Abstract
The recurrent neural network approach to combinatorial optimization has during the last decade evolved into a competitive and versatile heuristic method that can be used on a wide range of problem types. In the state-of-the-art neural approach the discrete elementary decisions (not necessarily binary) are represented by continuous Potts mean-field neurons, interpolating between the available discrete states, with a dynamics based on iteration of a set of mean-field equations. Driven by annealing in an artificial temperature, they will converge into a candidate solution.
Preview
Unable to display preview. Download preview PDF.
References
Bellman, R. (1958): On a routing problem. Quarterly of Appl. Math. 16, 87–90.
Durbin, R., and Willshaw, D. (1987): An analog approach to the traveling salesman problem using an elastic net method. Nature 326, 689–691.
Gislén, L., Peterson, C., and Söderberg, B. (1989): Teachers and Classes with Neural Networks. Int. J. Neural Syst. 1, 167–176.
Gislén, L., Peterson, C., and Söderberg, B. (1992a): Rotor neurons — Basic formalism and dynamics. Neural Computat. 4, 737–745.
Gislén, L., Peterson, C., and Söderberg, B. (1992b): Complex scheduling with Potts neural networks. Neural Computat. 4, 805–831.
Gyulassy, M., and Harlander, H. (1991): Elastic tracking and neural network algorithms for complex pattern recognition. Comput. Phys. Commun. 66, 31–46.
Häkkinen, J., Lagerholm, M., Peterson, C., and Söderberg, B. (1998): A Potts neuron approach to communication routing. Neur. Computat. 10, 1587–1599.
Hopfield, J.J. (1982): Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558.
Hopfield, J.J., and Tank, D.W. (1985): Neural computation of decisions in optimization problems. Biol. Cybern. 52, 141–152.
Jönsson, B., Peterson, C., and Söderberg, B. (1993): A variational approach to correlations in polymers. Phys. Rev. Lett. 71, 376–379.
Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P. (1983): Optimization by simulated annealing. Science 220, 671–680.
Lagerholm, M., Peterson, C., and Söderberg, B. (1997): Airline crew scheduling with Potts neurons. Neur. Computat. 9, 1589–1599.
Ohlsson, M., Peterson, C., and Söderberg, B. (1993): Neural networks for optimization problems with inequality constraints — The knapsack problem. Neural Computat. 5, 331–339.
Ohlsson, M., Peterson, C., and Yuille, A. (1992): Track finding with deformable templates — The elastic arms approach. Comput. Phys. Commun. 71, 77–98.
Ohlsson, M., and Pi, H. (1997): A study of the Mean Field Approach to Knapsack Problems. Neur. Netw. 10, 263–271.
C. Peterson (1990): Parallel distributed approaches to combinatorial optimization problems — Benchmark studies on TSP. Neural Computat. 2, 261–269.
Peterson, C., and Anderson, J. R. (1988): Neural Networks and NP-complete Optimization Problems — A Performance Study on the Graph Partition Problem. Compl. Syst. 2, 59–89.
Peterson, C., and Söderberg, B. (1989): A new method for mapping optimization problems onto neural networks. Int. J. Neural Syst. 1, 3–22.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag
About this paper
Cite this paper
Söderberg, B. (1999). Optimization with neural networks. In: Clark, J.W., Lindenau, T., Ristig, M.L. (eds) Scientific Applications of Neural Nets. Lecture Notes in Physics, vol 522. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104284
Download citation
DOI: https://doi.org/10.1007/BFb0104284
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65737-8
Online ISBN: 978-3-540-48980-1
eBook Packages: Springer Book Archive