## 2 Related Works
### Methods Based on Metaheuristic  
In the literature, metaheuristic-based algorithms have been widely used to mine numerical association rules. [PERSON] et al. (2008) proposed the MODENAR algorithm, which is an association rule mining method based on the Pareto multi-objective differential evolution algorithm [29]. MODENAR can optimize multiple objectives simultaneously, including support, confidence, and rule comprehensibility, and use interval amplitude as a metric to ensure that the mined rules have appropriate numerical intervals, avoiding rules that are too broad or narrow. The advantage of this method is that it does not require frequent generation of frequent itemsets, significantly reducing computational complexity, and demonstrating good performance on multiple datasets. [PERSON] et al. (2013) proposed a numerical association rule mining method based on a multi-objective genetic algorithm, which optimizes the interest and comprehensibility of rules by introducing multiple objective functions. By simulating the process of biological evolution, high-quality association rules are generated through selection, crossover, and mutation operations [30]. The experimental findings show that this method works well for obtaining association rules with high interest and comprehensibility. [PERSON] et al. (2014) proposed an association rule mining algorithm based on Bees Swarm Optimization (BSO), called the BSO-ARM algorithm [31]. This algorithm solves the problem of low efficiency of traditional ARM algorithms on large-scale datasets and improves search efficiency and rule quality by introducing metaheuristic methods optimized by bee colonies. The BSO-ARM algorithm combines two rule representation methods, binary encoding and integer encoding, and proposes three different search area strategies (modulo, next, syntactic) to explore the search space more extensively. The outcomes of the experiment demonstrate that the BSO-ARM algorithm surpasses conventional precision methods and evolutionary techniques in both CPU time efficiency and the quality of the resulting rules. [PERSON] et al. (2014) proposed a numerical association rule mining method (MOPAR) based on the multi-objective particle swarm optimization algorithm, which balances conflicting objectives such as confidence, comprehensibility, and interestingness through Pareto optimal theory [32]. Unlike traditional weighted sum-based methods, MOPAR can effectively mine diverse and informative numerical association rules. In addition, this algorithm does not require prior discretization processing, making the mining process more flexible and reducing information loss. [PERSON] et al. (2022) proposed an association rule mining method based on a hybrid whale optimization algorithm, which combines the whale optimization algorithm with other optimization techniques to improve search efficiency and rule quality [33]. The experimental findings indicate that this approach performs well in processing high-dimensional data and large-scale datasets. [PERSON] et al. (2024) proposed a numerical association rule mining method based on the Multi Objective Firefly Algorithm (MOFNAR), which optimizes the accuracy and conciseness of rules by introducing indicators such as balance measure and cosine square [34]. This algorithm avoids the problem of rules being too wide or too narrow by effectively controlling the length of numerical intervals and maintains population diversity through penalty strategies and crowding distances, ensuring that the algorithm can discover diverse high-quality rules. Despite the progress made in discretization and metaheuristic methods for mining numerical association rules, both approaches still have notable limitations. Discretization methods, while useful in handling uncertainty and enhancing rule comprehensibility, suffer from potential information loss and human bias in the discretization process. In high-dimensional datasets, the complexity of discretization increases significantly, leading tooverly complex rules or ineffective mining.