67,244 research outputs found
Constraint interface preconditioning for topology optimization problems
The discretization of constrained nonlinear optimization problems arising in
the field of topology optimization yields algebraic systems which are
challenging to solve in practice, due to pathological ill-conditioning, strong
nonlinearity and size. In this work we propose a methodology which brings
together existing fast algorithms, namely, interior-point for the optimization
problem and a novel substructuring domain decomposition method for the ensuing
large-scale linear systems. The main contribution is the choice of interface
preconditioner which allows for the acceleration of the domain decomposition
method, leading to performance independent of problem size.Comment: To be published in SIAM J. Sci. Com
Progressive construction of a parametric reduced-order model for PDE-constrained optimization
An adaptive approach to using reduced-order models as surrogates in
PDE-constrained optimization is introduced that breaks the traditional
offline-online framework of model order reduction. A sequence of optimization
problems constrained by a given Reduced-Order Model (ROM) is defined with the
goal of converging to the solution of a given PDE-constrained optimization
problem. For each reduced optimization problem, the constraining ROM is trained
from sampling the High-Dimensional Model (HDM) at the solution of some of the
previous problems in the sequence. The reduced optimization problems are
equipped with a nonlinear trust-region based on a residual error indicator to
keep the optimization trajectory in a region of the parameter space where the
ROM is accurate. A technique for incorporating sensitivities into a
Reduced-Order Basis (ROB) is also presented, along with a methodology for
computing sensitivities of the reduced-order model that minimizes the distance
to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced
optimization framework is applied to subsonic aerodynamic shape optimization
and shown to reduce the number of queries to the HDM by a factor of 4-5,
compared to the optimization problem solved using only the HDM, with errors in
the optimal solution far less than 0.1%
Optimization as a design strategy. Considerations based on building simulation-assisted experiments about problem decomposition
In this article the most fundamental decomposition-based optimization method
- block coordinate search, based on the sequential decomposition of problems in
subproblems - and building performance simulation programs are used to reason
about a building design process at micro-urban scale and strategies are defined
to make the search more efficient. Cyclic overlapping block coordinate search
is here considered in its double nature of optimization method and surrogate
model (and metaphore) of a sequential design process. Heuristic indicators apt
to support the design of search structures suited to that method are developed
from building-simulation-assisted computational experiments, aimed to choose
the form and position of a small building in a plot. Those indicators link the
sharing of structure between subspaces ("commonality") to recursive
recombination, measured as freshness of the search wake and novelty of the
search moves. The aim of these indicators is to measure the relative
effectiveness of decomposition-based design moves and create efficient block
searches. Implications of a possible use of these indicators in genetic
algorithms are also highlighted.Comment: 48 pages. 12 figures, 3 table
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