# Meta-Heuristic Optimization and Comparison for Battery Pack Thermal Systems Using Simulink
## 3 Meta-Heuristic Methods  
### Particle Swarm Optimization  
Particle swarm optimization is nature-inspired and mirrors the swarm dynamics observed in bird flocks or fish schools to solve optimization problems with specific constraints [18]. The genetic algorithm is rooted in evolution, whereas PSO is a swarm-centric search optimization methodology. The operational structure of PSO and GA is depicted in the flowchart in Figure 4. Within the PSO algorithm, each particle solution navigates the search space at a certain velocity, influenced by both local and global optimum positions. When these positions change, the relevant parameters update. The velocity describes the particle's movement pace and is determined by its current position, the global optimum, and random fluctuations. Consequently, particles closer to the local and global optimums tend to move slower. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\mathbf{R_{0}}\)/SOC & \(\mathbf{5}\)\({}^{\circ}\)C & \(\mathbf{20}\)\({}^{\circ}\)C & \(\mathbf{40}\)\({}^{\circ}\)C & \(\mathbf{R_{1}}\)/SOC & \(\mathbf{5}\)\({}^{\circ}\)C & \(\mathbf{20}\)\({}^{\circ}\)C & \(\mathbf{40}\)\({}^{\circ}\)C \\ \hline
0 & 0.0117 \(\Omega\) & 0.0085 \(\Omega\) & 0.009 \(\Omega\) & 0 & 0.0109 \(\Omega\) & 0.0029 \(\Omega\) & 0.0013 \(\Omega\) \\
10\% & 0.011 \(\Omega\) & 0.0085 \(\Omega\) & 0.009 \(\Omega\) & 10\% & 0.0069 \(\Omega\) & 0.0024 \(\Omega\) & 0.0012 \(\Omega\) \\
25\% & 0.0114 \(\Omega\) & 0.0087 \(\Omega\) & 0.0092 \(\Omega\) & 25\% & 0.0047 \(\Omega\) & 0.0026 \(\Omega\) & 0.0013 \(\Omega\) \\
50\% & 0.0107 \(\Omega\) & 0.0082 \(\Omega\) & 0.0088 \(\Omega\) & 50\% & 0.0034 \(\Omega\) & 0.0016 \(\Omega\) & 0.001 \(\Omega\) \\
75\% & 0.0107 \(\Omega\) & 0.0083 \(\Omega\) & 0.0091 \(\Omega\) & 75\% & 0.0033 \(\Omega\) & 0.0023 \(\Omega\) & 0.0014 \(\Omega\) \\
100\% & 0.0116 \(\Omega\) & 0.0085 \(\Omega\) & 0.0089 \(\Omega\) & 100\% & 0.0028 \(\Omega\) & 0.0017 \(\Omega\) & 0.0011 \(\Omega\) \\ \hline \(\mathbf{E_{\text{m}}}\)/SOC & \(\mathbf{5}\)\({}^{\circ}\)C & \(\mathbf{20}\)\({}^{\circ}\)C & \(\mathbf{40}\)\({}^{\circ}\)C & \(\mathbf{C_{1}}\)/SOC & \(\mathbf{5}\)\({}^{\circ}\)C & \(\mathbf{20}\)\({}^{\circ}\)C & \(\mathbf{40}\)\({}^{\circ}\)C \\ \hline
0 & 3.497 V & 3.506 V & 3.515 V & 0 & 1913 F & 12,447 F & 30,609 F \\
10\% & 3.552 V & 3.566 V & 3.565 V & 10\% & 4625.7 F & 18,872 F & 32,995 F \\
25\% & 3.618 V & 3.634 V & 3.640 V & 25\% & 23,306 F & 40,764 F & 47,535 F \\
50\% & 3.707 V & 3.713 V & 3.721 V & 50\% & 10,736 F & 18,721 F & 26,325 F \\
75\% & 3.913 V & 3.926 V & 3.938 V & 75\% & 18,036 F & 33,630 F & 48,274 F \\
100\% & 4.192 V & 4.193 V & 4.193 V & 100\% & 9023 F & 23,394 F & 30,606 F \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Battery properties utilized in this study. The rows indicate the state of charge, and the columns indicate cell temperature. [PERSON] and [PERSON] first introduced the basic particle swarm optimization algorithm [36]. Figure 1 provides a schematic representation of this basic PSO algorithm. Initially, the algorithm generates a distributed population of potential solutions, known as particles. In the search space, the current position \(x_{ij}\) of a particle can move until the algorithm reaches a predetermined maximum iteration, \(t_{max}\). As one particle identifies the best global positions within the entire swarm, other particles tend to follow its lead. Throughout the iterative process, every particle evaluates its performance and updates its personal best, or _Pbest_. Subsequently, the particle shares the most recent global best, _Gbest_, with all other particles and transitions to a new position. The velocity vector of individual particles, \(v_{ij}(t+1)\), can be determined. Following this, \(x_{ij}(t+1)\) is updated, as outlined in [36; 37].