Analysis of the behaviour of multilevel hierarchical systems of learning automata and their application for multimodal functions optimization

REFERENCES

• BUSH , R. R. and MOSTELLER , F. , 1958 , Stochastic Models for Learning ( New York Wiley ).
   Google Scholar
• LACKSHMIVARAHAN , S. , 1981 , Learning Algorithms Theory and Applications ( New York Springer-Verlag ).
   Google Scholar
• MACMUHTY , G. J. , and Fu , K. S. , 1966 . A variable structure automaton used as a multimodal searching technique. IEEE Transactions on Automatic Control , 11 , 379 – 387 .
   Google Scholar
• NAJIM , K. , 1988 , Multivariate control of liquid-liquid extraction columns using a probabilistic automaton. Proceedings of the Institution of Electrical Engineers , Pt D , 135 , 479 – 485 ; 1990,Modelling and hierarchical learning control of a dryer. Applied Mathematical Modelling, 14, 655–660 .
   Google Scholar
• NAJIM , K. , and POZNYAK , A. S. , 1994 , Learning Automata Theory and Applications ( London , U.K. Elsevier ).
   Google Scholar
• NARENDRA , K. S. , and WHEELER , R. M. , 1986 , Recent developments in learning automata , in Narendra, K. S. (Ed.) Adaptive and Learning Systems; Theory and Applications ( New York Plenum ).
   Google Scholar
• NAZIN , A. V. , and POZNYAK , A. S. , 1986 , Adaptive Choice of Variants ( Moscow Nauka ) ( in Russian ).
   Google Scholar
• POZNYAK , A. S. NAJIM , K. , and CHTOUROU , M. , 1996 , Learning automata with continuous inputs and their application for multimodal functions optimization. International Journal of Systems Science , 27 , 87 – 95 .
   Web of Science ®Google Scholar
• ROBBINS , H. , and SIEGMUND , D. , 1971 , A convergence theorem for non-negative almost supermartingales and some applications. Proc. of the Symposium on Optimizing Methods in Statistics , Ohio State University , 14–16 June 1971, edited by J. S, Rustagi , pp. 233 – 257 .
   Google Scholar
• THATHACHAR , M. A. L. , and RAMAKRISHNAN , K. R. , 1981 , A hierarchical system of learning automata. IEEE Transactions on Systems, Man and Cybernetics , 11 , 236 – 341 .
   Google Scholar
• TZYPKIN , YA. Z. , and POZNYAK , A. S. , 1972 , Learning finite automata. Technical Cybernetics , 3 , 127 – 140 ,
   Google Scholar
• VARSHAVSKIY V. I. , and VORONTSOVA , I. P. , 1963 , On the behavior of stochastic automata with variable structure. Automation and Remote Control , 24 , 327 – 333 .
   Google Scholar
• Tel: +(525) 747 70 00 EXTN 3229; Fax. + (525) 747 70 89
   Google Scholar
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