Enhanced Collaborative Optimization Using Alternating Direction Method of Multipliers
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 comp...
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Published in | Structural and multidisciplinary optimization Vol. 58; no. 4; pp. 1571 - 1588 |
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Main Authors | , , , , , |
Format | Journal Article |
Language | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2018
Springer Nature B.V |
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Abstract | 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. |
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AbstractList | 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. |
Author | Chen, Wei Shintani, Kohei Tao, Siyu Apley, Daniel W. Yang, Guang Meingast, Herb |
Author_xml | – sequence: 1 givenname: Siyu surname: Tao fullname: Tao, Siyu organization: Department of Mechanical Engineering, Northwestern University – sequence: 2 givenname: Kohei surname: Shintani fullname: Shintani, Kohei organization: Department of Mechanical Engineering, Northwestern University – sequence: 3 givenname: Guang surname: Yang fullname: Yang, Guang organization: Reliability Simulation and Innovation, Toyota Motor North America, Inc – sequence: 4 givenname: Herb surname: Meingast fullname: Meingast, Herb organization: Reliability Simulation and Innovation, Toyota Motor North America, Inc – sequence: 5 givenname: Daniel W. surname: Apley fullname: Apley, Daniel W. organization: Department of Industrial Engineering & Management Sciences, Northwestern University – sequence: 6 givenname: Wei orcidid: 0000-0002-4653-7124 surname: Chen fullname: Chen, Wei email: weichen@northwestern.edu organization: Department of Mechanical Engineering, Northwestern University |
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Cites_doi | 10.2514/6.2000-4720 10.1002/nme.2158 10.2514/1.15326 10.2514/1.14254 10.1016/j.jspi.2004.02.014 10.2514/1.J051895 10.2514/6.2008-5841 10.1115/DETC2008-50038 10.1007/s11081-005-1744-4 10.1115/1.4001346 10.2514/2.3825 10.1115/DETC2017-67976 10.1115/1.1582501 10.2514/1.22263 10.2514/6.2006-6950 10.2514/1.40649 10.1007/s10915-015-0048-x 10.2514/6.1994-4325 10.1007/s00158-005-0579-0 10.1016/0898-1221(76)90003-1 |
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Keywords | Alternating direction method of multipliers Distributed design optimization Collaborative optimization Enhanced collaborative optimization Multidisciplinary design optimization |
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SubjectTerms | Collaboration Computation Computational Mathematics and Numerical Analysis Constraint modelling Design optimization Engineering Engineering Design Multidisciplinary design optimization Multipliers Research Paper Suspension systems Theoretical and Applied Mechanics |
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