Treatment of combinatorial optimization problems using selection equations with cost terms. Part I. Two-dimensional assignment problems

Physica D: Nonlinear Phenomena

Volumn 134, Issue 2, 1999, Pages 227-241

  Haken, H ^a   Schanz, M ^b   Starke, J ^c  

^a UNIVERSITY OF STUTTGART   (Germany)

^b Inst Parallele Verteilte H   (Germany)

^c UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005896827     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00112-8     Document Type: Article

References (19)

1. H. Achatz, P. Kleinschmidt, K. Paparrizos, A dual forest algorithm for the assignment problem, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 4 (1991) 1-10.
2. M. Bestehorn, H. Haken, Associative memory of a dynamical system: the example of the convection instability, Zeitschrift für Physik B 82 (1991) 305-308.
3. M. Garey, D. Johnson, Computers and Intractability, Freeman, San Francisco, 1979.
4. H. Haken, Pattern formation and pattern recognition - an attempt at a synthesis, in: H. Haken (Ed.), Pattern Formation by Dynamic Systems and Pattern Recognition, vol. 5, Springer Series in Synergetics, Springer, Heidelberg, 1979, pp. 2-13.
5. H. Haken, Synergetics, An Introduction, Springer Series in Synergetics, Springer, Heidelberg, 1983.
6. H. Haken, Synergetic Computers and Cognition - A Top-Down Approach to Neural Nets, Springer Series in Synergetics, Springer, Heidelberg, 1991.
7. H. Haken, Decision making and optimization in regional planning, in: M. Beckmann, B. Johansson, F. Snickars, R. Thord (Eds.), Knowledge and Networks in a Dynamic Economy, Springer, Berlin, 1998.
8. M. Hestenes, Optimization Theory, Wiley, New York, 1975.
9. M. Hirsch, J. Starke, Combinatorial optimization based on coupled selection equations, Part II: piecewise continuous selection equations, unpublished, 1998.
10. J. Hopfield, D. Tank, Neural computation of decisions in optimization problems, Biological Cybernetics 52 (1985) 141-152.
11. M. Mezard, G. Parisi, M. Virasoro, Spin Glass Theory and Beyond, World Scientific, Singapore, 1987.
12. P. Molnár, J. Starke, Control of distributed autonomous robotic systems using principles of pattern formation in nature and pedestrian behaviour, submitted, 1999.
13. C. Papadimitriou, K. Steiglitz, Combinatorial Optimization-Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, NJ, 1982.
14. W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C, Cambridge University Press, Cambridge, 1992.
15. J. Starke, Cost oriented competing processes - a new handling of assignment problems, in: J. Doležal and J. Fidler (Eds.), System Modelling and Optimization, Chapman & Hall, London, 1996, pp. 551-558.
16. J. Starke, Kombinatorische Optimierung auf derBasis gekoppelter Selektionsgleichungen, Ph.D. thesis, Universität Stuttgart, Verlag Shaker, Aachen, 1997.
17. J. Starke, Combinatorial optimization based on coupled selection equations, Part I: continuous selection equations, unpublished, 1998.
18. J. Starke, M. Schanz, Dynamical system approaches to combinatorial optimization, in: D.-Z. Du and P. Pardalos (Eds.), Handbook of Combinatorial Optimization, vol. 2, Kluwer Academic Publishers, Dordrecht, 1998 pp. 471-524.
19. J. Starke, M. Schanz, H. Haken, Self-organized behaviour of distributed autonomous mobile robotic systems by pattern formation principles, in: T. Lueth, R. Dillmann, P. Dario, H. Wörn (Eds.), Distributed Autonomous Robotic Systems 3, Springer, Heidelberg, 1998, pp. 89-100.