## 5 Examples and Results
### Algorithm Comparison Analysis  
In order to test the performance of HDA-CR proposed in this paper and solve the multi-period allocation model of hazardous materials, HDA-CR is compared with the traditional MODE, the single period multi-dimensional allocation problem solving algorithm (ERNS-DE) in literature [40], as well as other classical multi-objective algorithms, such as NSGA-II [41] and multi-objective particle swarm optimization (MOPSO) [42], by combining the double-objective optimization model in Equation (18) and setting the confidence level \(\alpha^{u}=\alpha^{l}=0.05\). Among them, the basic parameters of MODE and ERNS-DE are consistent with the corresponding parameter settings in Table 2. NSGA-II and MOPSO use the corresponding parameters in literature [41] and literature [42], respectively. Figure 7a-h shows the comparison of the Pareto optimal solution evolution curves of five algorithms for solving the multi-objective model of the multi-period allocation of hazardous materials (Equation (18)) under different scenarios. It can be seen from the evolution curves of the Pareto optimal solution under eight scenarios that HDA-CR converges faster than other algorithms, and the size of Pareto solution space searched is larger than other algorithms. For example, as shown in Figure 7a, the evolution curve of the HDA-CR converges after about 120 iterations and can search 12 Pareto optimal solutions in \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experimental Scenarios** & **Environment Settings** & **Supply and Demand Cases** & **Period Numbers** \\ \hline See 1 & Environment 1 & Case 1 & 5 \\ See 2 & Environment 1 & Case 2 & 5 \\ See 3 & Environment 2 & Case 1 & 5 \\ See 4 & Environment 2 & Case 2 & 5 \\ See 5 & Environment 1 & Case 1 & 24 \\ See 6 & Environment 1 & Case 2 & 24 \\ See 7 & Environment 2 & Case 1 & 24 \\ See 8 & Environment 2 & Case 2 & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental scenarios settings. Scenario 1, while other algorithms converge relatively slowly and the number of Pareto optimal solutions searched does not exceed 9. It shows that HDA-CR can effectively improve the diversity of the population in the experimental scenario and accelerate the evolution efficiency of the population compared with other algorithms. In addition, it can be seen from the comparison results of (a-d) and (e-h) in Figure 7 that with the increase in the number of periods, the above five algorithms need more iterations to converge, but the advantages of HAD-CR still exist, and a greater difference in the number of Pareto optimal solutions is found. This indicates that HDA-CR has a better solution effect in the long-term allocation of hazardous materials. For example, Figure 7a,e is in the same experimental environment and resource configuration. In Figure 7e, HDA-CR can search 30 Pareto optimal solutions, and other algorithms can search no more than 23 Pareto optimal solutions. This shows that HDA-CR has more obvious search advantages when considering the number of allocated periods is 24 rather than 5. Figure 7: Comparison of algorithm evolution curves in different scenarios. Figure 8 shows the distribution of the Pareto solution set obtained by the above five algorithms in different scenarios clearly. According to the properties of the Pareto solution, it can be seen intuitively that the Pareto optimal solution obtained by HDA-CR is superior to the other four algorithms in terms of quantity and scale in different scenarios. For example, Figure 8h shows the distribution of two objective function values of the Pareto solution obtained by five algorithms in the multi-period allocation model of hazardous materials (Equation (18)) under Scenario 8. It can be seen that the distribution of Pareto solution set searched by HDA-CR is more uniform and the quality is obviously superior (the smaller the values of the two objective functions, the higher the quality of the solution).