## 3 SubChain Salp Swarm Algorithm Description and Experiment
### Numerical Experiments  
To verify the performance of the proposed SSSA (SubChain Salp Swarm Algorithm), we used six well-known benchmark functions. During the testing process, we compared the SSSA with the standard SSA, standard Genetic Algorithm (GA), particle swarm optimization (PSO), artificial hummingbird algorithm (AHA) [22; 23], Grasshopper Optimization Algorithm (GOA) [13; 24], Moth-Flame Optimization Algorithm (MFO) [25; 26], and Whale Optimization Algorithm (WOA) [27; 28]. For a fair comparison, we set the population size to 100, the dimension to 10, and the number of iterations to 300 for all algorithms. Each algorithm was run 50 times on each test function. The average of the 50 runs was taken as the final result to eliminate uncertainties during the search process. The final iteration results were compared with the number of iterations required to achieve the optimized results, and the results are shown in Table 1.  
The iteration plots are presented in Figure 1. Since the SSSA can reach the optimal solution very quickly in many cases, we selected verification functions with optimization space to demonstrate the optimization performance. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{Functions} & \multicolumn{2}{c}{SSSA} & \multicolumn{2}{c}{SSA} & \multicolumn{2}{c}{GA} & \multicolumn{2}{c}{PSO} \\ \cline{2-9}  & Avg & Std & Avg & Std & Avg & Std & Avg & Std \\ \hline [PERSON] & \(-7.27\) & \(0.69\) & \(-6.69\) & \(0.71\) & \(-3.61\) & \(0.53\) & \(-3.46\) & \(0.40\) \\ [PERSON] & \(-10.15\) & \(1.58\) & \(-7.60\) & \(3.50\) & \(-2.39\) & \(0.75\) & \(-1.54\) & \(0.66\) \\ [PERSON]\_6 & \(-3.01\) & \(4.23\times 10^{-2}\) & \(-2.99\) & \(5.02\times 10^{-2}\) & \(-2.68\) & \(0.11\) & \(-2.83\) & \(5.55\times 10^{-2}\) \\ [PERSON] & \(-194.72\) & \(2.583\) & \(-71.39\) & \(32.54\) & \(-36.03\) & \(38.03\) & \(-65.73\) & \(52.13\) \\ [PERSON] & \(4.61\times 10^{-7}\) & \(2.88\times 10^{-6}\) & \(4.89\times 10^{-2}\) & \(0.20\) & \(3.31\times 10^{-3}\) & \(5.07\times 10^{-3}\) & \(6.70\times 10^{-3}\) & \(8.34\times 10^{-3}\) \\ [PERSON]\_[PERSON] & \(-26.83\) & \(0.08\) & \(-24.85\) & \(1.68\) & \(-9.18\) & \(4.10\) & \(9.64\) & \(49.50\) \\ \hline \multirow{2}{*}{Functions} & \multicolumn{2}{c}{AHA} & \multicolumn{2}{c}{GOA} & \multicolumn{2}{c}{MPO} & \multicolumn{2}{c}{GWO} \\ \cline{2-9}  & Avg & Std & Avg & Std & Avg & Std & Avg & Std \\ \hline Michalewicz & \(-3.86\) & \(0.33\) & \(-6.29\) & \(1.20\) & \(-3.55\) & \(0.72\) & \(-3.81\) & \(0.54\) \\ Shekel & \(-2.07\) & \(0.42\) & \(-5.61\) & \(3.48\) & \(-8.70\) & \(2.97\) & \(-7.55\) & \(0.003\) \\ Hartmann\_6 & \(-2.74\) & \(0.14\) & \(-3.00\) & \(0.04\) & \(-3.00\) & \(0.04\) & \(-3.00\) & \(0.04\) \\ [PERSON] & \(391.12\) & \(145.92\) & \(-200.2\) & \(0.94\) & \(-195.4\) & \(11.95\) & \(-151.9\) & \(62.87\) \\ [PERSON] & \(0.02\) & \(0.01\) & \(0.03\) & \(0.39\) & \(5.59\times 10^{-9}\) & \(0.01\) & \(6.79\times 10^{-7}\) & \(0.01\) \\ [PERSON]\_[PERSON] & \(7.75\) & \(36.55\) & \(-20.12\) & \(1.71\times 10^{-6}\) & \(-20.12\) & \(2.64\times 10^{-8}\) & \(-19.74\) & \(1.72\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Averages and standard deviations of the algorithm using different functions. Figure 1: Results of algorithms with different functions. From the table and figure, it can be observed that, for both functions where SSA performs well and those where it does not, the SSSA consistently achieves better results with faster convergence and smaller variance in the results. This validates the effectiveness of the improvement proposed in this paper. The LTL Vehicle-Cargo Matching System Based on the SubChain Salp Swarm Algorithm: Design and Experiment  
In this section, we illustrate the details of our improved SubChain Salp Swarm Algorithm, including the design of individual SubChains, which is the major modification in our proposed method, in Section 4.1, along with experimental settings and results in Sections 4.2 and 4.3.