## 3 Multi-Directional and Parallel Ant Colony Optimization (MPACO)
Figure 4: MPACO algorithm-based route generation framework. Table 4 summarizes the comparison of the computation speed using ACO and the proposed MPACO. The network as shown in Figure 4 is used as a test network. Four ants are used in both algorithms, and the optimal paths are obtained in one iteration. Table 4 shows that the overall agents' movement using ACO is longer than the movement using MPACO. This indicates that the computation speed of MPACO is faster than the speed of ACO. Algorithm 1 explains the route search algorithm for detecting a collision node. As explained with the illustrations, initial agents are divided into two groups, which start at the S-node and T-node, respectively. ```
Initialize: Current iteration\(\rightarrow\)\(int\) Overall number of agents \(\rightarrow\)\(AN\) for k=1 to \(AN/2\) Ants start from \(S\) node and \(T\) node (\(S\) node has \(AN/2\) ants, and \(T\) node has \(AN/2\) ants). Choose the next node using a \(\mathrm{P}_{ij}^{(k)}\). (Equation (1)) endfor When ants in different groups meet in a node, it is classified as a collision node (q). If (the existence of q == false) Go to Algorithm 2. else Go to Algorithm 3. endif
```  
**Algorithm 1** Route search algorithm for detecting a collision node. When a collision node is not detected, MPACO follows the procedures of ACO algorithm, as shown in Algorithm 2. ```
Initialize: Evaporation rate \(\rho\in(0,1]\) The objective function is to minimize the distance of the route where the ants are moved (Equation (2)). Combine the distances moved in each section. Choose the optimal candidate route \(f_{\mathrm{best}}\) (Equation (3)). Evaporate the pheromones (Equation (5)). Update the pheromones on \(f_{\mathrm{best}}\) route (Equation (6)). return Algorithm 1
```  
**Algorithm 2** Route search in the case of the non-existence of a \"collision node\". \begin{table}
\begin{tabular}{c c c} \hline \hline  & ACO & MPACO \\ \hline Iterations & 1 & 1 \\ Computation speed (Agents’ Total Movement) & 70.64 & 61.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the computation speed between ACO and MPACO. Then, the subsequent process is to find an intermediate node (M\({}^{\text{int}}\)) with the highest pheromone value near a collision node. The reasoned M\({}^{\text{int}}\) is listed as another starting node, and agents start their search with an updated starting node list (M\({}^{(\text{int}+1)}\)), as shown in Algorithm 4. The updated node list (M\({}^{(\text{int}+1)}\)) at the following iteration (int+1) includes the initial starting point (S-node) and the target node (T-node). If the number of nodes in M\({}^{(\text{int}+1)}\) is greater than the number of overall agents (AN), additional detection processes for collision nodes and intermediate nodes are stopped. The numerical analyses using the proposed algorithm are provided in Section 5.1. ```
Initialize: Current iteration\(\rightarrow\) int+1 number of M\({}^{(int+1)}\rightarrow\) v for k=1 to AN/v  Ants start from all M\({}^{(int+1)}\) nodes that are detected. Choose the next node using P\({}_{ij}^{(k)}\) (Equation (1)). endfor
```  
**Algorithm 4**Route generation Algorithm with an intermediate node (M\({}^{(\text{int}+1)}\)). Dynamic Configurable Network and Convolution-Type Multi-Directional and Parallel Ant Colony Optimization (CMPACO)  
While the previous section shows the effectiveness of the proposed network with networks with static topology, a number of real networks have dynamic changes in their topologies and configurations due to various reasons, such as route constructions and heavy traffic jams. An algorithm that constructs an efficient route in a dynamic network has been used in many research fields, as provided in Table 5. The changes of network topologies for learning processes have resulted in low performances of the existing algorithms. This section provides a variation of the MPACO algorithm that overcomes the issue, and explains how it works.