2025 AIChE Annual Meeting

(681f) A New Approach for Multi-Objective Bayesian Optimization Based on Pareto Projection and Sampling

Authors

Brenda Cansino Loeza - Presenter, UNIVERSIDAD MICHOACANA DE SAN NICOLAS DE HIDALGO
J. E. Umaña, University of Wisconsin-Madison
Alejandro Ayala-Cortés, Instituto de Energías Renovables, UNAM
Victor M. Zavala, University of Wisconsin-Madison
Optimizing experimental and black-box systems often involves multiple conflicting objectives [1,2]. In such settings, it is necessary to build models for the different objectives using limited data; these models are then used to help discover and quantify trade-offs (typically in the form of a Pareto frontier). Bayesian Optimization (BO) is a powerful approach for doing this, as it leverages uncertainty information to guide data collection and to enable model building and optimization [3,4]. Most implementations of BO are targeted towards single-objective problems and extending BO to handle multiple objectives is challenging. The core difficulty in multi-objective BO (MOBO) lies in the need to identify non-dominated solutions and the Pareto front using few data points. The Expected Hypervolume Improvement (EHVI) approach is a widely used MOBO methodology that enables identification of non-dominated solutions but this requires the selection of reference points, which can lead to suboptimal exploration [5]. Other MOBO approaches include Thompson sampling and Pareto exploration using distance-based selection criteria [6]. These approaches are powerful but they are challenging to implement.

This work introduces a MOBO framework that relies on Pareto projections and sampling. This approach uses data to build probabilistic surrogate models for the different objectives and uses the models to build a predicted Pareto frontier (which captures the limiting predicted performance of the system). We note that this step projects the experimental design space into the objective space (which is often low-dimensional). In a subsequent step, we use uncertainty information of the surrogate models to identify regions in the predicted Pareto frontier that have the highest uncertainty and we select experiments at such points. The proposed 2-step framework naturally captures exploitation (used to build the predicted Pareto frontier) and exploration (used to target regions of high uncertainty). We show that this approach is easy to implement and is effective at discovering the real Pareto frontier in a few cycles/iterations. We also show that the approach is sample efficient, as probabilistic models effectively reconstruct the frontier (via interpolation) using sparse support points. The approach also enables batch experiment sampling and helps provide a comprehensive picture of the trade-off space (thus facilitating interpretability). We demonstrate the effectiveness of the approach using simulated and real experimental studies arising in reaction engineering, electrochemistry, and biomass processing. We also discuss challenges associated with handling many objectives; in such settings, we discuss alternatives that rely on low-dimensional Pareto projections.

References

[1] González, Leonardo D., and Victor M. Zavala. "Implementation of a Bayesian Optimization Framework for Interconnected Systems." Industrial & Engineering Chemistry Research (2025).

[2] Paulson, J. A., & Lu, C. (2022). COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information. Computers & Chemical Engineering, 160, 107700.

[3] Mockus, J. Bayesian Approach to Global Optimization. In Theory and Applications. Springer Science & Business Media, 2012.

[4] Paulson, J. A., & Tsay, C. (2024). Bayesian optimization as a flexible and efficient design framework for sustainable process systems. Current Opinion in Green and Sustainable Chemistry, 100983.

[5] Yang, K., Emmerich, M., Deutz, A., & Bäck, T. (2019). Efficient computation of expected hypervolume improvement using box decomposition algorithms. Journal of Global Optimization, 75, 3-34.

[6] Kudva, A., Tang, W. T., & Paulson, J. A. (2025). Multi-Objective Bayesian Optimization for Networked Black-Box Systems: A Path to Greener Profits and Smarter Designs. arXiv preprint arXiv:2502.14121.