# A Particle Swarm and Smell Agent-Based Hybrid Algorithm for Enhanced Optimization
## 2 Hybridization of PSO and SAO Algorithms
In order to improve the PSO's efficiency and prevent it from converging to suboptimal values, we incorporated the trailing mechanism from the SAO, for which the full working mechanism of the SAO algorithm can be accessed in [27; 30]. The SAO algorithm uses the phenomenon of smell and the intuitive trailing behavior of an agent to identify a smell source. The algorithm is inspired by the behavior of animals that use their sense of smell to locate food sources. The algorithm works by simulating the behavior of an agent that moves through a search space, leaving a trail of pheromones as it moves. The pheromones are then used to communicate information about the quality of the solutions found by the agent to other agents in the search space. The agents then use this information to guide their search towards better solutions. The algorithm is designed to balance exploration and exploitation of the search space, thus allowing it to find optimal solutions efficiently. The computational analysis of the SAO in [27; 30] demonstrates the robustness of SAO in finding optimal solutions for mechanical, civil, and industrial design problems. The experimental results obtained showed that the algorithm leads to an improvement in solution quality by 10-20% of other selected metaheuristics while solving constraint benchmarks and engineering problems, with further details available in [27; 30]. Figure 1: PSO operational flow process. +++ ==ERROR: No output for this page== \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multicolumn{1}{c}{**Fx**} & \multicolumn{1}{c}{**Name**} & \multicolumn{1}{c}{**D**} & \multicolumn{1}{c}{**Formula**} & \multicolumn{1}{c}{**C**} & \multicolumn{1}{c}{**Range**} & \multicolumn{1}{c}{**Fmin**} \\ \hline F33 & Quartic & 30 & \(f(i)=\sum_{i=1}^{2}\frac{i+1}{2}\) & \(i+1\) & \(rand(0,1)\) & S, MM & \([-128,128]\) & 0 \\ F4 & Rastrigino & 30 & \(f(i)=10+2\cdot(1,i)^{2}-100\)\(\geq(2\times(\
u_{\rm L}))\) & NS, MM & \([-52,512]\) & 0 \\ F35 & Rosenbrock & 30 & \(f(i)=\sum_{i=1}^{2}\) & \((100(i,2)+2\cdot(i+1)^{2})\) & NS, UM & \([-30,30]\) & 0 \\ F6 & Salomon & 30 & \(f(i)=1-\cos(2\sum_{i=1}^{2}\frac{i+1}{2})+0\)\(\sqrt{\sum_{i=1}^{2}\frac{i}{2}}\) & NS, MM & \([-100,100]\) & 0 \\ F87 & Sphere & 30 & \(f(i)=\sum_{i=1}^{2}\frac{i}{2}\) & S, MM & \([-100,100]\) & 0 \\ \hline \end{tabular}
\end{table} 
Table 1: Cont. Thus, based on the performance of the SAO algorithm, it demonstrated a good balance between exploitation and exploration, which significantly influenced the effectiveness of any population-based algorithm. Consequently, as the PSO's success relies heavily on the effectiveness of its velocity-computation technique and update process, there is potential for the trailing property of the SAO to be integrated into the PSO to prevent its convergence to suboptimal values. The trailing mode within the SAO algorithm carries significant importance as it directs agents from smell perception to evaporation locations. This mode captures both favorable and unfavorable odor molecules, which can serve as an occasional alternative to the position update behavior in PSO. The integration of this behavior in a hybrid algorithm will thus allow for dynamic position updates, using the solution found by the trailing behavior only if it surpasses the original PSO update solution. Moreover, this occasional switch eliminates the necessity of using velocity in the optimization process, facilitating a more extensive search. Furthermore, we note that in the trailing mode of the SAO, agents continuously track molecules with a higher concentration, hence directing them towards the best fitness location. The agents in the SAO algorithm possess olfaction capacities based on psychological and physical conditions, and the size of the olfactory lobe. A larger olfactory lobe favors exploitation, while a smaller lobe implies weaker olfaction.