## 2 Literature Review  
Recent advancements in optimization techniques have increasingly focused on hybrid algorithms to solve complex engineering design problems, capitalizing on the strengths of multiple approaches to enhance solution quality and convergence speed. [PERSON] and [PERSON] [8] introduced an advanced hybrid algorithm, haDEPSO, which integrates differential evolution (aDE) with particle swarm optimization (aPSO). The aDE component prevents premature convergence through novel mutation, crossover, and selection strategies, while aPSO utilizes gradually varying parameters to avoid stagnation. This hybrid approach was validated on five engineering design problems, demonstrating superior convergence characteristics through extensive numerical, statistical, and graphical analyses. [PERSON] et al. [9] introduced HMPANM, a hybrid optimization algorithm combining Marine Predators Optimization with the Nelder-Mead method to improve local exploitation capabilities. This algorithm was applied to the structural design optimization of automotive components, proving its effectiveness in achieving optimal designs under competitive industrial conditions. [PERSON] and [PERSON] [10] further explored hybrid metaheuristics for automotive engineering design, applying the hybrid Taguchi Salp Swarm-Nelder-Mead algorithm (HTSSA-NM) and manta ray foraging optimization (MRFO) to optimize the structure of automobile brake pedals. The results showed HTSSA-NM's superiority in minimizing mass while achieving better shape optimization compared to other algorithms. [PERSON] and [PERSON] [11] introduced a collaboration-based hybrid grey wolf optimizer and sine cosine algorithm (cHGWOSCA), which enhances global exploration through SCA while maintaining a balance with exploitation via a weight-based position update mechanism. This algorithm demonstrated high performance on IEEE CEC benchmarks and real-world engineering problems. Similarly, [PERSON] et al. [12] proposed the hybrid multi-population algorithm (HMPA), combining artificial ecosystem-based optimization (AEO) with Harris Hawks optimization (HHO). HMPA employs strategies like a Levy flight, local search mechanisms, and quasi-oppositional learning, resulting in improved exploration and exploitation. [PERSON] et al. [13] introduced the hybrid political algorithm (HPA), which enhances the political optimizer's exploration process for global optima by improving particle movement during computation. HPA was tested on engineering optimization problems, outperforming other algorithms in avoiding local optima. [PERSON] et al. [14] presented a Taguchi method-integrated hybrid harmony search algorithm (HHS), focusing on parameter optimization through statistical estimation of control parameter values, achieving rapid convergence in engineering design problems. [PERSON] et al. [15] introduced PSOSCANMS, a hybrid algorithm that integrates PSO with the sine cosine algorithm (SCA) and the Nelder-Mead simplex (NMS) technique. This approach addresses PSO's drawbacks, such as low convergence rates and local minima entrapment, by enhancing exploration-exploitation balance through mathematical formulations from SCA and NMS. The algorithm was benchmarked on various optimization problems, demonstrating significant improvements over traditional PSO. [PERSON] et al. [16] introduced a hybrid algorithm that integrates quantum-behaved particle swarm optimization (QPSO) with a binary tournament technique to tackle bound-constrained optimization problems. This algorithm demonstrated superior performance on several benchmark problems and engineering design challenges, offering promising results. [PERSON] et al. [17] developed the hybrid CSOAOA algorithm, combining the arithmetic optimization algorithm (AOA) with point set, optimal neighborhood learning, and crisscross strategies. CSOAOA was highly effective, with improved precision, faster convergence rates, and better solution quality.