MEBCMO: A Symmetry-Aware Multi-Strategy Enhanced Balancing Composite Motion Optimization Algorithm for Global Optimization and Feature Selection

To address the limitations of the traditional Balancing Composite Motion Optimization (BCMO) algorithm—namely weak directional global exploration, insufficient local exploitation accuracy, and a tendency to fall into local optima with reduced population diversity in feature selection tasks—this paper proposes a Multi-Strategy Enhanced Balancing Composite Motion Optimization algorithm (MEBCMO). From a symmetry perspective, MEBCMO exploits the symmetric and asymmetric relationships among candidate solutions in the search space to achieve a better balance between exploration and exploitation. The performance of MEBCMO is enhanced through three complementary strategies. First, an adaptive heat-conduction search mechanism is introduced to simulate thermal transmission behavior, where a Sigmoid function adjusts the heat-conduction coefficient α_T from 0.9 to 0.2 during iterations. By utilizing the symmetric fitness–distance relationship between the current solution and the global best, this mechanism improves the directionality and efficiency of global exploration. Second, a quadratic interpolation search strategy is designed. By constructing a quadratic model based on the current individual, a randomly selected individual, and the global best, the algorithm exploits local symmetric characteristics of the fitness landscape to strengthen local exploitation and alleviate performance degradation in high-dimensional spaces. Third, an elite population genetic strategy is incorporated, in which the top three individuals generate new candidates through symmetric linear combinations with non-elite individuals and Gaussian perturbations, preserving population diversity and preventing premature convergence. To evaluate MEBCMO, extensive global optimization experiments are conducted on the CEC2017 benchmark suite with dimensions of 30, 50, and 100, and comparisons are made with eight mainstream algorithms, including PSO, DE, and GWO. Experimental results demonstrate that MEBCMO achieves superior performance across unimodal, multimodal, hybrid, and composite functions. Furthermore, MEBCMO is combined with LightGBM to form the MEBCMO-LightGBM model for feature selection on 14 public datasets, yielding lower fitness values, higher classification accuracy, and fewer selected features. Statistical tests and convergence analyses confirm the effectiveness, stability, and rapid convergence of MEBCMO in symmetric and complex optimization landscapes.