By Marcus Brazil (auth.), Xiu Zhen Cheng, Ding-Zhu Du (eds.)
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Additional info for Steiner Trees in Industry
189-203.  E. Lodi, F . Luccio and L. Pagli, Routing in times square mode, In/aTm. Process. 35 (1990) pp. 41-48. 26 M. A. Melzak. On the problem of Steiner, Canad. Math. Bull. 143-148 . A. Melzak. Companion to Concrete Mathematics Vol. II, (John Wiley & Sons , New York , 1976) . H. A. Thomas, The calculus of variations and the Steiner problem, Ann. Oper. Res .. Vol. 33 (1991) pp. 481-499 .  M . Sarrafzadeh, Hierar-ch1;cal Approaches to VLSI Circuit Layout. D. thesis, University of Illinois at Urbana-Champaign, 1986.
If we just connect them by minimum spanning tree (MSpT) , we get a tree as in Fig. 3(a) with cost 10. But if we add an extra (Steiner) node, shown as solid circle in Fig. 3(b), then the distance of the tree is reduced by more than 10%. 4 ,4 6--- ~-- 6 (a) Figure 3: Minimum spanning tree vs. minimum Steiner tree: Example 1 Similar comparison is shown in Fig. 4. Fig. 4(a) is the M SpT and Fig. 4(b) is the MEStT, where three Steiner nodes are introduced. Finding M EStT is more flexible in the sense that one can add any number of intermediate nodes at any suitable locations to make the distance of the tree minimum.
The solution in its original form is referred to as phenotype, whereas its binary encoded version is called genotype or chromosome. It is best to have a one-to-one mapping between the solution of the problem and the chromosome representation. But it is possible to have a one-to-many mapping, where these redundant chromosomes could be the cause of inefficiency of GA. ails and need some post-processing. The phenotype may be thought of as the semantics or the interpretation of the genotype. In general, there should be an easy and preferably injective mapping from genotype to phenotype.
Steiner Trees in Industry by Marcus Brazil (auth.), Xiu Zhen Cheng, Ding-Zhu Du (eds.)