## 1 Introduction
### Population-Based Bio-Inspired Optimization Algorithms: An Overview
The Propagation Search Algorithm (PSA) takes its inspiration from wave propagation principles, specifically the transmission of voltage and current along lengthy power lines. PSA models these phenomena mathematically, using voltage and current as its search agents in the optimization process [35]. The Kepler Optimization Algorithm (KOA) is based on [PERSON]'s laws of planetary motion, utilizing these principles to calculate the precise positions and velocities of planets over time [36]. As a newer physics-based optimization method, the Archimedes Optimization Algorithm (AOA) is a metaheuristic approach that relies on Archimedes' law to drive its search process, showing significant efficiency in various applications [37]. Another notable example in physics-based optimization is the Gravitational Search Algorithm (GSA), which is inspired by [PERSON]'s gravitational theory, leveraging gravitational forces to guide its search agents towards optimal solutions [38]. Applications of Bio-Inspired Optimization in Engineering Problems Including PV Source Penetration in Distribution Systems  
Bio-inspired optimization algorithms have demonstrated remarkable success in addressing engineering design problems across various fields. In structural engineering, they assist in optimizing materials and geometries for load-bearing structures. In electrical engineering, they are used for the optimal placement and control of components in power distribution networks. Additionally, bio-inspired algorithms play a crucial role in mechanical design, control systems, and energy management, enabling engineers to achieve designs that balance multiple objectives, such as cost, performance, and sustainability. For example, the jellyfish search (JFS) algorithm was introduced in [39], inspired by the distinctive movement patterns of jellyfish. First, jellyfish can drift along with ocean currents or move within their own group. Where food sources are plentiful, jellyfish are drawn to these areas. Additionally, the numerical fitness function represents the amount of available food. JFS has shown promising applications across various engineering domains, including wind energy control via the PI controller design of a DFIG-based converter [40], path planning of unmanned aerial vehicles via evolutionary state estimation [41], over-current relay coordination with fault current limiters in power systems [42], maximum power extraction via PV array reconfigurations considering partial shadings [43], and the optimal array reconfiguration of thermoelectric generation considering varied temperature conditions [44]. Promoting the generation of energy from environmentally friendly sources, such as photovoltaic (PV) distributed electricity generation, has gained significant traction in recent years due to its potential to reduce emissions and enhance the sustainability of energy [45]. Meanwhile, enhancing savings on energy and minimizing losses in electricity have made electrical distribution network optimization crucial. Two effective methods to achieve these objectives are reactive power planning and PV production devices that are positioned and sized within the electricity network of distribution in an optimal manner [46]. Developing efficient optimization techniques is necessary to address the problems with solar power plants and capacitors in power networks [47]. Therefore, it is necessary to design innovative optimizing methods that can effectively address these issues and provide reliable solutions. Improved quality of power, regulation of voltage, and energy economy are just a few of the advantages that may be further realized in distribution systems by simultaneously optimizing the positioning and dimensions of photovoltaic panels and shunt capacitors. As a result, the distribution system's overall energy efficiency can be raised [48]. Solar energy systems can enable improvements in voltage during times of heavy demand, whereas shunt capacitors assist in stabilizing the level of voltage.