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Constraints Satisfaction through Recursive Neural Networks with Mixed Penalties: a Case Study

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Abstract

This paper investigates an industrial assignment problem. It is modelized as a constraint satisfaction problem of large size with linear inequalities and binary variables. A new analog neuron-like network is proposed to find out feasible solutions to problems having several thousands of 0/1 variables. The approach developed in this paper is based on mixed-penalty functions: exterior penalty functions together with interior penalty functions. Starting from a near-binary solution satisfying each linear inequality, the network generates trial solutions located outside or inside the feasible set, in order to minimize an energy function which measures the total binary infeasibility of the system. The performances of the network are demonstrated on real data sets.

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References

  1. S.M. Aourid, X.D. Do and B. Kaminska, “Penalty formulation for 0/1 linear programming problem: a neural network approach”, in: Proceedings of the International Conference on Neural Networks (ICNN'95). pp. 1690–1693. Perth, Western Australia, 1995.

  2. A. Cichocki and R. Unbehauen, “Neural networks for solving systems of linear equations and related problems”, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 39(2), 124–138, 1992.

    Google Scholar 

  3. S.P. Eberhardt, T. Daud, D.A. Kerns, T.X. Brown and A.P. Thakoor, “Competitive neural architecture for hardware solution to the assignment problem”, Neural Networks 4, 431–442, 1991.

    Google Scholar 

  4. L. Fang and T. Li, “Design of competition-based neural networks for combinatorial optimization”, International Journal of Neural Systems 1(3), 221–235, 1990.

    Google Scholar 

  5. C.C. Gonzaga, “Path-following methods for linear programming”, SIAM Review 34(2), 167–224.

  6. L. Hérault and J.J. Niez, “Neural networks & combinatorial optimization: a study of NP-complete graph problems”, in: E. Gelenbe (ed.) Neural Networks: Advances and Applications. Elsevier Science Publishers B.V. (North-Holland), pp. 165–213, 1991.

    Google Scholar 

  7. J. Hopfield and D. Tank, “Neural computation of decisions in optimization problems”, Biological Cybernetics 52, 141–152, 1985.

    Google Scholar 

  8. C. Privault and L. Hérault, “Solving a real world assignment problem with a metaheuristic”, to appear in the Journal of Heuristics, Kluwer Academic Publishers.

  9. A. Schrijver, Theory of Linear and Integer Programming. John Wiley ed., Chichester, 1986.

  10. K. Urahama and T. Yamada, “Constrained Potts mean field systems and their electronic implementation”, International Journal of Neural Systems 5(3), 229–239, 1994.

    Google Scholar 

  11. G.N. Vanderplaats, Numerical Optimization Techniques for Engineering Design. McGraw-Hill, New-York, 1984.

    Google Scholar 

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Privault, C., Hérault, L. Constraints Satisfaction through Recursive Neural Networks with Mixed Penalties: a Case Study. Neural Processing Letters 8, 15–26 (1998). https://doi.org/10.1023/A:1009660928212

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  • DOI: https://doi.org/10.1023/A:1009660928212

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