Global Optimization of Network Length and Simulation of Film Evolution
An idealized thin film when subjected to some constraints acquires length-minimizing properties. The length-minimizing curve of the film may achieve a configuration close to the Steiner minimal tree in the Euclidean plane. The Steiner problem asks for the shortest network that spans a given set of fixed points in the Euclidean plane. The main idea is to use the mathematical model for an idealized wet film, connecting the fixed points with some liquid inside the film. Gradually decreasing the interior area, the film may achieve the globally optimal solution. A system of equations and an algorithm for simulating wet film evolution are presented here. Computational experiments and tests show the abilities of global optimization. The investigation of a simple case illustrates how the film evolution leads up to the global optimum.
Key wordsglobal optimization Steiner problem unconventional computing wet film simulation
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