A micro-accelerometer MDO benchmark problem

Many optimization and coordination methods for multidisciplinary design optimization (MDO) have been proposed in the last three decades. Suitable MDO benchmark problems for testing and comparing these methods are few however. This article presents a new MDO benchmark problem based on the design optimization of an ADXL150 type lateral capacitive micro-accelerometer. The behavioral models describe structural and dynamic effects, as well as electrostatic and amplification circuit contributions. Models for important performance indicators such as sensitivity, range, noise, and footprint area are presented. Geometric and functional constraints are included in these models to enforce proper functioning of the device. The developed models are analytical, and therefore highly suitable for benchmark and educational purposes. Four different problem decompositions are suggested for four design cases, each of which can be used for testing MDO coordination algorithms. As a reference, results for an all-in-one implementation, and a number of augmented Lagrangian coordination algorithms are given. © 2009 The Author(s)

An augmented Lagrangian coordination method for distributed optimal design in MDO: Part II examples

The formulation flexibility and the numerical performance of the augmented Lagrangian coordination method proposed in the part I paper is demonstrated on several example problems. Results for a number of test problems indicate that the coordination method is effective and robust in finding solutions of the original non-decomposed problem, and does not introduce new local minima for non-convex problems. The required coordination costs are found to be determined by how the problem is partitioned and coordinated. These costs do not only depend on the number of quantities that have to be coordinated, but also on their coupling strengths. The formulation flexibility of the new method provides means to minimize these costs by adapting the problem at hand

An augmented Lagrangian coordination method for distributed optimal design in MDO: Part I formulation and algorithms

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 shared variables, not through constraints and/or objectives). In this paper we present a new coordination method for MDO problems with coupling variables as well as coupling objectives and constraints. Our approach employs an augmented Lagrangian penalty relaxation in combination with a block coordinate descent method. The coordination method can be shown to converge to KKT points of the original problem by using existing convergence results. 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. In a sequel paper we demonstrate the flexibility of the formulations, and investigate the numerical behavior of the proposed method

Compromise Based Evolutionary Multiobjective Optimization Algorithm for Multidisciplinary Optimization

International audienceMultidisciplinary Design Optimization deals with engineering problems composed of several sub-problems - called disciplines - that can have antagonist goals and thus require to find compromise solutions. Moreover, the sub-problems are often multiobjective optimization problems. In this case, the compromise solutions between the disciplines are often considered as compromises between all objectives of the problem, which may be not relevant in this context. We propose two alternative definitions of the compromise between disciplines. Their implementations within the well-known NSGA-II algorithm are studied and results are discussed

Block-separable linking constraints in augmented Lagrangian coordination

Augmented Lagrangian coordination (ALC) is a provably convergent coordination method for multidisciplinary design optimization (MDO) that is able to treat both linking variables and linking functions (i.e. system-wide objectives and constraints). Contrary to quasi-separable problems with only linking variables, the presence of linking functions may hinder the parallel solution of subproblems and the use of the efficient alternating directions method of multipliers. We show that this unfortunate situation is not the case for MDO problems with block-separable linking constraints. We derive a centralized formulation of ALC for block-separable constraints, which does allow parallel solution of subproblems. Similarly, we derive a distributed coordination variant for which subproblems cannot be solved in parallel, but that still enables the use of the alternating direction method of multipliers. The approach can also be used for other existing MDO coordination strategies such that they can include block-separable linking constraints

Extension of Analytical Target Cascading Using Augmented Lagrangian Coordination for Multidisciplinary Design Optimization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77083/1/AIAA-2008-5843-768.pd

Target Exploration for Disconnected Feasible Regions in Enterprise-Driven Multilevel Product Design

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77105/1/AIAA-13908-831.pd