## 1 Introduction  
The earliest approaches to optimization problems were mathematical or numerical [1], where the goal was to arrive at a zero-derivative point to arrive at the final answer. The search space expands exponentially as the number of dimensions rises, making it nearly impossible to use these techniques to solve nonlinear and non-convex problems with many variables and constraints. Additionally, numerical approaches may enter local optimality when the derivative is also zero. Such numerical approaches cannot guarantee the discovery of a globally optimal solution, since real-world problems usually exhibit stochastic behavior and have unexplored search areas [2]. To overcome the limitations of numerical approaches, more sophisticated meta-heuristic algorithms are routinely utilized to address difficult optimization issues. These techniques have the benefits of being easily applied to continuous and discrete functions, not requiring any extra complicated mathematical operations such as derivatives, and having a low incidence of falling into local optimality points. Single-solution-based methods and population-based methods are the two categories of meta-heuristic techniques. A solution (typically random) is generated and iteratively improved until the stopping criterion is reached in single-solution-based methods. Based on the interaction of information between the solutions, population-based methods create a random set of solutions in a predefined search space and are iteratively updated to find the (near) optimal solution. Deep learning is also a form of optimization technique that is frequently used in many different fields [3]. The most prevalent metaheuristic algorithms are those that draw their inspiration from evolutionary theory or normal social animal behaviors like foraging, mating, hunting, memory, and other behaviors. To more efficiently look for portions of the problem that are viable, this strategy can be applied in several different ways. Numerous swarm intelligence systems serve as examples. Particle Swarm Optimization (PSO) [4] is the birthplace of swarm intelligence algorithms, which are inspired by birds' foraging behavior. Ant Colony Optimization (ACO) [5] is an algorithm inspired by simulating the collective routing behaviors of ants in nature. Cuckoo Search (CS) [6] is an algorithm inspired by they raise their young using parasitism. Firefly Algorithms (FA) [7] are algorithms inspired by the flickering behavior of fireflies. Artificial Bee Colony (ABC) [8] is an algorithm inspired by imitating the honey collection mechanism of bees. New swarm intelligence algorithms have also been put forward in recent years. The Whale Optimization Algorithm (WOA) [9] is an algorithm inspired by the predatory behavior of whales. The Grey Wolf Optimizer (GWO) [10] is an algorithm inspired by the hunting behavior of grey wolf groups. The Seagull Optimization Algorithm (SOA) [11] is an algorithm inspired by simulating the migration of seagulls in the nature and the attack behavior (foraging behavior) in the migration process. The Slap Swarm Algorithm (SSA) [12] is an algorithm inspired by the aggregation behavior of slap swarms and their formation into a chain for predation and movement. The Butterfly Optimization Algorithm (BOA) [13] is an algorithm inspired by the behavior whereby butterflies receive, perceive and analyze the smell in the air to determine the food source and the potential direction of mating partners. Algorithms for swarm intelligence do, however, inevitably have significant shortcomings. A number of variables have an enormous impact on the algorithm. This is because swarm intelligence systems usually need a lot of modifications, including with respect to population size, iterations, inertia weights, etc. The choice of these parameters has a considerable impact on the algorithm, because various problems necessitate different parameter values, which are difficult to regulate.