Metaheuristic algorithms (MH) and machine learning (ML) are important components of artificial intelligence (AI). The synergy between MH’s optimization search capabilities and ML’s data analysis strengths has proven to be highly effective, providing a powerful combination for delivering high-quality solutions across diverse fields. Particularly in real-world applications such as autonomous driving and healthcare, the integration of MH and ML can significantly enhance the intelligence level and decision-making efficiency of systems, addressing the urgent societal and industrial demands for high-efficiency and high-precision solutions. This paper clarifies the logic behind the surge in research on MH-ML hybrid algorithms and addresses the gaps in current reviews regarding their timeliness and breadth of perspective. We begin by elucidating the fundamental concepts underpinning MH and ML, followed by a comprehensive classification framework that categorizes and synthesizes the latest research findings systematically. The paper concludes with an exploration of the challenges inherent in MH-ML hybrid algorithms and proposes future research directions. The analysis of the collected literature demonstrates that the integration of MH and ML generally enhances the performance of algorithms in specific problems. Despite progress from simple combinations to deeper integrations, challenges such as theoretical lag and interpretability remain. Future research will focus on solving these challenges by exploring further integration, using open-source tools, and adapting across diverse domains to expand the use of MH-ML hybrid algorithms.

Similarity representation plays a central role in increasingly popular anomaly detection techniques, which have been successfully applied in various realistic scenes. Until now, many low-rank representation techniques have been introduced to measure the similarity relations of data; yet, they only concern to minimize reconstruction errors, without involving the structural information of data. Besides, the traditional low-rank representation methods often take nuclear norm as their low-rank constraints, easily yielding a suboptimal solution. To address the problems above, in this article, we propose a novel anomaly detection method, which exploits kernel preserving embedding, as well as the double nuclear norm, to explore the similarity relations of data. Based on the similarity relations, a kind of probability transition matrix is derived, and a tailored random walk is further adopted to reveal anomalies. The proposed method can not only preserve the manifold structural properties of the data, but also alleviate the suboptimal problem. To validate the superiority of our method, extensive experiments with eight popular anomaly detection algorithms were conducted on 12 widely used datasets. The experimental results show that our detection method outperformed the state-of-the-art anomaly detection algorithms in most cases.