A Hybrid Evolutionary Algorithm for the Euclidean Steiner Tree Problem Using Local Searches

  • Byounghak Yang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4251)


In this paper we introduce a hybrid evolutionary algorithm for the Euclidean Steiner tree problem (ESTP) which is to find a minimum-length Euclidean interconnection of a set of terminals in the plane. The individual is an assembly of locations of a non-fixed number of Steiner points and number of Steiner points. We use the operators crossover, mutation and selection. A Steiner points pool is introduced base on the optimal 3-terminal Steiner points generation and the minimum spanning tree. An initial population is generated by random selecting from the Steiner points pool. To improve the solution quality, some Steiner points in individual are deleted and rearranged. Randomly generated Steiner points are inserted in selected individual to search a new solution. Experimental results show that the quality of solution is improved by the hybrid operator. The gap between the optimal solution and the solution of hybrid evolutionary algorithm is less than 0.3%.


Local Search Minimum Span Tree Steiner Tree Steiner Point Steiner Tree Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Byounghak Yang
    • 1
  1. 1.Industrial EngineeringKyungwon UniversitySeongnam-si, Kyunggi-doKorea

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