Abstract
In this paper we present a novel application to the cellular automata implementation of the diffusion-limited aggregation (DLA) model. This model, mainly used in Physics, Physical Chemistry, and Biology in the simulation of fractal growth phenomena is applied in the present work to the development of a heuristic problem-solving methodology. The method is applied in the solution of a hard combinatorial optimization problem, the Euclidean Traveling Salesman Problem. Experimental tests, carried out over a standard set of problem instances, show that the method outperforms, considering the quality of the produced solutions, another heuristic based on the real space renormalization theory. It is also found that it compares favourably (considering the computation time) with two other methods based on physical processes: The elastic net and simulated annealing methods.
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References
Witten T.A. and Sander L.M. Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon, Phys. Rev. Lett. 1981; 47: 1400
Witten T.A. and Sander L.M. Diffusion-Limited Aggregation, Phys. Rev. 1983; B 27: 5686
Sander L.M. Fractal Growth Processes, Nature 1986; 322: 789
Toffoli T. and Margolus N. Cellular Automata Machines: A New Environment for Modeling, The MIT Press Cambridge, 1987.
Stauffer D. Computer Simulations of Cellular Automata, J. Phys. 1991; A 24: 909
Vicsek T. Fractal Growth Phenomena, World Scientific Publishing, 1989.
Niemeyer L., Pietronero L., and Wiesmann H.J. Fractal Dimension of Dielectric Breakdown, Phys. Rev. Lett. 1984; 52: 1033
Fogedby H.C., Sorensen E.S., and Mouritsen O.G. Fractal Growth in Impurity Controlled Solidification, J. Chem. Phys. 1987; 87: 6706
Fogedby H.C. Modelling Fractal Growth of Bacillus Subtilis on Agar Plates, J. Phys. Soc. (Japan) 1991; 60: 704
Garey M.R. and Johnson D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, New York, 1979.
Miller D.L. and Pekny J.F. Exact Solution of Large Asymmetric Traveling Salesman Problems, Science 1991; 251: 754
Lin S. and Kernighan B.W., An Effective Heuristic Algorithm for the Traveling Salesman Problem, Oper. Res. 1973; 21: 498
Durbin R. and Willshaw D. An Analogue Approach to the Travelling Salesman Problem Using an Elastic Net Method, Nature 1987; 326: 689
Telfar G., Generally Applicable Heuristics for Global Optimisation: An Investigation of Algorithm Performance for the Euclidean Traveling Salesman Problem, M.Sc. Thesis, Victoria University of Wellington, New Zealand, October 1994.
Kirkpatrick S., Gelatt C.D. Jr., and Vecchi M.P. Optimization by Simulated Annealing, Science 1983; 220: 671
Goldberg D.E. Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, Massachusetts, 1989.
Zbigniew M. Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag New York, 1994.
Yoshiyuki U. and Yoshiki K. New Method of Solving the Traveling Salesman Problem Based on Real Space Renormalisation Theory, Phys. Rev. Lett. 1995; 75: 1683
Norman M.G. and Moscato P. The Euclidean Traveling Salesman Problem and a Space-Filling Curve, Chaos, Solitons, and Fractals 1995; 6: 389
Whitley D., Starkweather T. and Fuquay D’A. Scheduling Problems and Traveling Salesman: The Genetic Edge Recombination Operator. In Proc. of the Third International Conference on Genetic Algorithms. Schaffer J.D. ed. Morgan Kauffmann Publishers. Los Altos. CA, 1989.
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Moreno, J.A., Santos, J.G. (1998). A Problem-Solving Environment Based on Cellular Automata. In: Bandini, S., Serra, R., Liverani, F.S. (eds) Cellular Automata: Research Towards Industry. Springer, London. https://doi.org/10.1007/978-1-4471-1281-5_24
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DOI: https://doi.org/10.1007/978-1-4471-1281-5_24
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