## 1 Introduction  
Image segmentation aims to divide an image into several regions with similar features or semantic meanings for further processing and analysis [1]. This technique has attracted significant attention in various fields, including early disease detection [2], autonomous driving [3], and image processing applications [4]. To achieve accurate and robust segmentation, it is essential that the pixel characteristics within each region are consistent [1]. Threshold-based segmentation methods in image segmentation are typically divided into two categories [5]. Bi-level thresholding is a fundamental technique that segments an image into two separate classes by determining a single optimal threshold value. On the other hand, multi-level thresholding partitions the image into multiple segments by locating several threshold values. Multi-threshold segmentation refers to the process of dividing an image into several object and background regions by determining multiple threshold values [6]. Existing image thresholding segmentation techniques primarily include two classical approaches: the Otsu method and the Kapur entropy method. The Kapur entropy approach selectsthresholds based on the principles of information theory [1; 6]. It operates by evaluating the entropy values of pixel distributions at various grey levels within the image. The threshold corresponding to the maximum entropy is chosen as the optimal point for image segmentation. The Otsu method is a popular technique for image segmentation that relies on analyzing greyscale distributions [1; 6]. Its main strategy is to identify a threshold that separates the image into two groups, aiming to reduce the variance within each group as much as possible. By iteratively assessing intra-class variances, the method selects the threshold that yields the lowest total variance, leading to optimal binarization. The increase in the number of thresholds in multi-threshold image segmentation leads to an exponential rise in computational complexity, which in turn causes traditional multi-level thresholding techniques to suffer from reduced accuracy and slow convergence. To address these limitations, metaheuristic algorithms have been employed in image segmentation tasks, demonstrating impressive performance. There have been many metaheuristic algorithms presented in the last few decades. Metaheuristic algorithms are used to solve real-world problems in different dimensions. It is possible to find the best or near-optimal solution using metaheuristic algorithms. Based on the No-Free-Lunch (NFL) theory [7], it has been concluded that there is no algorithm that can find all the possible solutions to optimization problems. There is a large difference between a heuristic algorithm and a metaheuristic algorithm in avoiding local optima trapping. Unlike heuristic algorithms, metaheuristic algorithms try to find a global optimum or optimal solution. Metaheuristic algorithms avoid being trapped in local optima through the use of exploration and exploitation phases. In each metaheuristic algorithm, these phases are the main operations. In addition, the trade-off between these two phases is important. The process of exploration involves looking for the most effective solution(s) for a given area(s), while the process of exploitation involves focusing on the most effective solution(s) for a given area(s) [8]. In most cases, the exploration ability of search agents must be increased in the initial iterations in order to locate potential areas and then exploit the optimum solution once discovered. Metaheuristic algorithms can be divided into three categories: evolution-based, swarm-based, and physics-based. Evolutionary algorithms are largely based on natural laws and behaviors. Based on [PERSON]'s theory of evolution, the genetic algorithm is a metaheuristic algorithm [9]. Another evolution-based metaheuristic algorithm is differential evolution (DE) [10], another algorithm based on Darwinian theory, although it differs from GA in its selection phase.