Nonlinearities are ubiquitous in complex chemical engineering problems, particularly in those of optimal process design, but our previous algorithm is only applicable for linear frameworks. In this talk, we discuss the extension of ORCA to reduce the dimensionality of nonlinear MaOPs. An outer approximation-like method is used to systematically replace nonlinear objectives and constraints with a set of linear approximations that, when the nonlinear problem is convex, provides a relaxation of the original problem. [3]. To strategically generate new fixed linear approximation points likely to be active in determining the Pareto frontier of the MaOP, we adopt a random step direction within the cone defined by all objective gradient vectors. We demonstrate that identifying correlation strengths along the linearly relaxed constraint space can be sufficient for developing correlation strength weights for objective grouping. As in the linear case, once these strengths are determined, community detection can be used on the resulting objective correlation graph to determine groups of objectives that are correlated with each other but competing with other groups as the basis of objective dimensionality reduction.
The nonlinear ORCA algorithm is applied to a representative CCUS supply chain problem, incorporating nonlinear objectives related to total cost, carbon dioxide emissions, and quantified safety risk, as well as nonlinear constraints inherent in splitting carbon streams. Through dimensionality reduction, we uncover essential insights into the structure of the objective space and demonstrate how such analysis can guide more informed and balanced decision-making. For example, ORCA identifies that carbon dioxide emission and safety seem to be strongly correlated, an observation that we can justify by noting that underground carbon storage provides the best outcomes in both objectives. Overall, we demonstrate that through use of the ORCA algorithm, we can systematically assess tradeoffs between many sustainability objectives such as cost, emissions, and safety in order to find effective designs that balance the various goals and promote a net-zero carbon economy.
[1] Azadnia, A. H., McDaid, C., Andwari, A. M., & Hosseini, S. E. (2023). Green hydrogen supply chain risk analysis: A european hard-to-abate sectors perspective. Renewable and Sustainable Energy Reviews, 182, 113371.
[2] Oqbi, M., Véchot, L., & Al-Mohannadi, D. M. (2025). Safety-driven design of carbon capture utilization and storage (CCUS) supply chains: A multi-objective optimization approach. Computers & Chemical Engineering, 192, 108863.
[3] Russell, J. M., & Allman, A. (2023). Sustainable decision making for chemical process systems via dimensionality reduction of many objective problems. AIChE Journal, 69(2), e17962.