## 4 Proposed Improved HBMO Algorithm
### Efficiency Analysis of Improved HBMO Algorithm  
To minimize the makespan, the machining time and the machining cost, we solve the above cases by using the HBMO algorithm. Based on Matlab programming, the IPPS of aerospace complex components in the above example is implemented on a computer with 1.6 G CPU and 8G memory. The main parameters of the algorithm are determined by sensitivity analysis. The level of these major parameters are as follows: \(Gen_{\text{max}}=\{150\), 200, 250\(\}\), \(\mathbf{\alpha}=\{0.5,\,0.7,\,0.9\}\), \(threshold=\{0.001,\,0.045,\,0.1\}\) and \(SperNum=\{75,\,100,\,125\}\). The HBMO algorithm is run 10 times for each parameter combination. The max spread (MS) metric is applied to assess the performance of each combination. The main effect plot is available in Figure 13, and a larger value of MS indicates better performance. After several runs, the following parameters were adopted: iteration times or \(Gen_{\text{max}}=200\) of the algorithm, colony size or \(BeNum=200\), \(QueenNum=50\), energy and speed attenuation coefficient of the queen or \(\mathbf{\alpha}=0.9\), energy threshold or \(threshold=0.001\), seminal vesicle capacity or \(SperNum=100\), number of young bees or \(BroodNum=100\), number of worker bees or \(WorkerNum=5\), and iteration times of worker bees breeding young bees or \(LS_{\text{max}}=20\). The record Pareto solution is set after the program runs independently many times. On this basis, to verify the effectiveness of the improved HBMO algorithm proposed in this paper, we use NSGA-II to solve IPPS, and the Patreo solutions between the HBMO and NSGA-II optimizer in small-scale instances are summarized in Table 7. The parameters of NSGA-II are as follows: the population size is 200, the iteration times are 100, the crossover probability is 0.8, and the mutation probability is 0.1. The Pareto solution front is shown in Figure 14.  
From Figure 14, it can be seen that the improved HBMO algorithm retains 10 non-dominated solutions and the NSGA-II algorithm retains 8 non-dominated solutions under the condition of satisfying the number of iterations. It can be seen from Figure 14 that the frontier point of the improved HBMO algorithm is obviously better than that of the NSGA-II algorithm in terms of the makespan, the machining time and the machining cost. Comparing the data in Table 7, it can be seen that the solution obtained by the improved HBMO algorithm is better than that obtained by the NSGA-II algorithm in terms of the makespan and the machining cost, in which the completion time is reduced by 8.47%, and the machining cost is reduced by 2.19%, while the solutions obtained by the two algorithms are similar in terms of the total machine tool running time. The reasons for the above phenomenon are as follows:  
1. The improved HBMO algorithm has set up a queen bee collection preservation mechanism based on the crowding degree in each generation of the iterative process, which can save the current non-inferior solution of the bee colony and participate in the generation of the next generation, ensure the transmission of excellent genes and promote the optimization of the algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Tool Number**} & \multicolumn{2}{c}{**Tool Cost per Unit**} & \multirow{2}{*}{**Tool Number**} & \multicolumn{2}{c}{**Tool Cost per Unit**} \\  & **Time (h/CNY)** & & **Time (h/CNY)** \\ \hline T1 & 5 & T14 & 6 \\ T2 & 4 & T15 & 5 \\ T3 & 5 & T16 & 4 \\ T4 & 4 & T17 & 5 \\ T5 & 9 & T18 & 7 \\ T6 & 8 & T19 & 9 \\ T7 & 9 & T20 & 8 \\ T8 & 4 & T21 & 6 \\ T9 & 5 & T22 & 6 \\ T10 & 4 & T23 & 4 \\ T11 & 4 & T24 & 5 \\ T12 & 5 & T25 & 7 \\ T13 & 6 & T26 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Tool cost per unit time. 2.