A hybrid evolutionary algorithm for the Euclidean Steiner tree problem using local searches

Abstract

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%. © Springer-Verlag Berlin Heidelberg 2006.