Augmented Lagrangian coordination for distributed optimal design in MDO

• Published in: International journal for numerical methods in engineering Vol. 73; no. 13; pp. 1885 - 1910
• Main Authors: Tosserams, S., Etman, L. F. P., Rooda, J. E.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 26.03.2008; Wiley
• Subjects: Applied sciences; augmented Lagrangian; block coordinate descent; decomposition; distributed optimization; Exact sciences and technology; Mechanical engineering. Machine design; multidisciplinary design optimization; penalty methods; distributed optimization; Coordination; multidisciplinary design optimization; decomposition; Substructure; penalty methods; Optimization; Optimal design; Engineering design; Design process; block coordinate descent; Lagrange multiplier; Karush Kuhn Tucker method; Augmented Lagrangian; Descent method; Subsystem; Relaxation method; Lagrangian method; Numerical convergence; Multidisciplinary; Coordination method; Mathematical programming; Large scale system
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2158

Quite a number of coordination methods have been proposed for the distributed optimal design of large‐scale systems consisting of a number of interacting subsystems. Several coordination methods are known to have numerical convergence difficulties that can be explained theoretically. The methods for which convergence proofs are available have mostly been developed for so‐called quasi‐separable problems (i.e. problems with individual subsystems coupled only through a set of linking variables, not through constraints and/or objectives). In this paper, we present a new coordination approach for multidisciplinary design optimization problems with linking variables as well as coupling objectives and constraints. Two formulation variants are presented, offering a large degree of freedom in tailoring the coordination algorithm to the design problem at hand. The first, centralized variant introduces a master problem to coordinate coupling of the subsystems. The second, distributed variant coordinates coupling directly between subsystems. Our coordination approach employs an augmented Lagrangian penalty relaxation in combination with a block coordinate descent method. The proposed coordination algorithms can be shown to converge to Karush–Kuhn–Tucker points of the original problem by using the existing convergence results. We illustrate the flexibility of the proposed approach by showing that the analytical target cascading method of Kim et al. (J. Mech. Design‐ASME 2003; 125(3):475–480) and the augmented Lagrangian method for quasi‐separable problems of Tosserams et al. (Struct. Multidisciplinary Opt. 2007, to appear) are subclasses of the proposed formulations. Copyright © 2007 John Wiley & Sons, Ltd.