On steiner trees and genetic algorithms
Abstract
In this paper the application of a Genetic Algorithm (GA) to the Steiner tree problem is described. The performance of the GA is compared to that of the Simulated Annealing Algorithm (SA) and one of the best conventional algorithms given by RaywardSmith and Clare [1] (RCA).
Particular attention has been paid to find an optimal setting of the parameters and operators of the GA. A mutation probability P _{M}=0.01 and a crossover probability P _{C}=0.5 have been obtained according to the values found by Grefenstette [2]. An optimal population size has been chosen using a heuristic comparable to that of Goldberg
In addition the application of two problem specific heuristics is discussed, the removal of Steiner points of degree <3 and a local relaxation of the tree. A speedup of ≈20 was obtained if these heuristics were applied to the computation of the fitness only without changing the individuals themselves. For a fair comparison, these heuristics have been applied to the GA, the SA, and, in contrast to its original definition, to the RCA.
According to our results, all three algorithms find the optimum and converge equally fast, i.e., GA and SA need not more function evaluations than the RCA, that has even been improved by the relaxation heuristic. The GA reaches the optimum in a small number of generations which is considered the reason why it did not show an even better performance.
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 Title
 On steiner trees and genetic algorithms
 Book Title
 Parallelism, Learning, Evolution
 Book Subtitle
 Workshop on Evolutionary Models and Strategies Neubiberg, Germany, March 10–11, 1989 Workshop on Parallel Processing: Logic, Organization, and Technology — WOPPLOT 89 Wildbad Kreuth, Germany, July 24–28, 1989 Proceedings
 Pages
 pp 509525
 Copyright
 1991
 DOI
 10.1007/3540550275_30
 Print ISBN
 9783540550273
 Online ISBN
 9783540466635
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 565
 Series Subtitle
 Lecture Notes in Artificial Intelligence
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Author Affiliations

 1. Physics Institute, University of Heidelberg, Heidelberg, West Germany
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