## 2 Methods
### Optimization Algorithm Design
For decision-makers who value the balance of drone use and time requirements, the solution in box (c) is recommended. Table 5 shows the Pareto optimal scheme. Figure 8 is a visualization of Pareto's optimal solution. Figure 9 is a curve of the changing trend of the objective function value drawn by using the average value obtained after running the MIBSO algorithm 30 times, representing the algorithm's process of searching for the optimal solution. It can be seen from the figure that with the increase in the number of iterations, the values of multiple objective functions show a continuous optimization direction. Figure 8: Visualization of Pareto optimal solution. Figure 7: Analysis of Pareto optimal solution. (**a**) Suggested plan 1; (**b**)suggested plan 2; (**c**) suggested plan 3. ## 4 Algorithm Performance Analysis

This section mainly tests and evaluates the designed algorithm's convergence, distribution, and comprehensive performance (MIBSO). This paper's objective function and the independent variables' attributes led to the selection of three test functions from the DTLZ series [27]: DTLZ4, DTLZ5, and DTLZ7. These functions are variable tests of any scale concerning the number of decision variables and targets. Select generational distance (GD) and the Spacing metric as the algorithm's convergence and distribution evaluation index, respectively. Moreover, select Hypervolume (HV) and Inverted Generational Distance (IGD) as comprehensive evaluation indicators of the algorithm, which are described as follows:

GD [28]: Used to represent the interval distance between the solved Pareto frontier (PFobtained) and the true Pareto frontier (PFtrue), obtained by calculating the average minimum distance between each point in the solution set Pobtained and the reference set Ptrue. The smaller the GD value, the better the convergence. The function is Formula (38). \[GD\underline{\Delta}\frac{\left(\sum\limits_{i=1}^{n}d_{i}^{p}\right)^{1/p}}{n} \tag{38}\]

Spacing metric [28]: Used to evaluate the distribution of individuals in an approximate solution set in the target space by calculating the standard deviation of the minimum distance from each solution to the other solutions. The smaller the Spacing value, the more uniform the solution set. The function is defined as in Formula (39). \[\Delta=\sum\limits_{i=1}^{|PF|}\frac{d_{i}-\overline{d}}{|PF|} \tag{39}\]

HV [29]: Used to calculate the volume of the space region enclosed by the non-dominated solution set and the reference point. The larger the HV value, the better the comprehensive performance of the algorithm. The function is Formula (40). \[HV=\lambda\left(\cup_{i=1}^{|S|}v_{i}\right) \tag{40}\]

IGD [29]: Inverted generation distance is the inverse mapping of generation distance, obtained by calculating the distance average from each reference point Prue to the nearest solution Pobtained. The smaller the IGD value, the better the comprehensive performance of the algorithm. The function is Formula (41). \[IGD=\frac{\sum\limits_{\hat{j}\in PF*}d^{\prime}\hat{j}}{n} \tag{41}\]

Figure 9: The curve of the index changes the trend. (**a**) The trend curve of the total cost with the number of iterations; (**b**) the variation curve of the variance of the UAV energy residual with the number of iterations; (**c**) the trend curve of the task penalty value with the number of iterations. From Table 7, it can be seen that overall, MIBSO performs better than NSGA-II. MIBSO has good performance in convergence and distribution and is feasible. On DTLZ4, MIBSO outperforms NSGA-2 in all four indicators. On DTLZ5, MIBSO exceeds NSGA2 in three indicators, and on DTLZ7, MIBSO surpasses NSGA2 in two indicators. ## 5 Conclusions

1. Model: This paper comprehensively considers factors of UAV load, energy consumption, cargo quality, and volume, intending to minimize the total cost of drone distribution and the full punishment of tasks, as well as optimize the balance of drone usage.