Integrating Fractional Calculus Memory Effects and Laguerre Polynomial in Secretary Bird Optimization for Gene Expression Feature Selection

Abstract

Feature selection in high-dimensional datasets presents significant computational challenges, particularly in domains with large feature spaces and limited sample sizes. This paper introduces FL-SBA, a novel metaheuristic algorithm integrating fractional calculus enhancements with Laguerre operators into the Secretary Bird Optimization Algorithm framework for binary feature selection. The methodology incorporates fractional opposition-based learning utilizing Laguerre operators for enhanced population initialization with non-local memory characteristics, and a Laguerre-based binary transformation function replacing conventional sigmoid mechanisms through orthogonal polynomial approximation. Fractional calculus integration introduces memory effects that enable historical search information retention, while Laguerre polynomials provide superior approximation properties and computational stability. Comprehensive experimental validation across ten high-dimensional gene expression datasets compared FL-SBA against standard SBA and five contemporary methods including BinCOA, BAOA, BJSO, BGWO, and BMVO. Results demonstrate FL-SBA’s superior performance, achieving 96.06% average classification accuracy compared to 94.41% for standard SBA and 82.91% for BinCOA. The algorithm simultaneously maintained exceptional dimensionality reduction efficiency, selecting 29 features compared to 40 for competing methods, representing 27% improvement while achieving higher accuracy. Statistical analysis reveals consistently lower fitness values (0.04924 averages) and stable performance with minimal standard deviation. The integration addresses fundamental limitations in integer-based computations while enhancing convergence behavior. These findings suggest FL-SBA represents significant advancement in metaheuristic-based feature selection, offering theoretical innovation and practical performance improvements for high-dimensional optimization challenges.