ROMANSY 11 pp 355-362 | Cite as

# Hopfield’s Artificial Neural Networks In Multiobjective Optimization Problems of Resource Allocations Control

## Summary

Some robots cooperating each other to perform connected operations can be considered as a system. This system should be controlled to take advantages of different robots assigning to several operations. Indeed, a control of robot-operation allocations as a sequence of many static optimization task of resource allocations with different input parameters can be formulated. If some robot control problems are transformed to this resource allocation problem, then it is possible to use the proposed below methods. In this paper, analog Hopfield’s artificial neural networks are used by genetic algorithms for solving NP-hard binary multiobjective optimization problems, which can be considered in modeling of resource allocations control. This problem can be solved for improving the efficiency of a few connected robots dining their activities. Moreover, another neural approach for dynamic optimal control is elaborated. Finally, an example of two-layer feed-forward network in the adaptive control system of the underwater vehicle motion is submitted.

## Keywords

External Input Synaptic Weight Multiobjective Optimization Problem Gain Coefficient Adaptive Control System## Preview

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## References

- 1.Ayer S.V.B., Niranjan M., Failside F.:
*A Theoretical Investigation into the Per-formance of Hopfield Model*. IEEE Trans. on Neural Networks, vol 1, No. 2, 1990, pp. 204–215.CrossRefGoogle Scholar - 2.Ameljanczyk A.:
*Multicriterion Optimization*WAT, Warszawa 1986.(in polish)Google Scholar - 3.Balicki J, Kitowski Z.:
*Multicriteria Optimization of Computer Resource Allocations with Using Genetic Algorithms and Artificial Neural Networks*,Proceedings of the 12th International Conference on Systems Science, Vol. III, September 1995, Wroclaw, Poland, pp. 11–18.Google Scholar - 4.Cichocki A., Unbehauen R.:
*Neural Networks for Solving Systems of Linear Equations and Related Problems*. IEEE Trans. on Circuits and Systems, vol. 39, No. 2, February 1992, pp. 124–137.CrossRefMATHGoogle Scholar - 5.Charalambous C.:
*A New Approach to Multicriterion Optimization Problem and Its Application to the Design of 1-D Digital Filters.*IEEE Trans. on Circuits and Systems, Vol. 36, No. 6, June 1989, pp. 773–784.Google Scholar - 6.Cohen M.A., Grossberg S.:
*Absolute Stability of Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks*. WEE Trans. S.st., Man, and Cybem., vol SMC-13, September/October 1983, pp. 815–825.Google Scholar - 7.Ferreira RAY, Borges T.C.D.:
*System Modeling and Optimization Under Vector- Valued Criteria*. Automatica, Vol. 30, No. 2, 1994, pp. 331–336.CrossRefMATHMathSciNetGoogle Scholar - 8.Hertz J., Krogh A., Palmer R.:
*An Introduction to Neural Calculations Theory*. WNT, Warszawa 1993. (in polish)Google Scholar - 9.Hipel K.H., Radford K.J., Fang L.:
*Multiple Participant–Multiple Criteria Deci-sion*IEEE Trans. on Systems, Man, and Cybernetics, vol. 23, No.4, July/August 1993, pp. 1184–1189.Google Scholar - 10.Kitowski Z, Garas J.:
*A Structure and Principles of Operation of the Adaptive Control System of the Underwater Vehicle Motion*Proceedings of RoManSy 10: The Tenth CISM-IFToMM Symposium. Springer-Verlag, Wien New York, 1995, pp. 201–209.Google Scholar - 11.Lillo W.E., Hui S., Zak H:
*Neural Networks for Constrained Optimization Problems*. Int. J. of Circuit Theory and Applications, voL21, 1991, pp. 385–399.Google Scholar - 12.Seaman C. M., Desrochers A. A.:
*A Multiobjective Optimization Approach to Pla-stic Injection Molding*. IEEE Trans. on System, Man, and Cybernetics, Vol. 23, No. 2, March/April 1993, pp. 414–425.Google Scholar - 13.Sun K.T., Fu H.C.:
*A Hybrid Neural Model for Solving Optimization Problems*. WEE Trans. on Computers, vol. 42, No. 2, February 1993, pp. 219–227.Google Scholar - 14.Tarvainen K.:
*Generating Pareto - Optimal Alternatives by a Nonfeasible Hierar-chical Method. JOTA*, voL 80, No. 1, January 1994, pp. 181–185.Google Scholar - 15.Tagliarini A., Christ J.F., Page W:
*Optimization Using Neural Networks*. JEFF, Trans. on Computers, vo140, No. 12, December 1991, pp. 1347–1357.Google Scholar - 16.Tank D.W., Hopfield J.J.:
*Simple “Neural” Optimization Networks: An A/D Con- verter, Signal Decision Circuit,and Linear Programming Circuit*. JEFF Trans. on Circuits and Systems,voLCAS-33, May 1986, pp. 533–541.Google Scholar - 17.Bung S, ConstantindesAG.:
*Lagrange Programming Neural Networks*. IEEE Trans. on Circuits and Systems, vol. 39, No. 7, July 1992.Google Scholar