Figures (10)  Tables (6)

    • Figure 1. 

      Research model diagram.

    • Figure 2. 

      Hub selection schematic.

    • Figure 3. 

      Flow chart of IWOA. The modules marked in green correspond to the improvement mechanism, while the remaining modules follow the standard WOA process.

    • Figure 4. 

      Flowchart of IALNS. The modules marked in green correspond to the improvement mechanism, while the remaining modules follow the standard ALNS process.

    • Figure 5. 

      Hub location schematic. (a) Side view of spatial distribution. (b) Top view of spatial distribution.

    • Figure 6. 

      Planned trajectory diagram of WOA–ALNS; (a) side view, and (b) top view.

    • Figure 7. 

      Planned trajectory diagram of IWOA–IALNS; (a) side view, and (b) top view.

    • Figure 8. 

      Hub location schematic; (a) side view of spatial distribution, and (b) top view of spatial distribution.

    • Figure 9. 

      Planned trajectory diagram of WOA–ALNS; (a) side view, and (b) top view.

    • Figure 10. 

      Planned trajectory diagram of IWOA–IALNS; (a) side view, and (b) top view.

    • Vehicle Research scenario Dual-Layer algorithm Primary constraints Ref.
      Vehicle trajectory Vehicle merging Upper layer: DRL generates initial trajectory.
      Lower layer: MPC refines trajectory.      		 Risk; collision; dynamics Wu et al.[15]
      Electric bus vehicles Urban mobility Upper layer: ALNS planning and operations benefits.
      Lower layer: VNS computing charging costs.      		 Energy; charging; profitability Jiang et al.[16]
      Drone Urban airspace Upper layer: 3D flight path.
      Lower layer: time dimension conflict resolution.      		 Urban risk; conflict; time dimension Zheng et al.[17]
      Drone Urban airspace Upper layer: generate candidate solutions.
      Lower layer: resolve 4-time dimension conflicts.      		 Risk; conflict; timeliness Chen et al.[18]
      Logistics drones Urban airspace Upper layer: takeoff and landing point layout.
      Lower layer: flight route planning.      		 Coverage requirements; facility construction Zhang et al.[19]

      Table 1. 

      Comparative table of related studies.

    • Type Variable symbol Variable meaning
      Assembly $ I $ Task point collection, $ I=\left\{1,2,3,\cdot \cdot \cdot ,n\right\} $
      $ L $ Waypoint set, $ L=\left\{1,2,3,\cdot \cdot \cdot ,m\right\} $
      $ V $ Task points and hub points collection, where 0 denotes the distribution center. $ V=\left\{0,1,2,\cdot \cdot \cdot ,a\right\} $
      $ K $ Drones assemble. $ K=\left\{1,2,3,\cdots ,b\right\} $
      Parameters $ \left({x}_{G},{y}_{G},{z}_{G}\right) $ Coordinates of the distribution center requiring optimization
      $ i=\left({x}_{i},{y}_{i},{z}_{i}\right) $ Task point coordinates
      $ {d}_{i} $ The straight-line distance between task point $ i $ and the distribution center
      $ {L}_{i} $ The Euclidean distance between waypoint $ l $ and waypoint $ l+1 $
      $ {q}_{i} $ Task volume at point $ i $
      $ {p}_{c} $ The maximum operational workload that a drone can handle (kg)
      $ {w}_{i} $ Time of arrival at Task Point $ i $
      $ \begin{array}{cc}{w}_{i,1}, & {w}_{i,2}\end{array} $ The left and right time windows at Task Point $ i $ (min)
      $ \begin{array}{cc}{x}_{\max }, & {x}_{\min }\end{array} $ Upper and lower bounds of the candidate rectangle's x-boundary (km)
      $ \begin{array}{cc}{y}_{\max }, & {y}_{\min }\end{array} $ Upper and lower bounds of the candidate rectangle's y-boundary (km)
      $ \left({x}_{c},{y}_{c}\right) $ Candidate rectangle center
      $ \begin{array}{cc}{h}_{\mathrm{x}}, & {h}_{y}\end{array} $ The half-width and half-length of a rectangular boundary
      $ \begin{array}{cc}{z}_{\max }, & {z}_{\min }\end{array} $ Upper and lower limits of terrain surface elevation (km)
      $ \begin{array}{cc}{B}_{\max }, & {B}_{\min }\end{array} $ Upper and lower limits for distribution center construction costs (CNY)
      $ \rho $ Offset between the distribution center and the candidate rectangle center
      $ \delta $ Cost item weighting in the site selection model
      $ \alpha $ Cost weighting for site selection and flight path planning layer
      $ \omega $ Task allocation layer cost item weighting
      Decision Variable $ x_{ij}^{k}\in \left\{0,1\right\} $ When drone $ k $ flies from mission point$ i $ to mission point $ j $, $ x_{ij}^{k}=1 $; otherwise$ x_{ij}^{k}=0 $.
      $ {y}_{g}\in \left\{0,1\right\} $ When selecting candidate point $ {g}_{} $ as the sole distribution center, $ {y}_{g}=1 $; otherwise $ {y}_{m}=0 $.

      Table 2. 

      Variable symbols and their meanings.

    • Task point number Coordinates Time window Service hours Workload
      1 (50, 50) (600, 630) 20 40
      2 (380, 50) (570, 600) 20 10
      3 (50, 450) (60, 150) 20 40
      4 (450, 220) (540, 570) 20 10
      5 (250, 250) (20, 60) 20 20
      6 (100, 100) (480, 520) 20 10
      7 (200.360) (160, 200) 20 40
      8 (350.400) (220, 270) 20 30
      9 (300, 100) (460, 500) 20 10
      10 (300, 120) (300, 330) 20 5
      11 (273, 245) (160, 250) 20 40
      12 (101, 385) (50, 90) 20 20
      13 (242, 396) (94, 144) 20 30
      14 (380, 304) (567, 597) 20 5
      15 (387, 320) (194, 254) 20 30
      16 (418, 270) (144, 204) 20 40
      17 (291, 182) (588, 630) 20 30
      18 (134, 213) (219, 269) 20 20
      19 (361, 278) (589, 630) 20 30
      20 (206, 157) (258, 318) 20 20

      Table 3. 

      Starting and ending point coordinate information.

    • Performance indicators Parameters
      Maximum load 110
      Safety height 5
      Cruising speed 10

      Table 4. 

      Drone configuration information.

    • Algorithm model Drone serial number Route task point number Workload Flight distance
      WOA–ALNS 1 Hub-3-8-Hub 70 762.9931
      2 Hub-5-6-1-Hub 70 747.2684
      3 Hub-10-7-2-9-4-Hub 75 1,645.1407
      IWOA–IALNS 1 Hub-5-6-1-Hub 70 747.1739
      2 Hub-3-8-Hub 70 732.6863
      3 Hub-10-7-2-9-4-Hub 75 1,405.1481

      Table 5. 

      Statistics on the performance of unmanned aerial vehicles.

    • Algorithm model Drone serial number Route task point number Workload Flight distance
      WOA–ALNS 1 Hub-11-9-17-Hub 80 376.6751
      2 Hub-20-10-7-2-4-Hub 85 1,227.3709
      3 Hub-12-3-13Hub 90 644.8365
      4 Hub-18-1-6-Hub 70 723.4462
      5 Hub-16-19-Hub 70 337.6873
      6 Hub-5-15-8-14-Hub 85 622.632
      IWOA–IALNS 1 Hub-5-20-11-Hub 80 252.0177
      2 Hub-18-6-1-Hub 70 630.6304
      3 Hub-16-4-19-Hub 80 491.9512
      4 Hub-12-3-13-Hub 90 580.8365
      5 Hub-10-7-2-17-Hub 85 859.4272
      6 Hub-8-15-14-9-Hub 75 624.7721

      Table 6. 

      Statistics on the performance of UAVs.