Neuro-Optimizer: A New Artificial Intelligent Optimization Tool and Its Application for Robot Optimal Controller Design


The main objective of this paper is to introduce a new intelligent optimization technique that uses a predictioncorrection
strategy supported by a recurrent neural network for finding a near optimal solution of a given
objective function. Recently there have been attempts for using artificial neural networks (ANNs) in optimization
problems and some types of ANNs such as Hopfield network and Boltzmann machine have been applied in
combinatorial optimization problems. However, ANNs cannot optimize continuous functions and discrete
problems should be mapped into the neural networks architecture. To overcome these shortages, we introduce a
new procedure for stochastic optimization by a recurrent artificial neural network. The introduced neurooptimizer
(NO) starts with an initial solution and adjusts its weights by a new heuristic and unsupervised rule to
compute the best solution. Therefore, in each iteration, NO generates a new solution to reach the optimal or
near optimal solutions. For comparison and detailed description, the introduced NO is compared to genetic
algorithm and particle swarm optimization methods. Then, the proposed method is used to design the optimal
controller parameters for a five bar linkage manipulator robot. The important characteristics of NO are:
convergence to optimal or near optimal solutions, escaping from local minima, less function evaluation, high
convergence rate and easy to implement.


[1] J. Hopfield, and D. Tank, Neural computation
of decisions in optimization problems,
Biological Cybernetics, Vol. 52, 1985, pp. 141-
[2] G.E. Hinton, and T.J. Sejnowsky, Optimal
perceptual inference, Proceedings of the IEEE
Conference on Computer Vision and Pattern
Recognition, Washigton, 1983, pp. 448-453.
[3] D. Amit, H. Gutfreund, and H. Sompolinsky,
Spin-Glass models of neural networks,
Physical Review Letters A 32, 1985, pp. 1007-
[4] Y. Akiyama, A. Yamashita, M. Kajiura, and H.
Aiso, Combinatorial optimization with
gaussian machines, Proceedings IEEE
International Joint Conference on Neural
Networks 1, 1989, pp. 533–540.
[5] T. Kohonen, Self-Organized formation of
topologically correct feature maps, Biological
Cybernetics 43, 1982, pp. 59–69.
[6] A.H. Gee, and R. W. Prager, Limitations of
neural networks for solving traveling salesman
problems, IEEE Trans. Neural Networks, vol.
6, 1995, pp. 280–282.
[7] M. Goldstein, Self-Organizing feature maps for
the multiple traveling salesman problem
(MTSP), Proceedings IEEE International
Conference on Neural Networks, Paris, 1990,
pp. 258–261.
[8] Y. P. S. Foo, and Y. Takefuji, Stochastic neural
networks for job-shop scheduling: parts 1 and
2, Proceedings of the IEEE International
Conference on Neural Networks 2, 1988, pp.
[9] Y.P. S. Foo, and Y. Takefuji, Integer Linear
programming neural networks for job shop
scheduling, Proceedings of the IEEE
International Conference on Neural Networks
2, 1988, pp. 341–348.
[10] J.S. Lai, S.Y. Kuo, and I.Y. Chen, Neural
networks for optimization problems in graph
theory, Proceedings IEEE International
Symposium on Circuits and Systems 6, 1994,
pp. 269–272.
[11] D.E. Van Den Bout, and T.K. Miller, Graph
partitioning using annealed neural networks,
IEEE Transactions on Neural Networks 1,
1990, pp. 192–203.
[12] S. Vaithyanathan, H. Ogmen, and J. IGNIZIO,
Generalized boltzmann machines for
multidimensional knapsack problems,
Intelligent Engineering Systems Through
Artificial Neural Networks 4, ASME Press,
New York, 1994, pp. 1079–1084.
[13] A. Yamamoto, M. Ohta, H. Ueda, A. Ogihara,
and K. Fukunaga, Asymmetric neural network
and its application to knapsack problem, IEICE
Transactions Fundamentals E78-A, 1995, pp.
[14] K. Urahama, and H. Nishiyuki, Neural
algorithms for placement problems,
Proceedings International Joint Conference on
Neural Networks 3, Nagoya, 1993, pp. 2421–
[15] K.E. Nygard, P. Jueli, and N. Kadaba, Neural
networks for selecting vehicle routing
heuristics, ORSA Journal of Computing 2,
1990, pp. 353–364.
[16] A.I. Vakhutinsky, and B. L. Golden, Solving
vehicle routing problems using elastic nets,
Proceedings IEEE International Conference on
Neural Networks 7, 1994, pp. 4535–4540.
[17] L. Fang, W. H. Wilson, and T. Li, Mean-Field
annealing neural net for quadratic assignment,
Proceedings International Conference on
Neural Networks, Paris, 1990, pp. 282–286.
[18] G.A. Tagliarini, and E. W. Page, Solving
constraint satisfaction problems with neural
networks, Proceedings IEEE International
Conference on Neural Networks 3, 1987, pp.
[19] M. Kajiura, Y. Akiyama, and Y. Anzai, Solving
large scale puzzles with neural networks,
Proceedings Tools for AI Conference, Fairfax,
1990, pp. 562–569.
[20] N. Funabiki and Y. Takefuji, A neural network
parallel algorithm for channel assignment
problems in cellular radio networks, IEEE
Trans. Veh. Technol., vol. 41, Nov. 1992, pp.
[21] K. Smith, and M. Palaniswami, Static and
dynamic channel assignment using neural
networks, IEEE Journal on Selected Areas in
Communications 15, 1997, pp. 238–249.
[22] T. Bultan and C. Aykanat, Circuit partitioning
using parallel mean field annealing algorithms,
Proceedings 3rd IEEE Symposium on Parallel
and Distributed Processing, 1991, pp. 534–541.
[23] U. Halici, Artificial neural networks, EE 543
Lecture Notes, Middle East Technical
University, Ankara, Turkey, 2004.
[24] J.H. Holland, Adaptation in natural and
artificial systems, University of Michigan
Press, Ann Arbor, MI, Internal Report, 1975.
[25] Y. Shi, and R. Eberhart, A modified particle
swarm optimizer, Proceedings of the IEEE
international conference on evolutionary
computation, Piscataway, NJ: IEEE Press;
1998, pp. 69–73.
[26] J.G. Ziegler and N.B. Nichols, “Optimum
settlings for automatic controllers,” Trans. On
ASME., vol. 64, pp. 759-768, 1942.
[27] Z.L. Gaing, “A Particle Swarm Optimization
Approach for Optimum Design of PID
controller in AVR system,” IEEE Transactions
on Energy Conversion, vol. 9, no. 2, pp. 384-
391, 2003.
[28] Z.Y. Zhao, M. Tomizuka, and S. Isaka, “Fuzzy
gain scheduling of PID controllers,” IEEE
Trans. System, Man, and Cybernetics, vol. 23,
no. 5, pp. 1392-1398, 1993.
[29] S.Y. Chu, C.C. Teng, “Tuning of PID
controllers based on gain and phase margin
specifications using fuzzy neural network,”
Fuzzy Sets and Systems, vol. 101, no. 1, pp.
21-30, 1999.
[30] G. Zhou and J.D. Birdwell, “Fuzzy logic-based
PID autotuner design using simulated
annealing,” Proceedings of the IEEE/IFAC
Joint Symposium on Computer-Aided Control
System Design, pp. 67 – 72, 1994.
[31] R.A. Krohling and J.P. Rey, “Design of optimal
disturbance rejection PID controllers using
genetic algorithm,” IEEE Trans. Evol.
Comput., vol. 5, pp. 78–82, 2001.
[32] D.H. Kim, “Tuning of a PID controller using a
artificial immune network model and local
fuzzy set,” Proceedings of the Joint 9th IFSA
World Congress and 20th NAFIPS
International Conference, vol. 5, pp. 2698 –
2703, 2001.
[33] Y.T. Hsiao, C.L. Chuang, and C.C. Chien, “Ant
colony optimization for designing of PID
controllers,” Proceedings of the 2004 IEEE
Conference on Control Applications/
International Symposium on Intelligent
Control/International Symposium on Computer
Aided Control Systems Design, Taipei, Taiwan,
[34] D. Wang and M. Vidyasagar, “Modeling of a
five-bar-Linkage Manipulator with One
Flexible Link,” in Proc. IEEE Int. Symp,
subject, Turkey, pp. 21–26, 1988.
[35] D. Wang, J.P. Huissoon and K. Luscott, “A
teaching robot for demonstrating robot control
strategies,” manufacturing research corporation
of Ontario, 1993.