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References
Aarts, E.H.L. and Korst, J. (1989) Simulated Annealing and Boltzmann Machines. John Wiley & Sons., Essex.
Aiyer, S.V.B., Niranjan, M. and Fallside, F. (1990) A theoretical investigation into the performance of the Hopfield model. IEEE Transactions on Neural Networks, 1, 204–215.
Akiyama, Y., Yamashita, A., Kajiura, M. and Aiso, H. (1989) Combinatorial optimization with gaussian machines. Proceedings IEEE International Joint Conference on Neural Networks, 1, 533–540.
Amartur, S.C., Piraino, D. and Takefuji, Y. (1992) Optimization neural networks for the segmentation of magnetic resonance Images. IEEE Transactions on Medical Imaging, 11, 215–220.
Angeniol, B., Vaubois, G. and Le Texier, J.Y. (1988) Self-organizing feature maps and the travelling salesman problem. Neural Networks, 1, 289–293.
Barr, R.S., Golden, B.L., Kelly, J.P., Resende, M.G.C. and Stewart, W.R. (1995) Designing and reporting on computational experiments with heuristic methods. Journal of Heuristics, 1, 9–32.
Boeres, M.S.C., de Carvalho, L.A.V. and Barbosa, V.C. (1992) A faster elastic net algorithm for the traveling salesman problem. In: Proceedings of the International Joint Conference on Neural Networks. Baltimore, U.S.A., II-215-220.
Brandt, R.D., Wang, Y., Laub, A.J. and Mitra, S.K. (1988) Alternative networks for solving the travelling salesman problem and the list-matching problem. Proceedings International Conference on Neural Networks Vol. 2, 333–340.
Bruch, J. (1990) On the convergence properties of the Hopfield model. Proceedings of the IEEE, 78(10), 1579–1585.
Burke, L.I. (1994) Adaptive neural networks for the traveling salesman problem: insights from operations research. Neural Networks, 7, 681–690.
Burke, L.I. and Damany, P. (1992) The guilty net for the traveling salesman problem. Computers & Operations Research, 19, 255–265.
Burke, L.I. and Ignizio, J.P. (1992) Neural networks and operations research: an overview. Computers & Operations Research, 19, 179–189.
Chen, L. and Aihara, K. (1995) Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks, 8(6), 915–930.
Desieno, D. (1988) Adding a conscience mechanism to competitive learning. In: Proceedings of the IEEE International Conference on Neural Networks, San Diego, U.S.A., I-117-124.
Durbin, R. and Willshaw, D.J. (1987) An analogue approach to the traveling salesman problem using an elastic net method. Nature, 326, 689–691.
Favata, F. and Walker, R. (1991) A study of the application of Kohonen-type neural networks to the traveling salesman problem. Biological Cybernetics, 64, 463–468.
Foo, Y.P.S. and Szu, H. (1989) Solving large-scale optimization problems by divide-and-conquer neural networks. Proceedings IEEE International Joint Conference on Neural Networks, 1, 507–511.
Garey, M.R. and Johnson, D.S. (1979) Computers and Intractability. W.H. Freeman, New York.
Gee, A.H. (1993) Problem Solving with Optimization Networks, Ph.D. Dissertation, Queen’s College, Cambridge University, U.K.
Ghaziri, H. (1991) Solving routing problems by a self-organizing map. In: T. Kohonen, K. Makisara, O. Simula and J. Kangas (eds.), Artificial Neural Networks. North-Holland, Amsterdam, pp. 829–834.
Ghaziri, H. (1996) Supervision in the self-organizing feature map: application to the vehicle routing problem. In: I.H. Osman and J.P. Kelly (eds.), Meta-Heuristics: Theory & Applications. Kluwer, Boston, pp. 651–660.
Glover, F. (1994) Optimization by ghost image processes in neural networks. Computers & Operations Research, 21, 801–822.
Goldstein, M. (1990) Self-organizing feature maps for the multiple traveling salesmen problem. In: Proceedings of the International Neural Network Conference. Paris, France, pp. 258–261.
Hegde, S., Sweet, J. and Levy, W. (1988) Determination of parameters in a hopfield/tank computational network. Proceedings IEEE International Conference on Neural Networks, 2, 291–298.
Hinton, G.E., Sejnowski, T.J. and Ackley, D.H. (1984) Boltzmann machines: constraint satisfaction networks that learn. Carnegie Mellon University Technical Report CMU-CS-84-119.
Hopfield, J.J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, 79, 2554–2558.
Hopfield, J.J. (1984) Neurons with Graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences, 81, 3088–3092.
Hopfield, J.J. and Tank, D.W. (1985) Neural computation of decisions in optimization problems. Biological Cybernetics, 52, 141–152.
Hooker, J.N. (1995) Testing heuristics: we have it all wrong. Journal of Heuristics, 1, 33–42.
Johnson, D.S. (1990) Local optimization and the traveling salesman problem. In: G. Goos and J. Hartmanis (eds.), Automata, Languages and Programming, Lecture Notes in Computer Science 443. Springer-Verlag, Berlin, pp. 446–461.
Kamgar-Parsi, B. and Kamgar-Parsi, B. (1987) An efficient model of neural networks for optimization. Proceedings IEEE International Conference on Neural Networks, 3, 785–790.
Kamgar-Parsi, B. and Kamgar-Parsi, B, (1992) Dynamical stability and parameter selection in neural optimization. Proceedings IEEE International Conference on Neural Networks, 4, 566–571.
Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P. (1983) Optimization by simulated annealing. Science, 220, 671–680.
Kohonen, T. (1982) Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43, 59–69.
Kohonen, T. (1988) Self-Organization and Associative Memory. Springer, Berlin.
Lai, W.K. and Coghill, G.G. (1992) Genetic breeding of control parameters for the Hopfield/Tank neural net. Proceedings International Joint Conference on Neural Networks, 4, 618–623.
Lai, W.K. and Coghill, G.G. (1994) Initialising the continuous Hopfield net. Proceedings IEEE International Conference on Neural Networks, 7, 4640–4644.
Lin, S. and Kernighan, B.W. (1973) An effective heuristic algorithm for the travelling salesman problem. Operations Research, 21, 498–516.
Lo, J.T.-H. (1992) A new approach to global optimization and its applications to neural networks. Proceedings IEEE International Joint Conference on Neural Networks, 4, 600–605.
Looi, C.K. (1992) Neural network methods in combinatorial optimization. Computers & Operations Research, 19, 191–208.
Matsuyama, Y. (1991) Self-organization via competition, cooperation and categorization applied to extended vehicle routing problems. In: Proceedings of the International Joint Conference on Neural Networks. Seattle, U.S.A., I-385-390.
McCulloch, W.S. and Pitts, W. (1943) A logical calculus of ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5, 115–133.
Minsky, M. and Papert, S. (1969) Perceptrons. MIT Press, Cambridge, MA.
Naphade, K. and Tuzun, D. (1995) Initializing the Hopfield-Tank network for the TSP using a convex hull: a computational study. Intelligent Engineering Systems Through Artificial Neural Networks. vol. 5. ASME Press, New York, pp. 399–404.
Nemhauser, G.L. and Wolsey, L.A. (1988) Integer and Combinatorial Optimization. John Wiley & Sons, Canada.
Peterson, C. and Soderberg, B. (1989) A new method for mapping optimization problems onto neural networks. International Journal of Neural Systems, 1, 3–22.
Peterson, C. and Soderberg, B. (1993) Artificial neural networks. In: C.R. Reeves (ed.), Modern Heuristic Techniques for Combinatorial Optimisation, Chapter 5. Blackwell Scientific Publishers, Oxford, UK.
Potvin, J.Y. (1993) The traveling salesman problem: a neural network perspective. ORSA Journal on Computing, 5, 328–348.
Potvin, J.Y. and Robillard, C. (1995) Clustering for vehicle routing with a competitive neural network model. Neurocomputing, 8, 125–139.
Rosenblatt, F. (1958) The perceptron: a probabilistic model for information storage and organization in the brain. Psychological Review, 65, 386–408.
Rumelhart, D.E. and McClelland, J.L. (1986) Parallel distributed processing: explorations in the microstructure of cognition, I & II. MIT Press, Cambridge, MA.
Schwartz, B.L., Das, P. and Koch, J.B. (1991) Initialization in Hopfield networks. Neurocomputing, 3(3), 135–145.
Simmen, M. W. (1991) Parameter sensitivity of the elastic net approach to the traveling salesman problem. Neural Computation, 3, 363–374.
Smith, K.A. (1995) Solving the generalized quadratic assignment problem using a self-organizing process. In: Proceedings IEEE International Conference on Neural Networks 4, Perth, Australia, pp. 1876–1879.
Smith, K.A. (1999) Neural networks for combinatorial optimization: a review of more than a decade of research. INFORMS Journal on Computing, 11, 15–34.
Smith, K.A., Abramson, D. and Duke, D. (1999) Efficient timetabling formulations for Hopfield neural networks. In: C. Dagli et a), (eds.), Smart Engineering System Design: Neural Networks, Fuzzy Logic, Evolutionary Programming, Data Mining, and Complex Systems, vol. 9. ASME Press, pp. 1027–1032.
Smith, K.A., Palaniswami, M., Krishnamoorthy, M. (1996) A hybrid neural approach to combinatorial optimization. Computers & Operations Research, 23, 597–610.
Szu, H. and Hartley, R. (1987) Fast simulated annealing. Physics Letters A, 122, 157–162.
Szu, H. (1988) Fast TSP algorithm based on binary neuron output and analog input using zero-diagonal interconnect matrix and necessary and sufficient conditions of the permutation matrix. Proceedings IEEE International Conference on Neural Networks, 2, 259–266.
Takefuji, Y. and Szu, H. (1989) Design of parallel distributed Cauchy machines Proceedings IEEE International Joint Conference on Neural Networks, 1, 529–532.
Tank, D.W. and Hopfield, J.J. (1986) Simple neural optimization networks: an A/D converter, signal decision circuit and a linear programming circuit. IEEE Transactions on Circuit Systems, 33, 533–541.
Vakhutinsky, A.I. and Golden, B.L. (1994) Solving vehicle routing problems using elastic nets. Proceedings of the IEEE International Conference on Neural Networks, 7, 4535–4540.
Vakhutinsky, A.I. and Golden, B.L. (1995) A hierarchical strategy for solving traveling salesman problems using elastic nets. Journal of Heuristics, 1, 67–76.
Van Den Bout, D.E. and Miller, T.K. (1988) A travelling salesman objective function that works. Proceedings IEEE International Conference on Neural Networks, 2, 299–303.
Van Den Bout, D.E. and Miller, T.K. (1989) Improving the performance of the Hopfield-Tank neural network through normalization and annealing. Biological Cybernetics, 62, 129–139.
Van Den Bout, D.E. and Miller, T.K. (1990) Graph partitioning using annealed neural networks. IEEE Transactions on Neural Networks, 1, 192–203.
Willshaw, D.J. and von der Malsburg, C. (1979) A marker induction mechanism for the establishment of ordered neural mappings: its application to the retinotectal problem. Philosophical Transactions of the Royal Society, Series B, 287, 203–243.
Wilson, G. V. and Pawley, G.S. (1988) On the stability of the TSP algorithm of Hopfield and Tank. Biological Cybernetics, 58, 63–70.
Wolfe, W.J. (1999) A fuzzy Hopefield-Tank traveling salesman problem model. INFORMS Journal on Computing, 11(4), 329–344.
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Potvin, JY., Smith, K.A. (2003). Artificial Neural Networks for Combinatorial Optimization. In: Glover, F., Kochenberger, G.A. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 57. Springer, Boston, MA. https://doi.org/10.1007/0-306-48056-5_15
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