A Many-Objective Optimized Folded Cross Regression Model (FCRM) with Unspecified Targets: A Critical Analysis

Optimizing complex systems, particularly those without clearly defined target variables, remains a challenge across many fields such as agriculture, where numerous interdependent factors influence outcomes. To address this, we present a hybrid method that combines linear regression with evolutionary many-objective optimization using the Non-dominated Sorting Genetic Algorithm III (NSGA-III). The proposed Folded Cross Regression Model (FCRM) identifies the Pareto front of optimal solutions by jointly minimizing prediction errors measured through both Root Mean Square Error (RMSE) and Mean Square Error (MSE) across all features. This formulation enables the discovery of robust regression configurations and highlights trade-offs between competing objectives without requiring predefined targets. We validate FCRM on multiple benchmark datasets, including Abalone, Wind Speed, and Bike Sharing, demonstrating that the model effectively reveals Pareto-optimal relationships and structural dependencies within data-driven systems. FCRM thus provides a general framework for analyzing domains where target variables are ambiguous, context-dependent, or absent.