Parametric vs. non-parametric optimization

Parametric shape optimization “searches the space spanned by the design variables to minimize or maximize some externally defined objective function” (Jiaqin Chen, Vadim Shapiro, Krishnan Suresh and Igor Tsukanov, Spatial Automation Laboratory, University of Wisconsin–Madison, “Parametric and Topological Control in Shape Optimization,” Proceedings of ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference). “In other words, parametric shape optimization is essentially a sizing problem that is a natural extension of parametric computer-aided design.

“The downside of parametric shapes is that they do not provide any explicit information about the geometry or topology of the shape’s boundaries. This, in turn, leads to at least two widely acknowledged difficulties: boundary evaluation may fail, and topological changes in the boundaries may invalidate boundary conditions or the solution procedure.”

Non-parametric optimization, by contrast, operates at the node/element level to derive an optimal structure. It can offer greater design freedom, and can make use of existing CAE models without the need for parameterization. “The main advantage of non-parametric shape optimization is the ease of setup, avoiding tedious parameterization that may be too restrictive with respect to design freedom” (Michael Böhm and Peter Clausen, FE-DESIGN GmbH, “Non-Parametric Shape Optimization in Industrial Context,” PICOF (Problèmes Inverses, Contrôle et Optimisation de Formes) ’12). “One of the major disadvantages on the other hand is that the CAD interpretation of the shape optimization result is not trivial.”

Non-parametric optimization made some news when Dassault Systèmes last year acquired FE-DESIGN, developer of the respected TOSCA Fluid software for topology optimization of channel flow problems and TOSCA Structure for topology, shape and bead optimization of structures. Remarking on the move during Dassault Systèmes’ quarterly earnings call April 25, 2013, CEO Bernard Charlès said, “In our opinion [FE-DESIGN] is the technology leader for non-parametric optimization [and is] complementary to our parametric optimization capabilities”—the size, parametric shape and geometric parameter optimization of DS SIMULIA’s Isight.

Shape optimization of a connecting rod with TOSCA Structure
Source: DS SIMULIA & Ford Werke AG

In a subsequent call for North American investors the same day, Charlès sought to underscore how pervasive are technological acumen and discernment throughout the DS organization by playfully calling not on a technology executive but instead on the company’s chief financial officer, Thibault de Tersant, for color on the technical rationale. “Now, a very techie acquisition,” said Charlès. “And because, believe it or not, Thibault was the one who convinced me we should acquire this very scientific acquisition, I will let him comment to you why we bought this company.”

de Tersant was more than game. “Okay, why not! So the interest of non-parametric optimization is the topic here. Optimization—design optimization—is about designing for a certain targeted robustness of the product such that you can optimize your design and remove material until you have removed all material necessary for the targeted robustness of the car’s chassis, or whatever part you are doing.

“You have two methods to do that,” de Tersant continued. “One is parametric optimization; the other one is non-parametric optimization. And, believe it or not, the words here are confusing because the one which is more automated is the non-parametric optimization method, and [the other] one, the opposite. So this is the interest of this acquisition—it’s frankly the best technology for non-parametric optimization. And this does drive a lot of savings in time in order to run this optimization process.”

Charlès termed the FE-DESIGN deal “a very interesting acquisition with a company we already have an OEM relationship with, as we embedded some of their technology in SIMULIA,” specifically ATOM (Abaqus Topology Optimization Module), based on a subset of TOSCA Structure. FE-DESIGN became part of DS SIMULIA when the transaction closed April 23, 2013. Terms were not disclosed; DS reported FE-DESIGN had 50 employees and more than 200 customers at the time of acquisition.

Future posts will examine more of the techniques and algorithmic methods used in optimization software.