# Gaslike Social Motility: Optimization Algorithm with Application in Image Thresholding Segmentation
## 1 Introduction  
The \"No Free Lunch\" theorem asserts that no single algorithm can universally outperform all others across every possible problem [1]. Consequently, a diverse range of metaheuristic algorithms (MAs) has been developed, including Evolutionary Algorithms (EAs) and Swarm Intelligence Algorithms (SAs) [2]. Among the most prominent MAs are Differential Evolution (DE) [3], Artificial Bee Colony (ABC) [4], Particle Swarm Optimization (PSO) [5], Genetic Algorithm (GA) [6], and Ant Colony Optimization (ACO) [7]. Recent advancements have introduced innovative particle-based algorithms with notable performance. These include the Artificial Hummingbird Algorithm (AHA), whichemulates the foraging and flight behaviors of hummingbirds [8]; Colliding Bodies Optimization (CBO), which models solutions as physical bodies undergoing one-dimensional collisions [9]; and Enhanced Colliding Bodies Optimization (ECBO), an improved variant of CBO that incorporates mass and velocity to refine collision dynamics [10]. Additionally, hybrid approaches like the Artificial Hummingbird Algorithm with Aquila Optimization (AHA-AO) [11] and Social Network Search (SNS) have gained traction. SNS simulates social media interactions, where users influence one another through mood-driven behaviors such as Imitation, Conversation, Disputation, and Innovation, mirroring real-world opinion dynamics [12]. Metaheuristic algorithms (MAs) generate solutions by efficiently exploring the search space while progressively narrowing the search area. Their performance hinges on the ability to balance exploration, i.e., searching globally for diverse solutions, and exploitation, i.e., refining solutions within promising regions. Initially, when no prior information about the search space is available, MAs prioritize exploration to identify a wide range of potential solutions. As the algorithm progresses and converges toward potential optima, the focus shifts to exploitation, enhancing solution precision and accuracy [13]. Modern real-life optimization problems are often highly complex, making them difficult to solve using traditional exact methods. This complexity stems from factors such as high dimensionality, intricate parameter interactions, and multimodality [13]. Metaheuristic algorithms (MAs) have emerged as a robust alternative, offering effective solutions to these challenging problems [14]. Parametric identification is a crucial application in automatic control, but it presents significant challenges due to the complexity of the models involved. These models often include numerous parameters and multiple ordinary differential equations, making traditional identification methods inadequate. While parametric estimation techniques for linear systems are well-established [15], they often fail to address the complexities of non-linear systems. Conventional approaches are limited by their reliance on assumptions, such as unimodality, continuity, and differentiability of the objective function, which rarely apply to non-linear systems [16]. Another important application is in image analysis, where image segmentation remains a critical and extensively researched task [17]. This process is a critical preliminary step in image analysis, aiming to divide an image into meaningful and homogeneous regions based on characteristics such as gray values, edge information, and texture. Framing this as an optimization problem involves minimizing the cross-entropy between the object and the background. However, this approach often encounters multiple local minima, complicating the computational process. Furthermore, the computational time grows exponentially with the number of thresholds, making it a challenging and resource-intensive task. To address key limitations, particularly the high computational cost of threshold searches, numerous algorithms have been developed. In scenarios where traditional methods fall short, metaheuristic algorithms (MAs) offer a promising alternative.