Enhanced Collaborative Optimization Using Alternating Direction Method of Multipliers

Siyu Tao, Kohei Shintani, Guang Yang, Herb Meingast, Daniel W. Apley, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Enhanced collaborative optimization (ECO) is a recently developed multidisciplinary design optimization (MDO) method in the family of collaborative optimization (CO). While ECO achieves better optimization performance than its predecessors, its formulation is much more complex and incurs higher computation and communication costs, mainly due to the use of linear models of nonlocal constraints (LMNC). Consequently, ECO is often not the most desirable MDO method for large-scale and/or highly coupled applications. In this paper, we propose a new method named “ECO-ADMM” by introducing the alternating direction method of multipliers (ADMM) to ECO. With the aid of Lagrangian multipliers, ECO-ADMM increases each discipline’s “awareness” of global constraint conditions and search history at a negligible cost of Lagrangian multipliers updating. We also propose a simplified version of ECO-ADMM which removes LMNC from the original ECO-ADMM. With case studies of two analytic test problems and an industrial vehicle suspension design problem, two main advantages of ECO-ADMM over ECO are observed. First, ECO-ADMM achieves faster convergence and better solutions than ECO in most cases where both methods have comparable settings. Second, in the cases where LMNC are removed, ECO-ADMM maintains a much higher level of optimization performance than ECO. Therefore, ECO-ADMM is expected to outperform ECO in most application scenarios, and its simplified version provides designers with the option of trading a reasonable level of performance for ease of implementation and lower computation and communication costs.

Original languageEnglish (US)
Pages (from-to)1571-1588
Number of pages18
JournalStructural and Multidisciplinary Optimization
Issue number4
StatePublished - Oct 1 2018


  • Alternating direction method of multipliers
  • Collaborative optimization
  • Distributed design optimization
  • Enhanced collaborative optimization
  • Multidisciplinary design optimization

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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