# Automated Generation of Hybrid Metaheuristics Using Learning-to-Rank
## 1 Introduction  
Metaheuristic algorithms have attracted crucial attention due to their ability to obtain high-quality solutions within reasonable computational costs [1]. By simulating behaviors from nature or evolutionary mechanisms, these algorithms can effectively explore complex solution spaces and, to some extent, avoid the local optima that traditional methods are prone to [2]. However, despite demonstrating strong robustness and adaptability, metaheuristic algorithms still face critical limitations, such as their reliance on human expertise and insufficient flexibility when applied to diverse problem scenarios, which remains a major bottleneck to their broader application. Metaheuristic algorithms are usually designed to handle two primary tasks: exploration and exploitation. Ensuring a balanced transition between these tasks is essential. Such equilibrium plays a key role in determining the algorithm's success. As stated by the \"No Free Lunch\" theorem [3], no metaheuristics can guarantee optimal results for every optimization task. Moreover, studies have shown [4] that a single algorithm struggles to effectively handle high-dimensional and non-convex optimization problems, making algorithm hybridization one of the key strategies for performance enhancement. This opens up broad avenues for research and application in hybrid algorithm strategies and machine learning-driven improvements to metaheuristic algorithms. Recent research has increasingly emphasized fused and hybrid algorithms to boost efficiency and adaptability. Currently, common approaches involve integrating and optimizing classical algorithms such as the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE) [4]. The combination of genetic algorithms with simulated annealing has been applied to optimization tasks within complex search spaces, successfully achieving heuristic approximations of near-optimal solutions [5]. The Whale Optimization Algorithm (WOA) faces challenges due to the imbalance between exploration and exploitation. To mitigate this, the enhanced SEWOA [6], which embeds the hawk strategy, has been designed. Furthermore, research on the emerging \"Dwarf Mongoose Optimization Algorithm\" (DMOA) has demonstrated that algorithm hybridization strategies can effectively improve search efficiency and global convergence [7]. [PERSON] et al. [8] recently proposed an Improved Snow Geese Algorithm (ISGA) that integrates adaptive migration and clustering strategies to enhance exploration in engineering applications and clustering optimization. With the advancement of research on algorithm automation, hyper-heuristic algorithms and automated algorithm portfolio frameworks have emerged as new trends driving the development of intelligent algorithms [9]. By employing higher-level heuristic search and learning mechanisms, the dynamic selection and combination of multiple underlying heuristic algorithms have become effective approaches to enhancing algorithm generalization capabilities. Existing studies have proposed a unified classification system based on search components, promoting the deep integration of machine learning and metaheuristic algorithms [10]. Reinforcement learning methods have been applied to algorithmic behavior selection, utilizing historical search information to guide search strategies and thus improve solution efficiency [11]. To better balance algorithm convergence and diversity, approaches based on interactive learning frameworks and Learning-to-Rank models that significantly enhance solution performance by periodically collecting feedback and dynamically optimizing the search direction have been introduced [12]. Similarly, researchers have merged reinforcement learning with proximal policy optimization approaches to provide a general algorithm search framework, automating the design of metaheuristic algorithms across varied circumstances [1].