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This thesis presents a coordination method for the distributed design optimization of
engineering systems. The design of advanced engineering systems such as aircrafts,
automated distribution centers, and microelectromechanical systems (MEMS) involves
multiple components that together realize the desired functionality. The design requires
detailed knowledge of the various physics that play a role in each component. Since a
single designer is no longer able to oversee all relevant aspects of the complete system, the
design process is distributed over a number of design teams. Each team autonomously
operates on a single component or aspect of the system, and uses dedicated analysis and
design tools to solve the specific problems encountered for this subsystem. Consequently,
one team is often not familiar with the design considerations of other teams, and does
not know how its decisions affect the system as a whole.
An additional challenge in systems design is introduced by market competitiveness
and increasing consumer requirements, which pushes systems towards the limits of
performance and cost. Since each subsystem contributes to the system performance,
the interaction between these subsystems, and thus design teams, becomes critical and
needs to be controlled.
Design optimization is an effective and powerful approach to finding optimal designs
when parametric models are available to describe the relevant system behavior. To fully
exploit the available design expertise, a coordination approach for distributed system
optimization is required that respects the organization of design teams and their tools.
The augmented Lagrangian coordination (ALC) method presented in this thesis is a
coordination approach for distributed optimization that a) provides disciplinary design
autonomy, b) offers the designer a large degree flexibility in setting up the coordination
structure, c) maintains mathematical rigor, and d) is efficient in obtaining optimal and
consistent designs. ALC is based on a combination of augmented Lagrangian relaxation
and block-coordinate descent, two techniques from mathematical programming.
What distinguishes ALC from other coordination methods for distributed system design
is its flexibility in combination with its mathematical rigor. The flexibility relates both to
the structure of the coordination process, and to the type of coupling that is allowed.
Most coordination methods with convergence proof follow a hierarchical structure in
which a single master problem is in charge of coordination. The master problem
is superimposed over the disciplinary subproblems that communicate only with this
master problem. ALC allows a more general, non-hierarchical coordination structure
in which coordination may also be performed between disciplinary subproblems directly.
Furthermore, ALC can coordinate not only linking variables, but also coupling functions.
The mathematical rigor assures that, under suitable assumptions, the solutions obtained
with ALC algorithms are optimal and consistent. Specialized ALC algorithms based on
the efficient alternating direction method of multipliers are developed for problems that
have only linking variables and/or block-separable coupling constraints. Furthermore, we
demonstrate that the well-known analytical target cascading method is a subclass of ALC.
ALC algorithms can be proven to converge to locally optimal and consistent designs
under smoothness assumptions, provided that subproblem solutions are globally optimal.
Global optimality is however difficult, if not impossible, to guarantee in practice since
many engineering design problems are non-convex. When only local optimality can
be obtained, ALC methods can no longer be proven to yield optimal or consistent
solutions. Experiments with several non-convex problems show however that ALC with
locally optimal solutions to subproblems often still converges to a local or global system
optimum; however, occasionally inconsistent designs are encountered. Performing a
global search at subproblems improves the convergence behavior, and globally optimal
solutions are frequently obtained.
The work in this thesis is part of MicroNed, a national research programme on
microsystem technology. In the emerging field of microsystem technology, optimization
of cost, size, and performance are very relevant since these factors determine whether
microsystems can be successful alternatives for existing “macro” systems. Proper
functioning of the microdevice may increasingly depend on model-based optimization
during the design. To illustrate how coordination methods can be used in microsystem
optimal design, a micro-accelerometer design problem has been developed, inspired on a
commercially available device. The goal of the design problem is to find the dimensions
of the accelerometer such that its area is minimized subject to performance requirements
on sensitivity, noise, and bandwidth, while considering mechanical, electrostatic,
dynamic, and electrical constraints. The behavioral models are analytical, providing a
reproducible benchmark problem for performance assessments of coordination methods
in distributed optimization.