## 4 C-Monoa
### Main Steps of C-Monoa  
The C-Monoa proposed in this article is developed to work with both continuous and discrete data. It autonomously updates the upper and lower bounds of continuous data intervals and the discrete data values within the dataset, ultimately yielding suitable association rules. The primary step of C-Monoa involves encoding chromosomes based on the uniqueness of the data content by utilizing a combination of the cubic chaotic map and the Michigan method to initialize individuals within the population. Subsequently, the algorithm evaluates the fitness scores of each individual under the current objective function and employs fast non-dominated sorting techniques for efficient ranking of these individuals. The algorithm then traverses the entire population to perform update operations on each individual, aimed at enhancing their performance. Following this, a careful selection of \(N\) elite individuals, demonstrating exceptional fitness and diversity, is conducted from both the parent and offspring populations using a combination of fast non-dominated sorting and crowding distance calculations. This iterative process continues until the predefined termination conditions or iteration limits are met, thereby ensuring that C-Monoa can effectively explore and converge to the Pareto optimal solution set for the problem. The specific process of C-Monoa is shown in Algorithm 1. According to the algorithm process, the computational complexity of C-Monoa can be summarized as \(O(N\cdot NA\cdot NR\cdot T_{max})\), where \(NA\) represents the number of attributes, \(NR\) represents the number of records in the dataset. Although the computational complexity of the other algorithms used in the experimental comparison is similar to that of C-Monoa overall, they are more complex than C-Monoa in the population update process. ```
0:\(N\) (population size), \(T_{\text{max}}\) (maximum number of iterations), \(\rho\) (chaotic hyperparameters), \(\beta\) (Levy flight parameters), data. 0: Final population. 1: Initialize population \(P\). Using the Cubic Chaotic map Equation (18) generates a series of nutracker individuals in the form of chromosome rules encoding, calculates the fitness value of each objective function, and performs non-dominated sorting on the population. 2:while termination conditions are not met do
3: Generate random numbers \(m\) and \(n\) between 0 and 1. 4:if\(m<n\)then\(\triangleright\) Foraging and storage behavior
5: According to Equation (2), generates a random number \(\mu\)
6: Update the location of individual nutracker based on the foraging and storage behavior described in Equation (4)
7:else\(\triangleright\) Cache search and recovery behavior
8: Generate RP matrix based on Equations (8) and (9)
9: Update the location of individual nutracker based on the cache search and recovery behavior described by Equation (17)
10:endif
11: Calculate fitness values, use Pareto for fast non-dominated sorting, update crowding distance according to Equation (26), and select \(N\) elite individuals from the parent and child generations to continue iteration
12:endwhile
13:Output the optimal population after reaching the termination condition. ```  
**Algorithm 1** Main steps of C-Monoa  
```
0:\(N\) (population size), \(T_{\text{max}}\) (maximum number of iterations), \(\rho\) (chaotic hyperparameters), \(\beta\) (Levy flight parameters), data. 0: Final population. 1: Initialize population \(P\). Using the Cubic Chaotic map Equation (18) generates



## 5 Experiment and Results

This section mainly introduces the dataset used in the experiment, sets the experimental parameters, and analyzes the results. ### Data Set

In this section, the C-MONOA proposed in this paper is validated using the Cardiovascular Disease dataset [50], the Heart Disease dataset [51], and the Wholesale customers dataset [52], and is compared with well-known algorithms such as MOPSO, MOBMSASA, MOWOA, MOFA, as well as the original MONOA algorithm.