## 2 Literature Review  
### Metaheuristic Optimization Algorithms  
Numerical optimization algorithms are generally classified into two broad categories: deterministic and stochastic approaches [2], as illustrated in Figure 1. Deterministic algorithms operate under the assumption that the problem model is completely defined, with a clear and explicit link between potential solutions and their associated outcomes.  
Prominent examples of such algorithms include gradient descent, conjugate gradient methods, mixed-integer nonlinear programming, and the branch and bound technique. These methods typically leverage gradient information to navigate the solution space and are known for their robustness. Exact algorithms can guarantee optimal solutions, provided the problem is not NP-hard, in which case they may become computationally impractical. For complex, NP-hard problems commonly encountered in the real world, approximate methods (especially metaheuristic algorithms) have become increasingly popular. These approaches introduce randomness and probabilistic reasoning to efficiently explore the solution space. Rather than seeking the perfect solution, their goal is to find a sufficiently good one within a reasonable timeframe.  
As depicted in Figure 1, metaheuristic algorithms are commonly grouped into four categories: evolutionary, swarm intelligence, physics-based, and human-based methods. Among evolutionary algorithms, traditional techniques such as Genetic Algorithms (GA) and Differential Evolution (DE) remain widely used. More recent innovations include the Covariance Matrix Adaptation Evolution Strategy with Adaptive Population (CMAES-APOP) [17], the Love Evolution Algorithm (LEA) [18], and the Multi-Adaptation DE (MadDE) [19].  
Swarm intelligence-based algorithms have also found widespread use in engineering and optimization domains. Notable methods in this group include the Particle Swarm  
Figure 1: Classification of numerical optimization algorithms: exact and metaheuristic techniques.  
Optimization (PSO) [20], Whale Optimization Algorithm (WOA) [21], Quantum-based Avian Navigation Optimizer (QANA) [22], Starling Murmuration Optimizer (SMO) [23], and a modified version of Artificial Rabbits Optimization called MNEARO [24].  
Physics-inspired algorithms draw their strategies from physical phenomena. These include Nuclear Reaction Optimization (NRO), modeled after nuclear interactions [25]; the Flow Regime Algorithm (FRA), inspired by principles of fluid dynamics [26]; Plasma Generation Optimization (PGO), based on plasma generation processes [27]; and Colliding Bodies Optimization (CBO), which mimics the physics of object collisions [28]. Another example is the Doppler Effect-Mean Euclidean Distance Threshold (DE-MEDT), which draws from the Doppler shift phenomenon [29].  
Human-based metaheuristics are another fascinating class that has shown promise across various disciplines, including engineering, healthcare, and data analysis. These methods are inspired by social behaviors and cognitive processes. Some widely recognized human-based algorithms are Brain Storm Optimization (BSO) [30], Poor and Rich Optimization (PRO) [31], Teamwork Optimization Algorithm (TOA) [32], Skill Optimization Algorithm (SOA) [33], and the Gaining-Sharing Knowledge-Based Algorithm (GSK) [16].