###### Abstract  
Traditional numerical association rule mining optimization algorithms have limitations in handling discrete attributes, and they are susceptible to becoming trapped in local optima, uneven population distribution, and poor convergence. To address these challenges, we propose a multi-objective nutracker optimization algorithm based on a cubic chaotic map (C-MONOA), specifically designed for mining association rules from mixed data (continuous and discrete). Unlike existing models, C-MONOA leverages a chaotic map for population initialization, alongside Michigan rule encoding, to dynamically optimize feature intervals during the optimization process. This algorithm integrates continuous and discrete data more  
association rules can help identify the association between patient characteristics and disease occurrence, thereby assisting in clinical decision-making [3]. However, despite the broad application prospects of numerical association rule mining, existing methods still face many technical challenges when dealing with numerical data. Traditional numerical association rule mining methods usually rely on discretization techniques to convert continuous numerical attributes into discrete intervals and then apply association rule algorithms (such as the Apriori algorithm) for mining [4]. Although this approach is straightforward and easy to apply, it faces several practical limitations. Firstly, discretization may lead to information loss, especially when interval partitioning is unreasonable, which can significantly reduce the accuracy of rules [5]. Secondly, such methods often rely on pre-set minimum support and confidence thresholds, which are difficult to determine in complex datasets. In addition, with the increase in data dimensions, the time complexity of traditional algorithms sharply increases, making it difficult to cope with large-scale and high-dimensional numerical data. In recent years, a series of advanced optimization algorithms such as the genetic algorithm [6], firefly algorithm [7], particle swarm optimization algorithm [8], parameterized level set method [9], alternating active-phase algorithm [10], mantis search algorithm integrated with opposition-based learning and simulated annealing [11], batch subproblem coevolution with Gaussian process-driven linear models (BSCo-GPLMs) [12], collaborative neurodynamic approach to multi-objective optimization [13], etc., have shown wide application prospects in many fields. Researchers in the field of data mining have ingeniously applied these optimization algorithms to the mining process of numerical association rules, significantly improving mining efficiency and accuracy with their excellent flexibility and powerful global search capabilities. This type of algorithm does not require discretization, can directly mine rules on continuous numerical data, and can generate more meaningful rules by optimizing multiple objectives such as support and confidence [14]. However, existing evolutionary algorithm-based methods still have shortcomings, especially when dealing with mixed datasets (i.e., datasets containing both continuous and discrete features), making it difficult to effectively process both types of data simultaneously [15]. The reason why association rule mining in mixed datasets is important is that real-world data often contain both continuous and discrete features. Taking the medical field as an example, physiological indicators such as blood pressure and heart rate of patients belong to continuous data, while disease classification and lifestyle habits (such as smoking and drinking) belong to discrete data [16]. Effectively mining the association rules in such mixed data can help reveal complex patterns and relationships and assist decision-makers in better understanding and utilizing the data. Unfortunately, many existing algorithms tend to converge to local optima during the optimization process, resulting in uneven population distribution and poor convergence [17].