A modified search direction method for inequality constrained optimization problems using the singular-value decomposition of normalized response gradients

Chen, Long; Bletzinger, Kai‐Uwe; Geiser, Armin; Wüchner, Roland

doi:10.1007/s00158-019-02320-9

Cited by 8 publications

(10 citation statements)

References 21 publications

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“…We do not claim that the proposed method is the best option for shape optimization problems in general. The proposed algorithm should be considered as a good alternative to other successful optimization methods, such as inner-point (Chen et al 2019) or trust-region algorithms (Yuan 1999).…”

Section: Discussionmentioning

confidence: 99%

“…In our paper, we are interested in iterative optimization methods, where a continuous evolution of the design produced. Shape optimization is successfully used in many fields of application: aerospace engineering (Kroll et al 2007;Kenway et al 2014;Palacios et al 2012), automotive industry (Najian Asl et al 2017;Hojjat et al 2014), structural mechanics (Chen et al 2019; Grandhi 1986;Firl and Bletzinger 2012), fluid-structure interaction (FSI) (Hojjat et al 2010;Heners et al 2017), etc.…”

Section: Introductionmentioning

confidence: 99%

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Relaxed gradient projection algorithm for constrained node-based shape optimization

Antonau¹,

Hojjat

Bletzinger³

2021

Struct Multidisc Optim

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In node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Relaxed gradient projection algorithm for constrained node-based shape optimization

Antonau¹,

Hojjat

Bletzinger³

2021

Struct Multidisc Optim

Self Cite

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“…[15] has successfully used the same projection algorithm with a constant step length for imposing the nodal non-penetration constraints, however, without the correction therm in Equation 6. [21,22] have developed alternative optimization algorithms that have proven to work well with the Vertex Morphing parametrization.…”

Section: Optimization Algorithmmentioning

confidence: 99%

Aggregated Formulation of Geometric Constraints for Node-Based Shape Optimization With Vertex Morphing

Geiser¹,

Antonau²,

Bletzinger³

2021

14th International Conference on Evolutionary and Deterministic Methods for Design, Optimization and Control

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Node-based shape optimization methods like Vertex Morphing use every node of the surface mesh as design variables. The method's key advantages are the minimal effort for problem setup and the resulting largest possible design space that allows finding new and innovative shapes. Due to a large number of design variables, the application of gradient-based optimization methods becomes mandatory, and adjoint sensitivity analysis is the preferred way for efficient computation of the shape gradients.For some industrial applications, it is necessary to restrict the large design freedom in some sense, for example by limiting the geometric design space. In recent work, nodal nonpenetration constraints have been successfully applied in the context of Vertex Morphing, resulting in a potentially large number of active constraints. Aggregation methods are commonly used to reduce the number of constraints in the optimization problem and are investigated here to combine nodal geometric constraints in a single global constraint function.

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“…In addition to these geometric constraints, the optimization problem can be subjected to any number of physics-based equality and inequality constraints. Literature provides robust methods for enforcing these constraints [7,11,16].…”

Section: Shape Optimization Problemmentioning

confidence: 99%

Realization of a Framework for Simulation-Based Large-Scale Shape Optimization Using Vertex Morphing

Ghantasala

Asl

Geiser

et al. 2021

J Optim Theory Appl

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There is a significant tendency in the industry for automation of the engineering design process. This requires the capability of analyzing an existing design and proposing or ideally generating an optimal design using numerical optimization. In this context, efficient and robust realization of such a framework for numerical shape optimization is of prime importance. Another requirement of such a framework is modularity, such that the shape optimization can involve different physics. This requires that different physics solvers should be handled in black-box nature. The current contribution discusses the conceptualization and applications of a general framework for numerical shape optimization using the vertex morphing parametrization technique. We deal with both 2D and 3D shape optimization problems, of which 3D problems usually tend to be expensive and are candidates for special attention in terms of efficient and high-performance computing. The paper demonstrates the different aspects of the framework, together with the challenges in realizing them. Several numerical examples involving different physics and constraints are presented to show the flexibility and extendability of the framework.

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A modified search direction method for inequality constrained optimization problems using the singular-value decomposition of normalized response gradients

Cited by 8 publications

References 21 publications

Relaxed gradient projection algorithm for constrained node-based shape optimization

Relaxed gradient projection algorithm for constrained node-based shape optimization

Aggregated Formulation of Geometric Constraints for Node-Based Shape Optimization With Vertex Morphing

Realization of a Framework for Simulation-Based Large-Scale Shape Optimization Using Vertex Morphing

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