# Chaotic Lévy and adaptive restart enhance the Manta Ray foraging optimizer for gene feature selection

## TL;DR

A new optimization algorithm called CLA-MRFO improves gene feature selection by balancing exploration and exploitation, achieving high accuracy in identifying relevant genes for leukemia.

## Contribution

CLA-MRFO introduces chaotic Lévy flight modulation, phase-aware memory, and entropy-informed restarts to enhance optimization performance in high-dimensional spaces.

## Key findings

- CLA-MRFO outperformed other algorithms on 23 of 29 CEC’17 benchmark functions with a 31.7% average performance gain.
- CLA-MRFO identified compact gene subsets with high F1-scores (0.953 ± 0.012) for leukemia classification.
- The method showed consistent performance (<5% variance) but limited generalizability in multi-class diagnostic contexts.

## Abstract

Swarm-based optimization algorithms often face challenges in maintaining an effective exploration–exploitation balance in high-dimensional search spaces. Manta Ray Foraging Optimization (MRFO), while competitive, is hindered by static parameter settings and premature convergence. This study introduces CLA-MRFO, an adaptive variant incorporating chaotic Lévy flight modulation, phase-aware memory, and an entropy-informed restart strategy to enhance search dynamics. On the CEC’17 benchmark suite, CLA-MRFO achieved the lowest mean error on 23 of 29 functions, with an average performance gain of 31.7% over the next best algorithm; statistical validation via the Friedman test confirmed the significance of these results (\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$p < 0.01$$\end{document}). To examine practical utility, CLA-MRFO was applied to a high-dimensional leukemia gene selection task, where it identified ultra-compact subsets (\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\le$$\end{document}5% of original features) of biologically coherent genes with established roles in leukemia pathogenesis. These subsets enabled a mean F1-score of \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$0.953 \pm 0.012$$\end{document} under a stringent 5-fold nested cross-validation across six classification models. While highly effective in a binary classification setting, the method’s performance in a multi-class diagnostic context revealed constraints in generalizability, indicating that the identified biomarkers are highly context-dependent. Overall, CLA-MRFO exhibited consistent behavior (<5% variance across runs) and provides an adaptable framework for high-dimensional optimization tasks with applications extending to bioinformatics and related domains.