{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T15:23:44Z","timestamp":1777908224572,"version":"3.51.4"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T00:00:00Z","timestamp":1587513600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T00:00:00Z","timestamp":1587513600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2021,1]]},"DOI":"10.1007\/s11227-020-03293-z","type":"journal-article","created":{"date-parts":[[2020,4,22]],"date-time":"2020-04-22T09:03:28Z","timestamp":1587546208000},"page":"652-678","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Improving learning ability of learning automata using chaos theory"],"prefix":"10.1007","volume":"77","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3535-5093","authenticated-orcid":false,"given":"Bagher","family":"Zarei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3775-5565","authenticated-orcid":false,"given":"Mohammad Reza","family":"Meybodi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,4,22]]},"reference":[{"issue":"2","key":"3293_CR1","first-page":"43","volume":"1","author":"OR Bolouki Speily","year":"2018","unstructured":"Bolouki Speily OR, Kardan A (2018) Modeling the information spreading in online blog communities using learning automata. Int J Web Res 1(2):43\u201355","journal-title":"Int J Web Res"},{"key":"3293_CR2","doi-asserted-by":"crossref","unstructured":"Harmon ME, Harmon SS (1997) Reinforcement learning: a tutorial. WRIGHT LAB WRIGHT-PATTERSON AFB OH","DOI":"10.21236\/ADA323194"},{"key":"3293_CR3","volume-title":"Reinforcement learning: an introduction","author":"RS Sutton","year":"2018","unstructured":"Sutton RS, Barto AG (2018) Reinforcement learning: an introduction. MIT press, Cambridge"},{"key":"3293_CR4","volume-title":"Learning automata: an introduction","author":"KS Narendra","year":"2012","unstructured":"Narendra KS, Thathachar MA (2012) Learning automata: an introduction. Courier Corporation, North Chelmsford"},{"issue":"3","key":"3293_CR5","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1109\/TEVC.2003.810069","volume":"7","author":"R Caponetto","year":"2003","unstructured":"Caponetto R, Fortuna L, Fazzino S, Xibilia MG (2003) Chaotic sequences to improve the performance of evolutionary algorithms. IEEE Trans Evol Comput 7(3):289\u2013304","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"3293_CR6","doi-asserted-by":"publisher","first-page":"013125","DOI":"10.1063\/1.5120094","volume":"30","author":"B Zarei","year":"2020","unstructured":"Zarei B, Meybodi MR, Masoumi B (2020) Chaotic memetic algorithm and its application for detecting community structure in complex networks. Chaos Interdiscip J Nonlinear Sci 30(1):013125","journal-title":"Chaos Interdiscip J Nonlinear Sci"},{"key":"3293_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-72428-7","volume-title":"Recent advances in learning automata","author":"A Rezvanian","year":"2018","unstructured":"Rezvanian A, Saghiri AM, Vahidipour SM, Esnaashari M, Meybodi MR (2018) Recent advances in learning automata. Springer, Berlin"},{"key":"3293_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-10767-3","volume-title":"Learning automata approach for social networks","author":"A Rezvanian","year":"2019","unstructured":"Rezvanian A, Moradabadi B, Ghavipour M, Khomami MMD, Meybodi MR (2019) Learning automata approach for social networks. Springer, Berlin"},{"key":"3293_CR9","volume-title":"Networks of learning automata: techniques for online stochastic optimization","author":"MA Thathachar","year":"2011","unstructured":"Thathachar MA, Sastry PS (2011) Networks of learning automata: techniques for online stochastic optimization. Springer, Berlin"},{"key":"3293_CR10","volume-title":"On-line Q-learning using connectionist systems","author":"GA Rummery","year":"1994","unstructured":"Rummery GA, Niranjan M (1994) On-line Q-learning using connectionist systems. University of Cambridge, Cambridge"},{"key":"3293_CR11","unstructured":"Watkins CJCH (1989) Learning from delayed rewards. PhD thesis, Cambridge University"},{"key":"3293_CR12","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1109\/TSMC.1983.6313077","volume":"5","author":"AG Barto","year":"1983","unstructured":"Barto AG, Sutton RS, Anderson CW (1983) Neuronlike adaptive elements that can solve difficult learning control problems. IEEE Trans Syst Man Cybern 5:834\u2013846","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"3293_CR13","doi-asserted-by":"crossref","unstructured":"Schwartz A (1993) A reinforcement learning method for maximizing undiscounted rewards. In: Proceedings of the Tenth International Conference on Machine Learning, vol 298, pp 298\u2013305","DOI":"10.1016\/B978-1-55860-307-3.50045-9"},{"key":"3293_CR14","doi-asserted-by":"publisher","DOI":"10.1201\/9781482288988","volume-title":"The essence of chaos","author":"F Lorenzelli","year":"2014","unstructured":"Lorenzelli F (2014) The essence of chaos. CRC Press, Boca Raton"},{"key":"3293_CR15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511554544","volume-title":"Explaining chaos","author":"P Smith","year":"1998","unstructured":"Smith P (1998) Explaining chaos. Cambridge University Press, Cambridge"},{"key":"3293_CR16","doi-asserted-by":"publisher","DOI":"10.1201\/9781482295412","volume-title":"Chaos theory tamed","author":"G Williams","year":"1997","unstructured":"Williams G (1997) Chaos theory tamed. CRC Press, Boca Raton"},{"key":"3293_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-32023-7","volume-title":"The logistic map and the route to chaos: from the beginnings to modern applications","author":"M Ausloos","year":"2006","unstructured":"Ausloos M, Dirickx M (2006) The logistic map and the route to chaos: from the beginnings to modern applications. Springer, Berlin"},{"key":"3293_CR18","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198507239.001.0001","volume-title":"Chaos and nonlinear dynamics: an introduction for scientists and engineers","author":"RC Hilborn","year":"2000","unstructured":"Hilborn RC (2000) Chaos and nonlinear dynamics: an introduction for scientists and engineers. Oxford University Press on Demand, Oxford"},{"issue":"2","key":"3293_CR19","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1016\/j.jocs.2013.10.002","volume":"5","author":"AH Gandomi","year":"2014","unstructured":"Gandomi AH, Yang X-S (2014) Chaotic bat algorithm. J Comput Sci 5(2):224\u2013232","journal-title":"J Comput Sci"},{"issue":"4","key":"3293_CR20","doi-asserted-by":"publisher","first-page":"827","DOI":"10.1007\/s00521-014-1751-5","volume":"26","author":"AR Jordehi","year":"2015","unstructured":"Jordehi AR (2015) A chaotic artificial immune system optimisation algorithm for solving global continuous optimisation problems. Neural Comput Appl 26(4):827\u2013833","journal-title":"Neural Comput Appl"},{"key":"3293_CR21","first-page":"1","volume":"2014","author":"H Lu","year":"2014","unstructured":"Lu H, Wang X, Fei Z, Qiu M (2014) The effects of using chaotic map on improving the performance of multiobjective evolutionary algorithms. Math Prob Eng 2014:1\u201316","journal-title":"Math Prob Eng"},{"issue":"3","key":"3293_CR22","first-page":"122","volume":"1","author":"I Vorontsova","year":"1965","unstructured":"Vorontsova I (1965) Algorithms for changing stochastic automata transition probabilities. Probl Peredachi Inform 1(3):122\u2013126","journal-title":"Probl Peredachi Inform"},{"key":"3293_CR23","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1109\/TSSC.1969.300206","volume":"5","author":"B Chandrasekharan","year":"1968","unstructured":"Chandrasekharan B, Shen D (1968) On expediency and convergence in variable structure stochastic automata. IEEE Trans Syst Sci Cybern 5:145\u2013149","journal-title":"IEEE Trans Syst Sci Cybern"},{"issue":"4","key":"3293_CR24","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1109\/TSSC.1969.300228","volume":"5","author":"IJ Shapiro","year":"1969","unstructured":"Shapiro IJ, Narendra KS (1969) Use of stochastic automata for parameter self-optimization with multimodal performance criteria. IEEE Trans Syst Sci Cybern 5(4):352\u2013360","journal-title":"IEEE Trans Syst Sci Cybern"},{"issue":"2","key":"3293_CR25","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1109\/TSMC.1972.4309112","volume":"SMC-2","author":"R Viswanathan","year":"1972","unstructured":"Viswanathan R, Narendra KS (1972) A Note on the linear reinforcement scheme for variable-structure stochastic automata. IEEE Trans Syst Man Cybern SMC-2(2):292\u2013294","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"3293_CR26","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1109\/TSMC.1974.5408453","volume":"4","author":"KS Narendra","year":"1974","unstructured":"Narendra KS, Thathachar MA (1974) Learning automata-a survey. IEEE Trans Syst Man Cybern 4:323\u2013334","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"3293_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0020-0255(82)90029-9","volume":"28","author":"M Meybodi","year":"1982","unstructured":"Meybodi M, Lakshmivarahan S (1982) \u025b-Optimality of a general class of learning algorithm. Inform Sci 28:1\u201320","journal-title":"Inform Sci"},{"key":"3293_CR28","doi-asserted-by":"publisher","first-page":"1143","DOI":"10.1109\/TSMC.1983.6313191","volume":"6","author":"MA Thathachar","year":"1983","unstructured":"Thathachar MA, Oommen BJ (1983) Learning automata processing ergodicity of the mean: the two-action case. IEEE Trans Syst Man Cybern 6:1143\u20131148","journal-title":"IEEE Trans Syst Man Cybern"},{"issue":"7","key":"3293_CR29","doi-asserted-by":"publisher","first-page":"1002","DOI":"10.1109\/9.599982","volume":"42","author":"S Poznyak","year":"1997","unstructured":"Poznyak S, Najim K (1997) On nonlinear reinforcement schemes. IEEE Trans Autom Control 42(7):1002\u20131004","journal-title":"IEEE Trans Autom Control"},{"key":"3293_CR30","volume-title":"Learning by distributed automata","author":"EJ Friedman","year":"1992","unstructured":"Friedman EJ, Shenker S (1992) Learning by distributed automata. University of California, California"},{"key":"3293_CR31","unstructured":"Thathachar MA, Sastry PS (1984) A class of rapidly converging algorithms for learning automata. In: IEEE International Conference on Cybernetics and Society, pp 602\u2013606"},{"issue":"3","key":"3293_CR32","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/0925-2312(94)00027-P","volume":"7","author":"AV Vasilakos","year":"1995","unstructured":"Vasilakos AV, Papadimitriou GI (1995) A new approach to the design of reinforcement schemes for learning automata: stochastic estimator learning algorithm. Neurocomputing 7(3):275\u2013297","journal-title":"Neurocomputing"},{"key":"3293_CR33","doi-asserted-by":"crossref","unstructured":"Papadimitriou GI, Pomportsis AS, Kiritsi S, Talahoupi E (2001) Absorbing stochastic estimator learning algorithms with high accuracy and rapid convergence. In: Proceedings ACS\/IEEE International Conference on Computer Systems and Applications. IEEE, pp 45\u201351","DOI":"10.1109\/AICCSA.2001.933950"},{"issue":"6","key":"3293_CR34","doi-asserted-by":"publisher","first-page":"1473","DOI":"10.1109\/21.199471","volume":"22","author":"JK Lanct\u00f4t","year":"1992","unstructured":"Lanct\u00f4t JK, Oommen BJ (1992) Discretized estimator learning automata. IEEE Trans Syst Man Cybern 22(6):1473\u20131483","journal-title":"IEEE Trans Syst Man Cybern"},{"issue":"2","key":"3293_CR35","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1109\/21.31041","volume":"19","author":"R Simha","year":"1989","unstructured":"Simha R, Kurose JF (1989) Relative reward strength algorithms for learning automata. IEEE Trans Syst Man Cybern 19(2):388\u2013398","journal-title":"IEEE Trans Syst Man Cybern"},{"issue":"4","key":"3293_CR36","doi-asserted-by":"publisher","first-page":"582","DOI":"10.1109\/24.370222","volume":"43","author":"AV Vasilakos","year":"1994","unstructured":"Vasilakos AV, Paximadis G (1994) Fault-tolerant routing algorithms using estimator discretized learning automata for high-speed packet-switched networks. IEEE Trans Reliab 43(4):582\u2013593","journal-title":"IEEE Trans Reliab"},{"key":"3293_CR37","unstructured":"Thathachar MA, Sastry PS (1986) Estimator algorithms for learning automata. In: Proceedings of the Platinum Jubilee Conference on Systems and Signal Processing, Department of Electrical Engineering, Indian Institute of Science, Bangalore, India"},{"issue":"3","key":"3293_CR38","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1109\/3477.931507","volume":"31","author":"BJ Oommen","year":"2001","unstructured":"Oommen BJ, Agache M (2001) Continuous and discretized pursuit learning schemes: various algorithms and their comparison. IEEE Trans Syst Man Cybern Part B (Cybernet) 31(3):277\u2013287","journal-title":"IEEE Trans Syst Man Cybern Part B (Cybernet)"},{"issue":"4","key":"3293_CR39","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1109\/21.105092","volume":"20","author":"BJ Oommen","year":"1990","unstructured":"Oommen BJ, Lanct\u00f4t JK (1990) Discretized pursuit learning automata. IEEE Trans Syst Man Cybern 20(4):931\u2013938","journal-title":"IEEE Trans Syst Man Cybern"},{"issue":"6","key":"3293_CR40","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1109\/TSMCB.2002.1049608","volume":"32","author":"M Agache","year":"2002","unstructured":"Agache M, Oommen BJ (2002) Generalized pursuit learning schemes: new families of continuous and discretized learning automata. IEEE Trans Syst Man Cybern Part B (Cybern) 32(6):738\u2013749","journal-title":"IEEE Trans Syst Man Cybern Part B (Cybern)"},{"key":"3293_CR41","unstructured":"Ge H, Li S, Li J, Ren X (2017) A parameter-free learning automaton scheme. arXiv:1711.10111"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-020-03293-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-020-03293-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-020-03293-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T23:20:28Z","timestamp":1619047228000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-020-03293-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,22]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["3293"],"URL":"https:\/\/doi.org\/10.1007\/s11227-020-03293-z","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"value":"0920-8542","type":"print"},{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,22]]},"assertion":[{"value":"22 April 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}