Look the Partial Equilibrium with the Global Optimum from the Problem of the Shortest Circuit for Three Villages
Xiao Wei Jiang, Yu Hu, Yueting Yang, Tian Luan · Advanced materials research · 2014
We explore the relationship between the partial equilibrium and the global optimum from the problem of the shortest circuit for three villages (PSCTV). Using the related properties of Fermat point and the circumcenter of the triangle, we can come to the conclusion that the partial equilibrium sometimes brings into correspondence with the global optimum but there is a great deal of difference between the two by analysing the difference between the sum of distances from Fermat point to all vertices and the ones from circumcenter to all vertices.