## 4 The Proposed HABC  
ABC, a well-known swarm-based meta-heuristic algorithm, was initially presented by [PERSON] in 2005 [PERSON] (2005). The algorithm is modeled after the intelligent search behavior of honey bees. The ABC algorithm has been effectively utilized to address a diverse range of optimization problems, such as function optimization, parameter tuning, and feature selection. It is reputed for its uncomplicated nature, effectiveness, and ability to perform well on both unimodal and multimodal problems. The ABC algorithm utilizes a group of artificial bees to find the best possible solution to a problem. These bees are categorized into three types: employed bees, onlooker bees, and scout bees, all of which play a crucial role in the search process. The scout bees conduct random searches in the exploration area to identify fresh territories that have yet to be investigated. Exploring space is the responsibility of the scout bees. Some scout bees who possess a strong fitness function are transformed into employed bees. They evaluate the quality of the solutions using a fitness function, and communicate the information about their best solutions to the onlooker bees. Based on the input provided by the employed bees, the onlooker bees choose the most favorable solutions and enhance them by investigating the exploration space near those selected solutions. These bees have the dual role of carrying out both the exploration and exploitation phases of the algorithm. The ABC algorithm employs two main approaches to arrive at the best possible solution: scout and onlooker bees utilize random search, while employed and onlooker bees engage in neighbor search. Employed bees focus on exploring the solution positions and onlooker bees are created to select new food positions and explore the surrounding areas. In addition, the algorithm generates random scout bees to discover new food positions in the search space. The ABC algorithm can be represented mathematically using Equations (8)-(10) [PERSON] (2005). \[P_{i}=\frac{fit_{i}}{\sum_{n=1}^{SN}fit_{n}} \tag{8}\]  
\[V_{ij}=X_{ij}+\varphi_{ij}\left(X_{ij}-X_{kj}\right) \tag{9}\]  
\[X_{L}^{j}=X_{min}^{j}+rand(0,1)(X_{max}^{j}-X_{min}^{j}) \tag{10}\]  
where \(fit_{i}\) = the fitness function of the \(i\)-th solution, \(X_{min}^{j}\) = the low limit of search space, \(P_{i}\) = the probability of selecting employed bees by onlooker bees, \(V_{ij}\) = onlooker bee, \(X_{L}^{j}\) = scout bees, \(SN\) = number of employed bees, \(X_{max}^{j}\) = high limit of search space, \(i\in\)[1, 2,..., \(SN\)], \(j\) = dimension \(\in\) [1, 2,..., \(D\)], \(k\) = onlooker bee number, \(\varphi_{ij}\) is the random number \(\in\) [0, 1], and \(L\) = scout bee number. The standard ABC has limitations, such as low exploitation and the possibility of getting trapped in local minima. The standard ABC focuses on conducting localized searches around employed bees, while onlooker bees explore new food sources and conduct searches in their vicinity. The main goal of onlooker bees is to enhance the fitness function of solutions through targeted neighborhood searches around the employed bees. Suppose the onlooker bees venture beyond conducting neighborhood searches around employed bees, and also explore several of the best positions. In that case, this will result in the discovery of diverse optimal solutions and the exploration of previously unexplored regions of the search space. Consequently, the ABC executes a more effective local and global search while simultaneously promoting diversity in the solutions. This leads to an improvement in the algorithm's convergence rate. In this paper, two other operators are proposed to improve the exploitation and exploration of the standard ABC. To develop a hybrid ABC (HABC), the migration operator of the BBO is used to improve the exploitation of the algorithm. Moving towards the global best of PSO is also proposed to improve the exploration of the ABC.