Adriana Schulz
Justin Solomon
Wojciech Matusik
Skip Abstract Section
Skip Supplemental Material SectionAbstract
Typical design for manufacturing applications requires simultaneous optimization of conflicting performance objectives: Design variations that improve one performance metric may decrease another performance metric. In these scenarios, there is no unique optimal design but rather a set of designs that are optimal for different trade-offs (called Pareto-optimal). In this work, we propose a novel approach to discover the Pareto front, allowing designers to navigate the landscape of compromises efficiently. Our approach is based on a first-order approximation of the Pareto front, which allows entire neighborhoods rather than individual points on the Pareto front to be captured. In addition to allowing for efficient discovery of the Pareto front and the corresponding mapping to the design space, this approach allows us to represent the entire trade-off manifold as a small collection of patches that comprise a high-quality and piecewise-smooth approximation. We illustrate how this technique can be used for navigating performance trade-offs in computer-aided design (CAD) models.
Supplemental Material
- Shailen Agrawal and Michiel van de Panne. 2013. Pareto Optimal Control for Natural and Supernatural Motions. (2013).Google Scholar
- Moritz Bächer, Stelian Coros, and Bernhard Thomaszewski. 2015. LinkEdit: Interactive Linkage Editing Using Symbolic Kinematics. ACM Transactions on Graphics 34, 4 (July 2015), 99:1--99:8. Google ScholarDigital Library
- Sunith Bandaru and Kalyanmoy Deb. 2015. Temporal innovization: Evolution of design principles using multi-objective optimization. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)), Vol. 9018. Springer Verlag, 79--93.Google Scholar
- Gaurav Bharaj, David I. W. Levin, James Tompkin, Yun Fei, Hanspeter Pfister, Wojciech Matusik, and Changxi Zheng. 2015. Computational Design of Metallophone Contact Sounds. ACM Transactions on Graphics 34, 6 (Oct. 2015), 223:1--223:13. Google ScholarDigital Library
- Bernd Bickel, Moritz Bächer, Miguel A. Otaduy, Hyunho Richard Lee, Hanspeter Pfister, Markus Gross, and Wojciech Matusik. 2010. Design and Fabrication of Materials with Desired Deformation Behavior. ACM Transactions on Graphics 29, 4, Article 63 (July 2010), 10 pages. Google ScholarDigital Library
- Y. Boykov, O. Veksler, and R. Zabih. 2001. Fast approximate energy minimization via graph cuts. Pattern Analysis and Machine Intelligence, IEEE Transactions on 23, 11 (2001), 1222--1239. Google ScholarDigital Library
- Indraneel Das and J. E. Dennis. 1998. Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems. SIAM Journal on Optimization 8, 3 (1998), 631--657. Google ScholarDigital Library
- Kalyanmoy Deb and Kalyanmoy Deb. 2014. Multi-objective Optimization. In Search Methodologies. Springer US, Boston, MA, 403--449.Google Scholar
- Kalyanmoy Deb and Aravind Srinivasan. 2006. Innovization: Innovating Design Principles Through Optimization. In Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation (GECCO '06). ACM, New York, NY, USA, 1629--1636. Google ScholarDigital Library
- K. Deb, L. Thiele, M. Laumanns, and E. Zitzler. 2002. Scalable Multi-Objective Optimization Test Problems. In Congress on Evolutionary Computation (CEC 2002). IEEE Press, 825--830.Google Scholar
- Yue Dong, Jiaping Wang, Fabio Pellacini, Xin Tong, and Baining Guo. 2010. Fabricating Spatially-varying Subsurface Scattering. ACM Transactions on Graphics 29, 4, Article 62 (July 2010), 10 pages. Google ScholarDigital Library
- Tao Du, Adriana Schulz, Bo Zhu, Bernd Bickel, and Wojciech Matusik. 2016. Computational Multicopter Design. ACM Transactions on Graphics 35, 6 (Nov. 2016), 227:1--227:10. Google ScholarDigital Library
- Claus Hillermeier. 2001. Nonlinear multiobjective optimization: a generalized homotopy approach. Vol. 135. Springer Science & Business Media.Google Scholar
- Tao Ju, Scott Schaefer, and Joe Warren. 2005. Mean value coordinates for closed triangular meshes. In ACM Transactions on Graphics (TOG), Vol. 24. ACM, 561--566. Google ScholarDigital Library
- Frank Kursawe. 1991. A Variant of Evolution Strategies for Vector Optimization. In Proceedings of the 1st Workshop on Parallel Problem Solving from Nature (PPSN I). Springer-Verlag, London, UK, UK, 193--197. Google ScholarDigital Library
- Vittorio Megaro, Bernhard Thomaszewski, Maurizio Nitti, Otmar Hilliges, Markus Gross, and Stelian Coros. 2015. Interactive Design of 3D-printable Robotic Creatures. ACM Transactions on Graphics 34, 6 (Oct. 2015). Google ScholarDigital Library
- A. Messac, A. Ismail-Yahaya, and C.A. Mattson. 2003. The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization 25, 2 (01 Jul 2003), 86--98.Google Scholar
- Przemyslaw Musialski, Thomas Auzinger, Michael Birsak, Michael Wimmer, and Leif Kobbelt. 2015. Reduced-order Shape Optimization Using Offset Surfaces. ACM Transactions on Graphics 34, 4 (July 2015). Google ScholarDigital Library
- Romain Prévost, Emily Whiting, Sylvain Lefebvre, and Olga Sorkine-Hornung. 2013. Make It Stand: Balancing Shapes for 3D Fabrication. ACM Transactions on Graphics 32, 4 (July 2013), 81:1--81:10. Google ScholarDigital Library
- Adriana Schulz, Ariel Shamir, Ilya Baran, David I. W. Levin, Pitchaya Sitthi-Amorn, and Wojciech Matusik. 2017. Retrieval on Parametric Shape Collections. ACM Transactions on Graphics 36, 1 (Jan. 2017), 11:1--11:14. Google ScholarDigital Library
- Maria Shugrina, Ariel Shamir, and Wojciech Matusik. 2015. Fab Forms: Customizable Objects for Fabrication with Validity and Geometry Caching. ACM Transactions on Graphics 34, 4 (July 2015), 100:1--100:12. Google ScholarDigital Library
- Nobuyuki Umetani, Takeo Igarashi, and Niloy J. Mitra. 2012. Guided Exploration of Physically Valid Shapes for Furniture Design. ACM Transactions on Graphics 31, 4 (2012). Google ScholarDigital Library
- Nobuyuki Umetani, Yuki Koyama, Ryan Schmidt, and Takeo Igarashi. 2014. Pteromys: Interactive Design and Optimization of Free-formed Free-flight Model Airplanes. ACM Transactions on Graphics 33, 4 (July 2014), 65:1--65:10. Google ScholarDigital Library
- Emily Whiting, Hijung Shin, Robert Wang, John Ochsendorf, and Frédo Durand. 2012. Structural Optimization of 3D Masonry Buildings. ACM Transactions on Graphics 31, 6 (2012), 159:1--159:11. Google ScholarDigital Library
- Siu-Man Yau, Eitan Grinspun, Vijay Karamcheti, and Denis Zorin. 2006. Sim-X: parallel system software for interactive multi-experiment computational studies. In 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Proceedings, 25--29 April 2006, Rhodes Island, Greece. Google ScholarDigital Library
- M. Zeleny. 1973. Compromise Programming. In Multiple Criteria Decision Making, J. Cochrane and M. Zeleny (Eds.). University of South Carolina Press, Columbia, 262--301.Google Scholar
- J. Zhang and L. Xing. 2017. A Survey of Multiobjective Evolutionary Algorithms. In 2017 IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing (EUC), Vol. 1. 93--100.Google Scholar
- Qingfu Zhang and Hui Li. 2007. MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on evolutionary computation 11, 6 (2007), 712--731. Google ScholarDigital Library
- Aimin Zhou, Bo-Yang Qu, Hui Li, Shi-Zheng Zhao, Ponnuthurai Nagaratnam Suganthan, and Qingfu Zhang. 2011. Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm and Evolutionary Computation 1, 1 (2011), 32--49.Google ScholarCross Ref
- Bo Zhu, Mélina Skouras, Desai Chen, and Wojciech Matusik. 2017. Two-Scale Topology Optimization with Microstructures. ACM Transactions on Graphics 36, 5, Article 164 (July 2017), 16 pages. Google ScholarDigital Library
- E. Zitzler, K. Deb, and L. Thiele. 2000. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8, 2 (2000), 173--195. Google ScholarDigital Library
Index Terms
- Interactive exploration of design trade-offs
Recommendations
Trade-off analysis approach for interactive nonlinear multiobjective optimization
When solving multiobjective optimization problems, there is typically a decision maker (DM) who is responsible for determining the most preferred Pareto optimal solution based on his preferences. To gain confidence that the decisions to be made are the ...
Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches
A nadir objective vector is constructed from the worst Pareto-optimal objective values in a multiobjective optimization problem and is an important entity to compute because of its significance in estimating the range of objective values in the Pareto-...
Wastewater treatment plant design and operation under multiple conflicting objective functions
Wastewater treatment plant design and operation involve multiple objective functions, which are often in conflict with each other. Traditional optimization tools convert all objective functions to a single objective optimization problem (usually ...
Comments