Parametric optimization solves optimization problems as a function of uncontrollable or unknown parameters. Such an approach allows designers to gather more information than traditional optimization procedures during design. The benefits of parametric optimization are seen in systems design, problems with currently unknown parameters, and problems with changing operational parameters. These types of problems arise in many fields including engineering design. Existing methods for parametric optimization of computationally or monetarily expensive functions can be too time-consuming or impractical to solve. Therefore, new methods for the parametric optimization of expensive functions need to be explored. The optimization of expensive functions is not new to the design optimization community, but its extension to parametric problem formulations has not yet been investigated.

This work proposes a novel algorithm that leverages the advantages of two existing optimization algorithms. This new algorithm is called efficient parametric optimization (EPO). EPO enables adaptive sampling of high-fidelity design spaces using an inexpensive low-fidelity response surface model similar to the efficient global optimization (EGO) algorithm. Furthermore, the new EPO algorithm takes advantage of an existing parametric optimization algorithm (P3GA) to extend the adaptive sampling formulation to a parametric context. One of the inherent advantages of this parametric adaptive sampling technique is the ability to evaluate more than one design per sampling step. Such an approach largely reduces the required number of high-fidelity computations.

The proposed method is benchmarked against two analytic test problems in addition to an engineering case study requiring finite element analysis of a panel under buckling considerations. For all problems considered, the new EPO is compared to the performance of the existing P3GA in terms of solution accuracy and solution variance, and how these change with the number of high-fidelity function evaluations. For this work, the solution accuracy is determined by calculating the parametric hypervolume indicator of the parametric solution sets. The hypervolume indicator is a desirable metric because if one solution dominates another, the hypervolume indicator of the dominating set must be greater than that of the dominated set.

Results show that EPO largely outperforms the alternative, P3GA, for single parameter problems. Further, the application of EPO on a two-parameter problem shows that EPO is more precise than the alternative with a similar mean performance. Future studies include evaluating the new EPO on a wider variety of problem types including those with more parameters. Additionally, the extension of this algorithm into a multi-objective context is an area of ongoing research.


Efficient Parametric Optimization for Expensive Single Objective Problems

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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