A Ricci Curvature-Guided Optimization Operator for Population-Based Metaheuristics

Population-based metaheuristic algorithms generally guide the search process using objective function evaluations while largely ignoring the intrinsic geometric structure formed by the population in the search space. This limitation may reduce the balance between exploration and exploitation, particularly for high-dimensional and ill-conditioned optimization problems. Motivated by recent advances in discrete differential geometry, this study introduces a Ricci curvature-guided search operator that incorporates local geometric information into the optimization process. The proposed operator constructs a k-nearest-neighbor graph from the current population and estimates the local Ollivier–Ricci curvature of graph edges using entropy-regularized optimal transport. The estimated curvature is then employed to generate a curvature-guided correction step that complements the original search dynamics without modifying the underlying optimization equations. To preserve algorithmic robustness, the curvature-corrected candidate competes against the original candidate through greedy selection, ensuring that the proposed operator cannot deteriorate the solution quality during an iteration. As a preliminary proof of concept, the proposed operator is integrated into the Grey Wolf Optimizer (GWO), resulting in the Ricci Curvature-Guided Grey Wolf Optimizer (RC-GWO). The method is evaluated on six widely used scalable benchmark functions, including Sphere, Schwefel, Rosenbrock, Rastrigin, Ackley, and Griewank, in 2, 10, and 30-dimensional search spaces. Experimental results demonstrate that the proposed geometric guidance consistently improves convergence quality and solution stability, with particularly notable gains on non-separable and multimodal problems in higher dimensions. These findings indicate that Ricci curvature provides informative structural cues for population-based optimization and has the potential to serve as a general-purpose enhancement operator that can be incorporated into a broad range of metaheuristic algorithms.