Abstract
The rectilinear Steiner tree problem (RSTP) is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree (MST) on some set Steiner points. The RSTP is known to be NP-complete. The RSTP has received a lot of attention in the literature and heuristic and optimal algorithms have been proposed. A key performance measure of the algorithm for the RSTP is the reduction rate that is achieved by the difference between the objective value of the RSTP and that of the MST without Steiner points. An evolution algorithm for RSTP based upon the Prim algorithm was presented. The computational results show that the evolution algorithm is better than the previously proposed other heuristics. The average reduction rate of solutions from the evolution algorithm was about 11%, which is almost similar to that of optimal solutions.
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References
Bäck, T.: Evolutionary Algorithm in Theory and Practice. Oxford University Press, Oxford (1996)
Beasley, J.E.: OR-Library: distributing test problems by electronic mail. Journal of the Operational Research Society 41, 1069–1072 (1990)
Beasley, J.E.: A heuristic for Euclidean and rectilinear Steiner problems. European Journal of Operational Research 58, 284–292 (1992)
France, R.L.: A note on the optimum location of new machines in existing plant layouts. J. Industrial Engineering 14, 57–59 (1963)
Ganley, J.L.: Computing optimal rectilinear Steiner trees: A survey and experimental evaluation. Discrete Applied Mathematics 90, 161–171 (1999)
Garey, M.R., Johnson, D.S.: The rectilinear Steiner tree problem is NP-complete. SIAM Journal on Applied Mathematics 32, 826–834 (1977a)
Hanan, M.: On Steiner’s problem with rectilinear distance. SLAM Journal on Applied Mathematics 14, 255–265 (1966)
Hesser, J., Manner, R., Stucky, O.: Optimization of Steiner Trees using Genetic Algorithms. In: Proceedings of the Third International Conference on Genetic Algorithm, pp. 231–236 (1989)
Lee, J.L., Bose, N.K., Hwang, F.K.: Use of Steiner’s problem in suboptimal routing in rectilinear metric. IEEE Transaction son Circuits and Systems 23, 470–476 (1976)
Smith, J.M., Lee, D.T., Liebman, J.S.: An O(n log n) heuristic algorithm for the rectilinear Steiner minimal tree problem. Engineering Optimization 4, 172–192 (1980)
Smith, J.M., Liebman, J.S.: Steiner trees, Steiner circuits and the interface problem in building design. Engineering Optimization 2, 15–36 (1979)
Soukup, J., Chow, W.F.: Set of test problems for the minimum length connection networks. ACM/SIGMAP Newsletter 15, 48–51 (1973)
Warme, D.M., Winter, P., Zachariasen, M.: Exact Algorithms for Plane Steiner Tree Problems: A Computational Study. In: Du, D.Z., Smith, J.M., Rubinstein, J.H. (eds.) Advances in Steiner Tree. Kluwer Academic Publishers, Dordrecht (1998)
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Yang, B. (2005). An Evolution Algorithm for the Rectilinear Steiner Tree Problem. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424925_27
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DOI: https://doi.org/10.1007/11424925_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25863-6
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