(679g) The Objective Reduction Community Algorithm (ORCA)

Many-objective optimization problems (MaOPs), particularly those involving four or more objectives, inherently appear in decision making for sustainable process systems but present significant challenges in computation and decision-making due to the high dimensionality of the objective space. The resulting high dimensional Pareto frontier is challenging to visualize and interpret [1], while generating a Pareto frontier using rigorous methods such as weighted sum and epsilon constraint approaches is prohibitive due to the number of single objective problems to solve scaling exponentially with objective dimensionality. To address this, we have developed a novel algorithm capable of systematically reducing the objective dimensionality of both mixed-integer linear and nonlinear MaOPs [2], which we call the Objective Reduction Community Algorithm (ORCA). For linear MaOPs, derivatives of objectives are projected onto the constraint surfaces of the problem. Strength of interaction is defined as the inner product of the projected vectors and a weighted sum of the interaction strengths over all constraints is used is used to determine the total objective correlation strength. For nonlinear problems, we extend this approach using an outer approximation-like method to generate linearized constraint surfaces. We strategically sample the region most likely to be active in determining the Pareto frontier by generating new linearization points using steps within the cone of objective gradients, converting the original nonlinear problem and to a linear problem. Objective correlation strengths are embedded as edge weights in a graph where each objective function is a node. Community detection is used on this graph to reduce objective dimensionality by identifying groupings of objectives whereby all objectives in the same group are correlated, while objectives in different groups are competing.

To enhance its accessibility and impact, we are developing an open-source package in Julia and Python named ORCA. This tool will enable users to define the variables, constraints, and objectives within their MaOP of interest and automatically apply our dimensionality reduction algorithm to determine two or three groups of objectives, which can then form the basis of a solvable and interpretable multi-objective optimization problem with minimal tradeoff information loss. Designed to integrate with existing optimization workflows (JuMP and Pyomo), ORCA empowers practitioners and researchers to effectively interpret the tradeoffs between many sustainability objectives. We conclude the talk by discussing a few examples of the successful application of ORCA. For example, ORCA has been used to analyze the competing or correlated nature of cost and emissions objectives in green ammonia production [3]. It has also identified the objective groupings in process design problems [4] and elucidated relationships between planetary boundaries in hydrogen supply chain optimization, providing insights into maintaining sustainable indices.

[1] de Freitas, A. R., Fleming, P. J., & Guimaraes, F. G. (2015). Aggregation trees for visualization and dimension reduction in many-objective optimization. Information Sciences, 298, 288-314.

[2] Russell, Justin M., and Andrew Allman. "Sustainable decision making for chemical process systems via dimensionality reduction of many objective problems." AIChE Journal 69.2 (2023): e17962.

[3] Wang, H., & Allman, A. (2024). Analysis of the correlating or competing nature of cost-driven and emissions-driven demand response. Computers & Chemical Engineering, 181, 108520.

[4] Wang, H., & Allman, A. Dimensionality Reduction in Optimal Process Design with Many Uncertain Sustainability Objectives. Syst. Control Trans, 3, 920-926.