google Scholar 

  15. Kota, L.; Jarmai, K.: Mathematical modeling of multiple tour multiple traveling salesman problem using evolutionary programming. Appl. Math. Model. 39(12), 3410–3433 (2015)

    MathSciNet  MATH  Google Scholar 

  16. Conti, E.; Madhavan, V.; Such, F.P.; Lehman, J.; Stanley, K.; Clune, J.: Improving exploration in evolution strategies for deep reinforcement learning via a population of novelty-seeking agents. In: Bengio, S., Wallach, H., Larochelle, H., Grauman, K., Cesa-Bianchi, N., Garnett, R. (eds.) Advances in Neural Information Processing Systems, pp. 5032–5043 (2018).

  17. Kennedy, J.: Particle swarm optimization. In: Encyclopedia of Machine Learning, pp. 760–766. Springer, Boston (2011)

  18. Dorigo, M.; Di Caro, G.: Ant colony optimization: a new meta-heuristic. In: Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), vol. 2, pp. 1470–1477. IEEE (1999)

  19. Mirjalili, S.: The ant lion optimizer. Adv. Eng. Softw. 83, 80–98 (2015)

    Google Scholar 

  20. Mirjalili, S.; Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016)

    Google Scholar 

  21. Mirjalili, S.; Mirjalili, S.M.; Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014)

    Google Scholar 

  22. Dhiman, G.; Kumar, V.: Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv. Eng. Softw. 114, 48–70 (2017)

    Google Scholar 

  23. Karaboga, D.; Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Glob. Optim. 39(3), 459–471 (2007)

    MathSciNet  MATH  Google Scholar 

  24. Yang, X.S.: A new metaheuristic bat-inspired algorithm. In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), pp. 65–74. Springer, Berlin (2010)

  25. Wolpert, D.H.; Macready, W.G.: No free lunch theorems for search. Technical Report SFI-TR-95-02-010, vol. 10. Santa Fe Institute (1995)

  26. Mirjalili, S.; Gandomi, A.H.; Mirjalili, S.Z.; Saremi, S.; Faris, H.; Mirjalili, S.M.: Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114, 163–191 (2017)

    Google Scholar 

  27. Wang, H.; Wu, Z.; Liu, Y.; Wang, J.; Jiang, D.; Chen, L.: Space transformation search: a new evolutionary technique. In: Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation, pp. 537–544. ACM (2009)

  28. Yu, S.; Wu, Z.; Wang, H.; Chen, Z.: A hybrid particle swarm optimization algorithm based on space transformation search and a modified velocity model. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (eds.) High Performance Computing and Applications, pp. 522–527. Springer, Berlin (2010)

    Google Scholar 

  29. Rahnamayan, S.; Tizhoosh, H.R.; Salama, M.M.: Opposition-based differential evolution. IEEE Trans. Evol. Comput. 12(1), 64–79 (2008)

    Google Scholar 

  30. Dinkar, S.K.; Deep, K.: Opposition based Laplacian ant lion optimizer. J. Comput. Sci. 23, 71–90 (2017)

    MathSciNet  Google Scholar 

  31. Wu, G.; Mallipeddi, R.; Suganthan, P.N.: Problem definitions and evaluation criteria for the CEC 2017 competition on constrained real-parameter optimization. National University of Defense Technology, Changsha, Hunan, PR China and Kyungpook National University, Daegu, South Korea and Nanyang Technological University, Singapore, Technical Report (2017)

  32. Rizk-Allah, R.M.; Hassanien, A.E.; Elhoseny, M.; Gunasekaran, M.: A new binary salp swarm algorithm: development and application for optimization tasks. Neural Comput. Appl. 2, 1–23 (2018)

    Google Scholar 

  33. Hegazy, A.E.; Makhlouf, M.A.; El-Tawel, G.S.: Improved salp swarm algorithm for feature selection. J. King Saud Univ. Comput. Inform. Sci. 10, 37 (2018)

    Google Scholar 

  34. Ibrahim, H.T.; Mazher, W.J.; Ucan, O.N.; Bayat, O.: Feature selection using salp swarm algorithm for real biomedical datasets. IJCSNS 17(12), 13 (2017)

    Google Scholar 

  35. Ahmed, S.; Mafarja, M.; Faris, H.; Aljarah, I.: Feature selection using salp swarm algorithm with chaos. In: Proceedings of the 2nd International Conference on Intelligent Systems, Metaheuristics and Swarm Intelligence, pp. 65–69. ACM (2018)

  36. Wang, J.; Gao, Y.; Chen, X.: A novel hybrid interval prediction approach based on modified lower upper bound estimation in combination with multi-objective salp swarm algorithm for short-term load forecasting. Energies 11(6), 1561 (2018)

    Google Scholar 

  37. Abusnaina, A.A.; Ahmad, S.; Jarrar, R.; Mafarja, M.: Training neural networks using salp swarm algorithm for pattern classification. In: Proceedings of the 2nd International Conference on Future Networks and Distributed Systems, p. 17. ACM (2018)

  38. Majhi, S.K.; Bhatachharya, S.; Pradhan, R.; Biswal, S.: Fuzzy clustering using salp swarm algorithm for automobile insurance fraud detection. J. Intell. Fuzzy Syst. 36(3), 2333–2344 (2019)

    Google Scholar 

  39. El-Fergany, A.A.; Hasanien, H.M.: Salp swarm optimizer to solve optimal power flow comprising voltage stability analysis. Neural Comput. Appl. 1, 1–17 (2019)

    Google Scholar 

  40. Ateya, A.A.; Muthanna, A.; Vybornova, A.; Algarni, A.D.; Abuarqoub, A.; Koucheryavy, Y.; Koucheryavy, A.: Chaotic salp swarm algorithm for SDN multi-controller networks. Eng. Sci. Technol. Int. J. (2019). https://doi.org/10.1016/j.jestch.2018.12.015

    Article  Google Scholar 

  41. Qais, M.H.; Hasanien, H.M.; Alghuwainem, S.: Enhanced salp swarm algorithm: application to variable speed wind generators. Eng. Appl. Artif. Intell. 80, 82–96 (2019)

    Google Scholar 

  42. Kanoosh, H.M.; Houssein, E.H.; Selim, M.M.: Salp swarm algorithm for node localization in wireless sensor networks. J. Comput. Netw. Commun. 2019, 1 (2019)

    Google Scholar 

  43. Singh, N.; Chiclana, F.; Magnot, J.P.: A new fusion of salp swarm with sine cosine for optimization of non-linear functions. Eng. Comput. 1, 1–28 (2019)

    Google Scholar 

  44. Hussien, A.G.; Hassanien, A.E.; Houssein, E.H.: Swarming behaviour of Salps algorithm for predicting chemical compound activities. In: 2017 Eighth International Conference on Intelligent Computing and Information Systems (ICICIS), pp. 315–320. IEEE (2017)

  45. Aljarah, I.; Mafarja, M.; Heidari, A.A.; Faris, H.; Zhang, Y.; Mirjalili, S.: Asynchronous accelerating multi-leader salp chains for feature selection. Appl. Soft Comput. 71, 964–979 (2018)

    Google Scholar 

  46. Ibrahim, R.A.; Ewees, A.A.; Oliva, D.; Elaziz, M.A.; Lu, S.: Improved salp swarm algorithm based on particle swarm optimization for feature selection. J. Ambient Intell. Humanized Comput. 1, 1–15 (2018)

    Google Scholar 

  47. Sayed, G.I.; Khoriba, G.; Haggag, M.H.: A novel chaotic salp swarm algorithm for global optimization and feature selection. Appl. Intell. 1, 1–20 (2018)

    Google Scholar 

  48. Faris, H.; Mafarja, M.M.; Heidari, A.A.; Aljarah, I.; Ala’m, A.Z.; Mirjalili, S.; Fujita, H.: An efficient binary salp swarm algorithm with crossover scheme for feature selection problems. Knowl. Based Syst. 154, 43–67 (2018)

    Google Scholar 

  49. Khamees, M.; Albakr, A.Y.; Shaker, K.: A new approach for features selection based on binary Slap swarm algorithm. J. Theor. Appl. Inform. Technol. 96(7), 1 (2018)

    Google Scholar 

  50. Khamees, M.; Albakry, A.; Shaker, K.: Multi-objective feature selection: hybrid of salp swarm and simulated annealing approach. In: International Conference on New Trends in Information and Communications Technology Applications, pp. 129–142. Springer, Cham (2018)

  51. Liu, X.; Xu, H.: Application on target localization based on salp swarm algorithm. In: 2018 37th Chinese Control Conference (CCC), pp. 4542–4545. IEEE (2018)

  52. Hegazy, A.E.; Makhlouf, M.A.; El-Tawel, G.S.: Feature selection using chaotic salp swarm algorithm for data classification. Arab. J. Sci. Eng. 1, 1–16 (2018)

    Google Scholar 

  53. Sun, Z.X.; Hu, R.; Qian, B.; Liu, B.; Che, G.L.: Salp swarm algorithm based on blocks on critical path for reentrant job shop scheduling problems. In: International Conference on Intelligent Computing, pp. 638–648. Springer, Cham (2018)

  54. Achelia, D.: A chaotic binary salp swarm algorithm for solving the graph coloring problem. In: Modelling and Implementation of Complex Systems: Proceedings of the 5th International Symposium, MISC 2018, December 16–18, 2018, Laghouat, Algeria (Vol. 64, p. 106). Springer (2018)

  55. Meraihi, Y.; Ramdane-Cherif, A.; Mahseur, M.; Achelia, D.: A chaotic binary salp swarm algorithm for solving the graph coloring problem. In: International Symposium on Modelling and Implementation of Complex Systems, pp. 106–118. Springer, Cham (2018)

  56. Ibrahim, A.; Ahmed, A.; Hussein, S.; Hassanien, A.E.: Fish image segmentation using salp swarm algorithm. In: International Conference on Advanced Machine Learning Technologies and Applications, pp. 42–51. Springer, Cham (2018)

  57. Zhang, J.; Wang, Z.; Luo, X.: Parameter estimation for soil water retention curve using the salp swarm algorithm. Water 10(6), 815 (2018)

    Google Scholar 

  58. Barik, A.K.; Das, D.C.: Active power management of isolated renewable microgrid generating power from Rooftop solar arrays, sewage waters and solid urban wastes of a smart city using salp swarm algorithm. In: Technologies for Smart-City Energy Security and Power (ICSESP), 2018, pp. 1–6. IEEE (2018)

  59. Wang, J.; Gao, Y.; Chen, X.: A novel hybrid interval prediction approach based on modified lower upper bound estimation in combination with multi-objective salp swarm algorithm for short-term load forecasting. Energies 11(6), 1561 (2018)

    Google Scholar 

  60. Baygi, S.M.H.; Karsaz, A.; Elahi, A.: A hybrid optimal PID-Fuzzy control design for seismic exited structural system against earthquake: a salp swarm algorithm. In: 2018 6th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), pp. 220–225. IEEE (2018)

  61. Sahu, P.C.; Prusty, R.C.; Panda, S.: Salp swarm optimized multistage PDF plus (1 + PI) controller in AGC of multi source based nonlinear power system. In: International Conference on Soft Computing Systems, pp. 789–800. Springer, Singapore (2018)

  62. El-Fergany, A.A.: Extracting optimal parameters of PEM fuel cells using salp swarm optimizer. Renew. Energy 119, 641–648 (2018)

    Google Scholar 

  63. Tolba, M.; Rezk, H.; Diab, A.; Al-Dhaifallah, M.: A novel robust methodology based salp swarm algorithm for allocation and capacity of renewable distributed generators on distribution grids. Energies 11(10), 2556 (2018)

    Google Scholar 

  64. Asaithambi, S.; Rajappa, M.: Swarm intelligence-based approach for optimal design of CMOS differential amplifier and comparator circuit using a hybrid salp swarm algorithm. Rev. Sci. Instrum. 89(5), 054702 (2018)

    Google Scholar 

  65. Ekinci, S.; Hekimoglu, B.: Parameter optimization of power system stabilizer via salp swarm algorithm. In: 2018 5th International Conference on Electrical and Electronic Engineering (ICEEE), pp. 143–147. IEEE (2018)

  66. Asasi, M.S.; Ahanch, M.; Holari, Y.T.: Optimal allocation of distributed generations and shunt capacitors using salp swarm algorithm. In: Iranian Conference on Electrical Engineering (ICEE), pp. 1166–1172. IEEE (2018)

  67. Patnana, N.; Pattnaik, S.; Singh, V.P.: Salp swarm optimization based PID controller tuning for Doha reverse osmosis desalination plant. Int. J. Pure Appl. Math. 119(12), 12707–12720 (2018)

    Google Scholar 

  68. Nayak, C.; Saha, S.K.; Kar, R.; Mandal, D.: Optimal SSA-based wideband digital differentiator design for cardiac QRS complex detection application. Int. J. Numer. Model. Electron. Netw. Dev. Fields 32, e2524 (2018)

    Google Scholar 

  69. Bairathi, D.; Gopalani, D.: Salp swarm algorithm (SSA) for training feed-forward neural networks. In: Bansal, J.C., Das, K.N., Nagar, A., Deep, K., Ojha, A.K. (eds.) Soft computing for problem solving, pp. 521–534. Springer, Singapore (2019)

    Google Scholar 

  70. Abbassi, R.; Abbassi, A.; Heidari, A.A.; Mirjalili, S.: An efficient salp swarm-inspired algorithm for parameters identification of photovoltaic cell models. Energy Convers. Manag. 179, 362–372 (2019)

    Google Scholar 

  71. Panda, N.; Majhi, S. K.: How effective is the salp swarm algorithm in data classification. In: Computational Intelligence in Pattern Recognition, pp. 579–588. Springer, Singapore (2020)

  72. Mirjalili, S.: SCA: a sine cosine algorithm for solving optimization problems. Knowl. Based Syst. 96, 120–133 (2016)

    Google Scholar 

  73. Mirjalili, S.: Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl. Based Syst. 89, 228–249 (2015)

    Google Scholar 

  74. F-Distribution Table (2018). Retrieved from http://www.socr.ucla.edu/applets.dir/f_table.html

  75. Normal Distribution Table. Retrieved from http://math.arizona.edu/~rsims/ma464/standardnormaltable.pdf

  76. Svozil, D.; Kvasnicka, V.; Pospichal, J.: Introduction to multi-layer feed-forward neural networks. Chemometr. Intell. Lab. Syst. 39(1), 43–62 (1997)

    Google Scholar 

  77. Bache, K.; Lichman, M.: UCI Machine Learning Repository. University of California. School of information and computer science, 28. Irvine, CA. http://archive.ics.uci.edu/ml (2013)

    Google Scholar 

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  1. Department of Computer Science and Engineering, Veer Surendra Sai University of Technology, Burla, Odisha, 768018, India

    Nibedan Panda & Santosh Kumar Majhi

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Panda, N., Majhi, S.K. Improved Salp Swarm Algorithm with Space Transformation Search for Training Neural Network. Arab J Sci Eng 45, 2743–2761 (2020). https://doi.org/10.1007/s13369-019-04132-x

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