Abstract
This work proposes an Artificial Immune System to find a set of k spanning trees with low costs and distinct topologies. The attainment of this set of solutions is necessary when the problem has restrictions or when the interest is to present good alternative solutions for posterior decision making. Solving this problem means to explore an enormous space of solutions that grows as the number of graph nodes increases; it becomes impractible using exact or comparative methods. However, it is known that bio-inspired algorithms have a high capacity of exploration and exploitation of the search space. Moreover, inherent characteristics of AIS become the search mechanism more efficient allowing the resolution of this problem in a feasible computational time.
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References
Ahuja, R.K., Magnati, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms and Applications, 1st edn. Prentice-Hall, United States (1993)
Ali, M., Ramamurthy, B., Deogun, J.S.: Routing and Wavelenght Assignment with Power Considerations in Optical Networks. Computer Networks 32, 539–555 (2000)
Almeida, T.A., Yamakami, A.: Evolutionary Computation Applied to Solve the Minimum Spanning Tree Problem with Fuzzy Parameters. Master Thesis, School of Electrical and Computing Engineering, State University of Campinas (in Portuguese) (2006)
Coello Coello, C.A., Cortés, N.C.: Solving Multiobjective Optimization Problems Using an Artificial Immune System. Genetic Programming and Evolvable Machines 6, 163–190 (2005)
Dasgupta, D.: Artificial Immune Systems and Their Applications, 1st edn. Springer, Nova York (1998)
De Castro, L.N., Von Zuben, F.J.: Immune Engineering: Development and Application of Computational Tools Inspired in Artificial Immune Systems. PhD Thesis, State University of Campinas, School of Electrical and Computing Engineering (in Portuguese) (2001)
Keko, H., Skok, M., Skrlec, D.: Artificial Immune Systems in Solving Routing Problems. Computer as Tool. In: EUROCON 2003. Computer as Tool, The IEEE Region, vol. 8(1), pp. 62–66 (2003)
Lederberg, J.: Ontogeny of the Clonal Selection Theory of Antibody Formation. Annals of the New York Ac. of Sc. 546, 175–182 (1988)
Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, 3rd edn. Springer, Heidelberg (1996)
Minty, G.J.: A Simple Algorithm for Listing All the Trees of a Graph. IEEE Transactions on Circuit Theory CT-12, 120 (1965)
Murty, K.G.: An Algorithm for Ranking All the Assignments in Order of Increasing Cost. Operations Research 16, 682–687 (1986)
Okada, S.: Interactions Among Paths in Fuzzy Shortest Path Problems. In: Proceedings of the 9th International Fuzzy Systems Associations World Congress, pp. 41–46 (2001)
Raidl, R.G., Julstrom, B.A.: Edge-Sets: An Effective Evolutionary Coding of Spanning Trees. Research Report, Vienna University of Technology, Institute of Computer Graphics and Algorithms (2001)
Sörensen, K., Janssens, G.K.: An Algorithm to Generate All Spanning Trees of a Graph in Order of Increasing Cost. Operacional Research 25, 219–229 (2005)
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Berbert, P.C., Freitas Filho, L.J.R., Almeida, T.A., Carvalho, M.B., Yamakami, A. (2007). Artificial Immune System to Find a Set of k-Spanning Trees with Low Costs and Distinct Topologies. In: de Castro, L.N., Von Zuben, F.J., Knidel, H. (eds) Artificial Immune Systems. ICARIS 2007. Lecture Notes in Computer Science, vol 4628. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73922-7_34
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DOI: https://doi.org/10.1007/978-3-540-73922-7_34
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