Alternating Direction Method of Multipliers as Simple Heuristic for Topology Optimization of a Truss With Uniformed Member Cross Sections

Abstract

This paper presents a simple and effective heuristic for topology optimization of a truss under the constraint that all the members of the truss have the common cross-sectional area. The proposed method consists of multiple restarts of the alternating direction method of multipliers (ADMM) with random initial points. It is shown that each iteration of the ADMM can be carried out very easily. In the numerical experiments, the efficiency of the proposed heuristic is compared with the existing global optimization method based on the mixed-integer second-order cone programming (MISOCP). It is shown that even for large-scale problem instances that the global optimization method cannot solve within practically acceptable computational cost, the proposed method can often find a feasible solution having a fairly good objective value within moderate computational time.