## 4 Proposed Algorithm  
In this section, the proposed algorithm will be described in detail. The key problem of the three algorithm frameworks proposed is to determine an appropriate encoding method for the small scale problem. A new encoding method is introduced, as the scheduling scheme \(S^{uw}=\{<5,2,3>,<4,1>\}\). It consists of two vectors, and each of the vectors determines the order in which a UAV delivers packages. For example, the distribution scheme of the above example \(S^{uw}\) is that UAV \(u_{1}\) delivers packages \(p_{5}\), \(p_{2}\), \(p_{3}\), and UAV \(u_{2}\) delivers packages \(p_{4}\), \(p_{1}\), respectively. Each UAV completes its package tasks through multiple flights. The number of flights is determined by the load capacity of the UAV c. The encoding method is essentially a sequence of packages. It can accurately assign each package task and find a better solution when the search space is small. As our algorithm is a hybrid of Initial Solution Generation Algorithm (ISG) and heuristic algorithms, we first provide a brief description about ISG algorithm as follows. Once a better initial solution can be found to participate in the iterations, more satisfactory efficiency will be achieved. Since the initial solution to the scheduling scheme \(S^{uw}\) is essentially a sort of packages, ISG is used to generate it. The shortest path through all express cabinets is calculated by a simple Simulated Annealing (SA) algorithm (Lines 1-15). According to the shortest path and the best delivery time \(t_{i}^{0}\), the elements in \(S^{init}\) are ordered as the initial solution (Lines 16-18). ``` Initial Solution Generation Algorithm \(ISG()\) \(L\leftarrow\{s_{1},s_{2},\ldots,s_{m}\}\)\(\prime



### Local Search Algorithm Framework

Local Search algorithm (\(LS\)) is applied to improve the initial solution. A new solution in the local search is generated by random swapping. The approximate optimal solution to the scheduling scheme \(S^{uw}\) is calculated by iteration (Lines 2-6). \begin{tabular}{l l} \hline \hline \multicolumn{2}{l}{Local Search algorithm framework \(LS()\)} \\ \hline
1 & \(S^{uw}\gets ISG()\) ; \\
2 & **While** not Termination Criterion **do** \\
3 & Generation of candidate neighbor \(S^{uw}\); \\
4 & **if**\(Fit(S^{uw})<Fit(S^{uw})\) **then** \\
5 & \(S^{uw}\gets S^{uw}\) ; \\
6 & **return**\(S^{uw}\); \\ \hline \hline \end{tabular}  where \(Fit\) function is the fitness of the solution defined as a linear weighted sum:

\[Fit=\omega A+(1-\omega)B\;(\omega\in(0,1)) \tag{12}\]

### Simulated Annealing Algorithm Framework

As our algorithm is a hybrid of Initial Solution Generation Algorithm (ISG) and heuristic algorithms, we first provide a brief description about ISG algorithm as follows. Simulated Annealing algorithm is a greedy algorithm. It is derived from the principle of solid annealing. SA accepts an inferior solution with the certain probability, and this probability varies with the temperature. The SA algorithm framework is used to compute the integrated objective \(C\). We obtain the approximate optimal solution by the Simulated Annealing algorithm framework. ISG is used to generate the initial solution (Line 1). The approximate optimal solution to the scheduling scheme \(S^{uw}\) is calculated by iteration (Lines 2-14). In the iterative process, the global optimal solution is recorded (Lines 8-9) and an inferior solution is accepted with probability \(p\) (Lines 11-14).