Alternating Direction Method of Multipliers for Truss Topology Optimization with Limited Number of Nodes: A Cardinality-Constrained Second-Order Cone Programming Approach

TL;DR

This paper introduces a heuristic method based on the alternating direction method of multipliers to efficiently solve truss topology optimization problems with limited nodes, recast as a cardinality-constrained second-order cone program.

Contribution

It proposes a novel heuristic approach for cardinality-constrained truss optimization using ADMM, offering a computationally efficient alternative to global mixed-integer methods.

Findings

The proposed method often finds solutions with good objective values.

It requires less computational time compared to global optimization.

Numerical experiments validate the effectiveness of the heuristic.

Abstract

This paper addresses the compliance minimization of a truss, where the number of available nodes is limited. It is shown that this optimization problem can be recast as a second-order cone programming with a cardinality constraint. We propose a simple heuristic based on the alternative direction method of multipliers. The efficiency of the proposed method is compared with a global optimization approach based on mixed-integer second-order cone programming. Numerical experiments demonstrate that the proposed method often finds a solution having a good objective value with small computational cost.