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Extracting subgraphs by Mixed Integer Programming for discrete design of truss structures

In this paper, we consider a discrete design problem of two-dimensional truss structures. We are given a set of potential nodes and a set of potential bars connecting these nodes, i.e., a ground structure. Then we only treat solutions which are combinations of accepted nodes and accepted bars in the ground structure. We present a linear inequality system with integrality constraints to extract a subgraph from the ground structure, which tries to model the subgraph on a simple truss. The linear inequality system delivers a MIP (Mixed Integer Programming) formulation of the discrete design problem. We also conduct numerical experiments to examine the solutions obtained by solving the MIP problem, and report some valid examples. The test problem instances are exactly solved by GLPK (GNU Linear Programming KIT), which is one of well-known open source softwares solving MIP and LP (Linear Programming) problems.