Braden Hancock and Dr. Christopher Mattson, Department of Mechanical Engineering

Introduction

In my proposal for an ORCA grant, I provided a plan to assist design engineers in the early stages of the design process. This I proposed to do through the development of a computational environment wherein design engineers could more fully and simply analyze the relationships between the various design objects (variables, constraints, and objectives) that define a multiobjective optimization problem (MOP). Thanks to the opportunity that I received to pursue this research, that technology has been developed and disseminated in the scientific community through two academic journals, two professional conferences, and one student conference.

Results

A major motivation for my research was the need recognized by pioneers of Multidisciplinary Design Optimization (MDO) in a 2010 NSF Workshop for design strategies that would allow for (i) divergent exploration and (ii) dynamic problem formulation [1]. I initially intended to meet this need by developing a visual environment wherein designers would be able to dynamically adjust design objects and observe the relationships between them. This would allow for more thorough and creative exploration of new design concepts in the early stages of design. However, as I investigated existing visualization techniques and commercial packages that render physical design characteristics (such as Physics Illustrator [2]), I soon discovered that the limiting factor for divergent exploration in early design was not the visual designer-computer interface, but rather the basic formulation of the MOP.

In most design scenarios, design objects are established and a numerical optimization is performed. In order to explore a new design scenario, the designer must reformulate the problem. For example, this may include adjusting which objectives will be minimized/maximized or which fixed parameters will be allowed instead to vary between certain bounds. Using the standard MOP formulation, the designer must find the multiple locations within the code that define these various design objects and make these changes. This repeated action can prove tedious and hinder the designer’s willingness to explore a sufficiently diverse set of design concepts and formulations.

Thus, working with other members of the Design Exploration Research Group at BYU, I developed a dynamic formulation for MOPs—one in which design objects can easily be adjusted, added, deleted, or transformed into other objects. In this new formulation, all design objects can be passed in a single data structure and have their roles in the new formulation specified in a single matrix. This differs from the classic formulation, where objectives, constraints, and variables are handled separately in different parts of the code. Thus, the changes required for exploring a new design concept using the dynamic formulation could be made with significantly fewer modifications to the code. Between example problems that we developed and problems from the literature in our discipline, we were able to demonstrate quantitatively and qualitatively a number of situations in which this dynamic formulation would prove useful and advantageous for a designer to use in the early stages of design over the classic formulation.

Publications and Awards

The results from this research have been published/presented or accepted for future publication in the following journals/conferences (awards are given in bold with their respective conferences):

Structural and Multidisciplinary Optimization (SMO) journal

• Accepted Aug. 2012
• “Divergent Exploration in Design with a Dynamic Multiobjective Optimization Formulation”

Research in Engineering Design (RED) journal

• Accepted Dec. 2012
• “Use Scenarios for Design Space Exploration with a Dynamic Multiobjective Optimization Formulation”

8th AIAA Multidisciplinary and Design Optimization Specialists (MDO) Conference 2012

• Presented Apr. 2012
• “Divergent Exploration in Design with a Dynamic Multiobjective Optimization Formulation”

ASME 2012 International Design Engineering Technical Conference (DETC)

• Presented Aug. 2012
• “Use Scenarios for Design Space Exploration with a Dynamic Multiobjective Optimization Formulation”
• Best Paper in Design Automation in 2012 (awarded by the ASME Design Automation Committee as 1 of 10 out of 153 papers considered)

AIAA 2012 Region VI Student Technical Paper Competition

• Presented Apr. 2012
• “Design Space Exploration with a Dynamic Multiobjective Optimization Formulation” o Best Paper in Region VI – Freshman/Sophomore Category

Acknowledgments

In addition to the support from the Office of Research and Creative Activities, this research was made possible with much assistance from my colleagues at BYU. Dr. Christopher Mattson provided exceptional guidance as a mentor, particularly in preparing our findings for publication to the scientific community. Fellow student Shane Curtis spearheaded the coding of the new optimization formulation and the testing of the new approach on numerous example problems from the engineering world. Doctoral candidate Patrick Lewis assisted in the development of the theory for the new optimization formulation. Finally, I would be negligent if I did not thank all of the student researchers in Dr. Mattson’s Design Exploration Research Group, including the aforementioned individuals, who often assisted in brainstorming, editing, and creating the ideal mentored research environment in which to work.

References

[1] T. W. Simpson and J. R. R. A. Martins. The future of multidisciplinary design optimization: advancing the design of complex engineered systems. In NSF Workshop Report, Fort Worth, Texas, September 16, 2010, September 16 2010.
[2] R. Davis. Magic paper: Sketch-understanding research. Computer, 40(9):34–41, Sept. 2007.