## 1 Introduction
Metaheuristic algorithms based on swarms and societies in nature are called swarm-based algorithms. In order to find a solution to these algorithms, members of groups interact with one another within a search space. One of the most well-known algorithms in this category is particle swarm optimization (PSO) [11]. PSO simulates flocking birds' social behavior. There are several possible solutions represented by each particle in the group. Among the other algorithms in this category are ant colony optimization (ACO) [12], grey wolf optimization [13], and Sand Cat Swarm Optimization [14]. Metaheuristic algorithms with physics-based inputs are derived from physical laws and theories, like gravity and particle movement. Among the well-known physics-based metaheuristic algorithms are the Gravitational Search Algorithm (GSA) [15], the Big-Bang Big-Crunch (BBBC) [16], and the Charged System Search (CSS) [17]. In [5], the proposed modified grey wolf optimizer (MGWO) is applied to multi-level thresholding color image segmentation to achieve the optimum threshold. The authors used some strategies in leader selection and position update; in addition, they used a mutation operator to lead search agents to the optimum solution. In [1], the authors proposed a hybrid algorithm based on crayfish optimization and a differential evolution algorithm named ACOADE to use in color multi-threshold image segmentation. This hybrid algorithm maximizes the foraging parameter of crayfish optimization and uses the base process of the differential evolution (DE) algorithm to achieve the optimum threshold value of the image segmentation technique using the Otsu and Kapur entropy methods as objective functions. The authors of [18] proposed an improved whale optimization algorithm to overcome the limitations of the classical WOA in color multi-threshold image segmentation. In this way, enhancement significantly improved the segmentation accuracy and robustness of the results. In [19], the black widow optimization (BWO) algorithm is applied to a multi-level thresholding image segmentation problem. Similar to other studies in this field, the Otsu and Kapur entropy methods are used to evaluate as their objective function. Learning Enthusiasm-Based Teaching-Learning-Based Optimization (LebTLBO) is a recent metaheuristic known for its simplicity and low computational cost [20]. Its effectiveness in image segmentation is evaluated using the Berkeley Segmentation Dataset 500 (BSDS500). This dataset provides diverse and high-quality images suitable for benchmarking. Objective functions such as [PERSON]'s method and Kapur's entropy are employed to assess segmentation performance. Improved elephant herding optimization (IEHO) integrates opposition-based learning and chaotic sequences to enhance the exploration-exploitation balance [21]. Its efficiency is tested on multi-level thresholding (MTH) for image segmentation. [PERSON]'s entropy, [PERSON]'s method, and Masi entropy are used as objective functions to determine optimal thresholds. Recently, a novel 3D memristive cubic map employing dual discrete memristors (3D-MCM) has been proposed, exhibiting rich dynamical behaviors, including coexisting attractors, making it suitable for secure image encryption tasks [22]. To address the growing demand for secure and efficient image transmission, a novel color image encryption algorithm based on the 2D Logistic-Rulkov Neuron Map (2D-LRNM) was proposed, offering enhanced complexity and unpredictability through a hybrid chaotic model [23]. PSEQADE is a quantum differential evolutionary algorithm that uses a quantum-adaptive mutation strategy and a population state evaluation framework to address excessive mutation in QDE. The experimental results show excellent convergence performance, high accuracy, and stability in solving high-dimensional complex problems [24].