A New Geometric Algorithm for Steiner Minimal Tree Problem by referring Visualization Experiment

It is well known that the Steiner minimal tree problem is one of the classic 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 forming stabilized system shortest path when the number of given points are increased and irregular distribution. A new algorithm, geometry-experiment algorithm (GEA), is constructed to solve system shortest path using the nature of Delaunay diagram and basic philosophy of geo-Steiner algorithm, and matching up with the visualization experiment approach (VEA) when given points are increasing in this paper. The approximate optimizing results are received by GEA and VEA for some practical power transmission grid system. 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.