## 1 Introduction
### Population-Based Bio-Inspired Optimization Algorithms: An Overview  
Population-based bio-inspired optimization algorithms mimic collective behaviors observed in nature, where individual agents (particles, organisms, etc.) interact and evolve toward optimal solutions. Generally, the following four main types of meta-heuristic algorithms are classified: physics-based, evolutionary, swarm intelligence, and human-based algorithms [3]. These four categories capture the diversity of meta-heuristic optimization techniques. Each category has unique advantages, with applications suited to different types of engineering challenges, from static problems requiring reliable convergence to dynamic, multi-dimensional problems demanding adaptability and exploration. Evolutionary algorithms are inspired by biological evolution principles, specifically Darwinian concepts of selection, mutation, and reproduction. They simulate a population of candidate solutions that evolve over generations, continually improving based on fitness functions such as Genetic Algorithms (GAs) [4; 5], Evolutionary Programming (EP) [6; 7], Differential Evolution (DE) [8; 9], and Backtracking Search Algorithm (BSA) [10; 11]. These methods operate by iteratively evolving a population of potential solutions through operations inspired by biological processes like reproduction, mutation, cooperation, and competition. Their flexibility, coupled with the ability to explore complex landscapes efficiently, makes them ideal for a range of engineering applications. Swarm intelligence algorithms take inspiration from the collective behaviors observed in social animals, such as birds flocking, ant colonies, and fish schooling. In bird flocking, birds/particles represent solutions which adjust their velocities and consequently positions based on their own experiences and the experiences of their neighbors such as the Particle Swarm Optimizer (PSO) [12], hummingbird algorithm [13; 14], and satin bowerbird optimizer [15]. Similarly, Ant Colony Optimization (ACO) mimics the pheromone trail-laying behavior of ants, guiding individual agents based on the collective information left by others [16; 17]. Also, Fish Schooling Algorithms (FSA) are inspired by the collective, coordinated movement of fish in schools [18]. FSA mimics these behaviors by simulating individual fish as agents that interact with each other and their environment to locate optimal solutions such as the White Shark Optimizer (WSO) [19], salp swarm algorithm [20; 21],marine predator optimization [22; 23], manta ray foraging algorithm [24; 25], and the Tuna Swarm Optimizer (TSO) [26]. Human-based algorithms are a relatively new category in meta-heuristics, based on the emulation of human social interactions, behaviors, and decision-making processes. These algorithms model complex social behaviors, such as cultural evolution, competition, cooperation, and learning from shared experiences such as Teaching-Learning-Based Optimization (TLBO) [27; 28], Harmony Search Algorithm (HSA) [29], and human memory optimizer [30]. Several optimization problems were successfully addressed via recently developed algorithms in this category such as the Preschool Education Optimization Algorithm (PEOA) [31], mountaineering team-based optimization [32] and migration algorithm [33]. Physics-based algorithms are inspired by principles and phenomena in physics, particularly those that involve naturally occurring optimization processes. These algorithms simulate physical laws, such as gravity, electrical charge interactions, or thermal dynamics, to drive optimization. In optimization, the Prism Refraction Search (PRS) is a new, straightforward, yet highly effective single-solution metaheuristic algorithm designed for single-objective real-parameter optimization. PRS is rooted in physics principles and is inspired by ray optics, specifically the behavior of light refraction through a triangular prism [34].