Pareto Gamuts: Exploring Optimal Designs Across Varying Contexts
1MIT CSAIL 2Chinese University of Hong Kong 3University of Washington


Manufactured parts are usually optimized for many distinct contexts: here, turbine designs are optimized for mass and power (performance) under various wind speeds (context). Each context yields a distinct Pareto set, or collection of designs with optimal performance trade-offs. Existing tools require a separate optimization for each context of interest. As an alternative, we augment the standard multi-objective optimization framework to simultaneously consider design and context variables. This allows us to find the Pareto gamut (left, colored by context), which captures the Pareto-optimal designs over a range of contexts. From this gamut, we can extract any fixed-context Pareto set (right, top) and its image in performance space (right, bottom).


Manufactured parts are meticulously engineered to perform well with respect to several conflicting metrics, like weight, stress, and cost. The best achievable trade-offs reside on the Pareto front which can be discovered via performance-driven optimization. The objectives that define this Pareto front often incorporate assumptions about the context in which a part will be used, including loading conditions, environmental influences, material properties, or regions that must be preserved to interface with a surrounding assembly. Existing multi-objective optimization tools are only equipped to study one context at a time, so engineers must run independent optimizations for each context of interest. However, engineered parts frequently appear in many contexts: wind turbines must perform well in many wind speeds, and a bracket might be optimized several times with its bolt-holes fixed in different locations on each run. In this paper, we formulate a framework for variable-context multi-objective optimization. We introduce the Pareto gamut, which captures Pareto fronts over a range of contexts. We develop a global/local optimization algorithm to discover the Pareto gamut directly, rather than discovering a single fixed-context "slice" at a time. To validate our method, we adapt existing multi-objective optimization benchmarks to contextual scenarios. We also demonstrate the practical utility of Pareto gamut exploration for several engineering design problems.

[Lamp Example: 4D gamut and several extracted Pareto fronts]
Simple Lamp design problem, over a context specifying the vertical height of the focal point we'd like to illuminate. This example shows the quality of the individual fixed-context Pareto fronts extracted from our gamut. (Left) 4D Pareto gamut for our lamp. Performance values are plotted spatially, and color indicates the context. (Right) 3D fixed-context Pareto fronts, embedded in 2D space using barycentric coordinates. High-performing designs \wrt each metric are located near the labeled edge. Grayscale value indicates the lamp heights. As expected, higher focal points yield taller lamps (light gray), but the most lightweight, stable lamps (dark gray) persist through all contexts.

[Solar Roof Design: 3D gamut and several extracted designs]
Using the Pareto gamut to optimize over quanitfiable metrics (power output) while exploring the impact of qualitative choices (global house orientation). (Center) Pareto gamut for a solar roof, optimized for output at different times of day, over a context that controls the building's orientation. (Left/Right) Renderings of the single most extreme point on each end of the highlighted fixed-context fronts. Although the achievable performance of each morning- or evening-focused solution is roughly equivalent, the design that realizes this performance varies dramatically in different contexts. By efficiently exposing the functionally-optimal designs for all contexts, our Pareto gamut could allow architects to focus on more aesthetic implications that are difficult to quantify.

[Bicycle Design: efficiently exploring assemblies by optimizing adjacent components under shared, adjustable constraints]
Efficiently exploring assemblies by optimizing adjacent components under shared, adjustable constraints. (Left) Pareto gamuts for two parts of a bicycle suspension, over a shared context indicating the vertical position of their mutual pivot point (Right, green boxes). Engineers explore many pivot positions to adjust high-level assembly characteristics like anti-squat (R,Top). The part-wise Pareto gamuts offer direct access to the optimized designs for each pivot choice (R,Bottom), which provides additional insight about the impact of each assembly-level decision.

Pareto Gamuts: Exploring Optimal Designs Across Varying Contexts
ACM Transactions on Graphics, Proceedings of ACM SIGGRAPH, 2021
[Paper] [Video] [Code] [Slides]

  author={Makatura, Liane and Guo, Minghao and Schulz, Adriana and Solomon, Justin and Matusik, Wojciech},
  title={Pareto Gamuts: Exploring Optimal Designs Across Varying Contexts},
  journal={ACM Transactions on Graphics (SIGGRAPH)},
  publisher = {ACM},
  address = {New York, NY, USA},
  doi = {10.1145/3450626.3459750},
  url = {}

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