S. Tosserams

Globally Convergent Optimization Algorithm Using Conservative Convex Separable Diagonal Quadratic Approximations

We implement and test a globally convergent sequential approximate optimization algorithm based on (convexified) diagonal quadratic approximations. The algorithm resides in the class of globally convergent optimization methods based on conservative convex separable approximations developed by Svanberg. At the start of each outer iteration, the initial curvatures of the diagonal quadratic approximations are estimated using historic objective and/or constraint function value information, or by building the diagonal quadratic approximation to the reciprocal approximation at the current iterate. During inner iterations, these curvatures are increased if no feasible descent step can be made. Although this conditional enforcement of conservatism on the subproblems is a relaxation of the strict conservatism enforced by Svanberg, global convergence is still inherited from the conservative convex separable approximations framework developed by Svanberg. A numerical comparison with the globally convergent version of the method of moving asymptotes and the nonconservative variants of both our algorithm and method of moving asymptotes is made.

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

Analytical target cascading (ATC) is a method originally developed for translating system-level design targets to design specifications for the elements comprising the system. ATC has also been shown to be useful for coordinating distributed design optimization of hierarchical, multilevel systems. The traditional ATC formulation uses a hierarchically decomposed problem structure, in which coordination is performed by communicating target and response values between parents and children. This paper presents two extensions of the ATC formulation to allow non-hierarchical target-response coupling between subproblems and to introduce system-wide constraints that depend on local variables of two or more subproblems. The ATC formulation with these extensions belongs to a subclass of augmented Lagrangian coordination, and has thus converge properties under the usual convexity and continuity assumptions. A supersonic business jet design problem reported earlier in the literature is used to illustrate these extensions.

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.

An Augmented Lagrangian Decomposition Method for Quasi-Separable Problems in MDO

Several decomposition methods have been proposed for the distributed optimal design of quasiseparable problems encountered in Multidisciplinary Design Optimization (MDO). Some of these methods are known to have numerical convergence difficulties that can be explained theoretically. We propose a new decomposition algorithm for quasi-separable MDO problems. In particular, we propose a decomposed problem formulation based on the augmented Lagrangian penalty function and the block coordinate descent algorithm. The proposed solution algorithm consists of inner and outer loops. In the outer loop, the augmented Lagrangian penalty parameters are updated. In the inner loop, our method alternates between solving an optimization master problem and solving disciplinary optimization subproblems. The coordinating master problem can be solved analytically; the disciplinary subproblems can be solved using commonly available gradient-based optimization algorithms. The augmented Lagrangian decomposition method is derived such that existing proofs can be used to show convergence of the decomposition algorithm to S. Tosserams (B) · L. F. P. Etman · J. E. Rooda Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands e-mail: s.tosserams@tue.nl L. F. P. Etman e-mail: l.f.p.etman@tue.nl J. E. Rooda e-mail: j.e.rooda@tue.nl Karush–Kuhn–Tucker points of the original problem under mild assumptions. We investigate the numerical performance of the proposed method on two example problems.