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Research Papers: Design Automation

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

[+] Author and Article Information
Yoshihiro Kanno

Mathematics and Informatics Center,
The University of Tokyo,
Hongo 7-3-1,
Tokyo 113-8656, Japan
e-mail: kanno@mist.i.u-tokyo.ac.jp

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 2, 2018; final manuscript received July 31, 2018; published online October 10, 2018. Assoc. Editor: Samy Missoum.

J. Mech. Des 141(1), 011403 (Oct 10, 2018) (9 pages) Paper No: MD-18-1178; doi: 10.1115/1.4041174 History: Received March 02, 2018; Revised July 31, 2018

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.

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Figures

Grahic Jump Location
Fig. 1

Example (I). The problem setting for (NX,NY)=(8,2).

Grahic Jump Location
Fig. 2

Example (I). The optimal solutions of the conventional optimization problem: (a) (NX,NY)=(8,2), (b) (NX,NY)=(10,2), (c) (NX,NY)=(12,2), and (d) (NX,NY)=(14,2).

Grahic Jump Location
Fig. 3

Example (I). The solutions obtained by the ADMM approach (20 trials): (a) (NX,NY)=(8,2), (b) (NX,NY)=(10,2), (c) (NX,NY)=(12,2), and (d) (NX,NY)=(14,2).

Grahic Jump Location
Fig. 4

Example (I). The solutions obtained by the ADMM approach (100 trials): (a) (NX,NY)=(12,2) and (b) (NX,NY)=(14,2).

Grahic Jump Location
Fig. 5

Example (I). The optimal solutions obtained by the MISOCP approach: (a) (NX,NY)=(8,2), (b) (NX,NY)=(10,2), and (c) (NX,NY)=(12,2).

Grahic Jump Location
Fig. 6

Example (I). The best feasible solution obtained by the MISOCP approach for (NX,NY)=(14,2).

Grahic Jump Location
Fig. 7

Example (II). The problem setting for (NX,NY)=(11,4).

Grahic Jump Location
Fig. 8

Example (II). The optimal solutions of the conventional optimization problem: (a) (NX,NY)=(11,4), (b) (NX,NY)=(16,4), (c) (NX,NY)=(26,6), and (d) (NX,NY)=(30,8).

Grahic Jump Location
Fig. 9

Example (II). The best feasible solutions obtained by the ADMM approach: (a) (NX,NY)=(11,4); (b) (NX,NY)=(16,4); (c) (NX,NY)=(26,6), and (d) (NX,NY)=(30,8).

Grahic Jump Location
Fig. 10

Example (II). The best feasible solutions obtained by the MISOCP approach: (a) (NX,NY)=(11,4), (b) (NX,NY)=(16,4), (c) (NX,NY)=(26,6), and (d) (NX,NY)=(30,8).

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