# A Particle Swarm and Smell Agent-Based Hybrid Algorithm for Enhanced Optimization
Furthermore, research has develed into the concept of adaptive PSO, another common PSO variant that dynamically adjusts the algorithm's parameters during optimization to enhance its performance [22; 23]. Various strategies, such as altering the inertia weight or adapting the learning component, have been explored to fine-tune the PSO update equation. These adaptations serve to balance the exploration and exploitation phases of the algorithm, ultimately improving the convergence speed and accuracy. Moreover, the multi-objective PSO is a specialized PSO modification tailored for solving multi-objective optimization problems [24; 25; 26]. Multi-objective optimization tasks involve the simultaneous consideration of conflicting objectives [24]. The multi-objective PSO employs a Pareto-based approach to generate a set of non-dominated individuals that represent the trade-offs between the different objectives. Essentially, the PSO algorithm and its variants stand as potent optimization techniques with widespread applications in solving diverse optimization problems, including mathematical test functions. The selection of a specific PSO variant hinges on the unique characteristics of the problem under investigation. In this paper, based on the smell agent optimization (SAO) algorithm, we introduce a hybrid method, denoted as the PSO-SAO algorithm, aimed at enhancing the convergence accuracy of the original PSO algorithm. We achieved this by modifying the velocity update process of the original PSO through the incorporation of the trailing mode from the SAO algorithm (proposed in [27]). Hence, the specific objective of our study is to use the concept of the trailing mode in the SAO algorithm to continuously introduce agents to track molecules with higher concentrations, thus guiding the particles in the PSO towards optimal fitness locations. The velocity update process in PSO has been adapted to depend on a newly introduced parameter called the hopping frequency in PSO-SAO. This parameter dictates whether our hybrid algorithm uses the trailing mode or the standard PSO velocity update equation. The optimal value for the hopping frequency can be determined through experimental analysis, taking into consideration the specific application area of interest. Our proposed PSO-SAO algorithm holds significant importance in the field of optimization techniques due to its ability to enhance convergence accuracy and efficiently navigate complex solution spaces. Its incorporation of the trailing mode from the SAO algorithm introduces adaptability, providing a promising approach for addressing optimization challenges. The algorithm's potential applications span various domains, including precision agriculture, path loss prediction, path planning, machine learning, and deep learning models. By offering an effective tool for optimizing complex systems, the PSO-SAO algorithm creates opportunities for enhancing decision-making processes, resource utilization, and overall system performance in practical applications. Therefore, in line with this concept, our study's primary contribution revolves around the innovative integration of PSO with the trailing mode of SAO, resulting in an improved performance. To evaluate its robustness, we follow standard benchmark procedures [28] and assess the PSO-SAO algorithm across 37 standard benchmark test functions [29], comparing it to the original PSO and SAO algorithms. The remainder of this paper is structured as follows: Section 2 details the proposed PSO-SAO algorithm, Section 3 presents the results and discussions, and Section 4 provides the paper's concluding remarks.