A Novel Objective Reduction Algorithm for Nonlinear Many-Objective Optimization Problems

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 group�s 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.