How does model uncertainty affect multi-objective optimization?

Various real-world applications involve modeling complex systems with immense uncertainty and optimizing multiple objectives based on the uncertain model. Being able to quantify the impact of such model uncertainty on the operational objectives of interest is critical, for example, to design optimal experiments that can most effectively reduce the uncertainty that affect the objectives pertinent to the application at hand. In fact, such objective-based uncertainty quantification (objective-UQ) has been shown to be much more efficient for optimal experimental design (OED) compared to other approaches that do not explicitly aim at reducing the “uncertainty that actually matters”.

The concept of MOCU (mean objective cost of uncertainty) provides an effective means to quantify this objective uncertainty, but its original definition was limited to the case of single objective operations.

In our recent paper, we extend the original MOCU to propose the mean multi-objective cost of uncertainty (multi-objective MOCU), which can be used for objective-based quantification of uncertainty for complex uncertain systems considering multiple operational objectives:

Byung-Jun Yoon, Xiaoning Qian, Edward R. Dougherty, “Quantifying the multi-objective cost of uncertainty“, IEEE Access, vol.9, pp. 80351-80359, 2021, doi: 10.1109/ACCESS.2021.3085486.

Based on several examples, we illustrate the concept of multi-objective MOCU and demonstrate its efficacy in quantifying the operational impact of model uncertainty when there are multiple, possibly competing, objectives.

For more information regarding the concept of objective-UQ, optimal experimental design (OED), and other relevant resources, please visit:

The multi-objective MOCU quantifies the expected performance gap between the robust multi-objective operator that needs to be used to main good performance in the presence of model uncertainty and the optimal multi-objective operator for the true (but unknown) model.