Geometry-Experiment Algorithm for Steiner Minimal Tree Problem

Abstract

It is well known that the Steiner minimal tree problem is one of the classical nonlinear combinatorial optimization problems. A visualization experiment approach succeeds in generating Steiner points automatically and showing the system shortest path, named Steiner minimum tree, physically and intuitively. However, it is difficult to form stabilized system shortest path when the number of given points is increased and irregularly distributed. Two algorithms, geometry algorithm and geometry-experiment algorithm (GEA), are constructed to solve system shortest path using the property of Delaunay diagram and basic philosophy of Geo-Steiner algorithm and matching up with the visualization experiment approach (VEA) when the given points increase. The approximate optimizing results are received by GEA and VEA for two examples. The validity of GEA was proved by solving practical problems in engineering, experiment, and comparative analysis. And the global shortest path can be obtained by GEA successfully with several actual calculations.