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Sustainability is increasingly recognized as a critical global issue. Multi-objective optimization is an important approach for sustainable decision-making, but problems with four or more objectives are hard to interpret due to its high dimensions. In our groups previous work, an algorithm capable of systematically reducing objective dimensionality for (mixed integer) linear Problem has been developed. In this work, we will extend the algorithm to tackle nonlinear many-objective problems. An outer approximation-like method is employed to systematically replace nonlinear objectives and constraints. After converting the original nonlinear problem to linear one, previous linear algorithm can be applied to reduce the dimensionality. The benchmark DTLZ5(I, M) problem set is used to evaluate the effectiveness of this approach. Our algorithm demonstrates the ability to identify appropriate objective groupings on benchmark problems of up to 20 objectives when algorithm hyperparameters are appropriately chosen. We also conduct extensive testing on the hyperparameters to determine their optimal settings. Additionally, we analyze the computation time required for different components of the algorithm, ensuring efficiency and practical applicability. 

The study of sustainable design has gained prominence in response to the growing emphasis on environmental and social impacts of critical infrastructure. Addressing the different dimensions inherent in sustainability issues necessitates the application of many-objective optimization techniques. In this work, an illustrative four-objective design system is formulated, wherein uncertainties lie within two different socially-oriented objectives. A stochastic community detection approach is proposed to identify robust groupings of objectives. The findings reveal that the modularity of the optimal solution surpasses that of the average graph, thus demonstrating the efficacy of the proposed approach. Furthermore, a comprehensive exploration of the Pareto frontiers for both the robust and single-scenario best groupings is undertaken, demonstrating that using the robust grouping results in little to no information loss about tradeoffs.