## 1 Introduction  
Metaheuristic techniques represent a prominent area of study in the field of computational optimization, offering a variety of methods for solving complex and often intractable problems across various domains [1]. These techniques, characterized by their ability to escape local optima and explore the global search space, have gained substantial traction due to their versatility and efficacy in tackling a wide array of optimization challenges [2]. The genesis of metaheuristic algorithms can be traced back to the 1960s and 1970s, with the advent of strategies like Genetic Algorithms (GAs) [3] and Simulated Annealing (SA) [4], which drew inspiration from biological evolution and thermodynamics, respectively. However, the term \"metaheuristic\" was formally coined in the late 1980s and early 1990s and began to see widespread adoption in academic and research circles. This period marked a paradigm shift in optimization techniques, moving from traditional, deterministic methods to more stochastic and heuristic-based approaches [5]. At its core, a metaheuristic is a high-level problem-independent algorithmic framework that provides a set of guidelines or strategies to develop heuristic optimization algorithms. Metaheuristics do not guarantee an optimal solution [6]; instead, they seek to find a sufficiently good solution within a reasonable time frame, making them particularly useful for practical applications where time and resources are limited [7]. The landscape of metaheuristic techniques is diverse, encompassing a broad spectrum of algorithms inspired by natural phenomena, psychological processes, and even human-made systems, including Evolutionary Algorithms (EAs) [8], Swarm Intelligence (SI)-based [9] algorithms like Particle Swarm Optimization (PSO) [10] and Ant Colony Optimization (ACO) [11], and physics-based methods like the Gravitational Search Algorithm (GSA) [12]. Each of these algorithms operates on the principle of iterative improvement, where a set of candidate solutions undergoes various processes such as selection, crossover, mutation (in the case of EAs), or movement and updating of positions (in swarm intelligence algorithms) to converge towards an optimal or near-optimal solution [13]. The application of metaheuristic techniques spans numerous domains, ranging from engineering design optimization to financial modeling [14], from logistics and supply chain management to bioinformatics, and from machine learning to network design. Their adaptability and robustness in handling multi-modal, non-linear, and high-dimensional problems make them an indispensable tool in the arsenal of modern-day researchers and practitioners [15; 16]. However, there are several limitations and challenges associated with metaheuristics, including the risk of premature convergence, the balance between exploration and exploitation, and the need for parameter tuning [17]. Thus, the choice of a suitable metaheuristic algorithm is decided based on the specific nature and requirements of the problem at hand. In the evolving landscape of metaheuristic algorithms, a notable gap exists in their ability to fully meet the intricate requirements of complex engineering optimization problems. This gap analysis identifies these shortcomings and explores how the Hybrid FVIMDE Algorithm aims to address them, enhancing the overall efficacy of optimization processes. Further, the No-Free-Lunch (NFL) Theorem asserts that no single optimization algorithm is universally superior across all problem types. Established by [PERSON] and [PERSON], it emphasizes that an algorithm's effectiveness is highly problem-specific, challenging the notion of a one-size-fits-all solution in algorithm design. This theorem asserts the importance of selecting the right algorithm based on the specific characteristics of the problem at hand and has encouraged the development of more adaptive, hybrid algorithms that combine the strengths of various approaches to address a broader range of optimization challenges [18].