American Institute of Mathematical Sciences

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doi: 10.3934/jimo.2022015
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Aggregation and Adjustment mechanisms for disaster relief task allocation with uneven distribution

Xinwei Ma 1,2, , Danli Wang 1,2,, , Nan Zheng 1,2, and  Song Zhang 1,2,

1. 

The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, China
2. 

School of Artificial Intelligence, University of Chinese Academy of Sciences, China

* Corresponding author: Danli Wang

Received  April 2021 Revised  November 2021 Early access February 2022

Fund Project: This research is supported by the National Natural Science Foundation of China under Grant No. 61872363 and 61672507; the National Key Research and Development Program under Grant No. 2016YFB0401202; the Research and Development Foundation of The Institute of Automation, Chinese Academy of Sciences under Grant No.Y9J2FZ0801; the Natural Science Foundation of Beijing & Key project of Science and Technology Plan of Beijing Municipal Education Commission under Grant No. 21JD0044; and the Ruwei Dai Academician Station of Tengzhou of Shangdong Province

The use of unmanned aerial vehicles (UAVs) to perform disaster relief task is becoming more and more popular. Generally, UAVs for rescuing are required to be heterogeneous, since the types of rescue missions are diverse. There are many researches on the task allocation of heterogeneous UAVs, in which they setup tasks to be randomly distributed when simulation. However, in most cases the distribution of tasks is regular rather than random. Therefore, we setup a set of special scenarios to simulate real disaster relief tasks, where most tasks concentrate in a few small areas and others are distributed randomly. LAL algorithm is an appropriate alternative to deal with assignment problems in scenarios where tasks are completely randomly distributed, but with a bit poor performance in the scenarios above mentioned. In order to obtain better results, this paper proposes three algorithms based on LAL algorithm in such scenarios. They are the Aggregation-LAL (A-LAL) using aggregation mechanism, Dynamic Adjustment-LAL (DA-LAL) using dynamic adjustment mechanism and Aggregation and Adjustment (AA-LAL) algorithms.Through the experiments in the NetLogo simulation environment, the proposed algorithms are evaluated. The result shows improvements, which are average 5% obtained by AA-LAL, of task allocation in our special scenarios compared with existing algorithms.

Keywords: Task allocation, Swarm intelligence, Heterogeneous UAVs, Threshold-based method, Disaster relief.
Mathematics Subject Classification: Primary: 68T42, 90C27.
Citation: Xinwei Ma, Danli Wang, Nan Zheng, Song Zhang. Aggregation and Adjustment mechanisms for disaster relief task allocation with uneven distribution. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022015
References:
[1]

A. Altan, Ö. Aslan and R. Hacıoğlu, Model reference adaptive control of load transporting system on unmanned aerial vehicle,, in 2018 6th International Conference on Control Engineering & Information Technology (CEIT), IEEE, 2018, 1–5. doi: 10.1109/CEIT.2018.8751858.

[2]

A. Altan, Ö. Aslan and R. Hacıoğlu, Real-time control based on narx neural network of hexarotor uav with load transporting system for path tracking,, in 2018 6th International Conference On Control Engineering & information Technology (CEIT), IEEE, 2018, 1–6. doi: 10.1109/CEIT.2018.8751829.

[3]

A. Altan and R. Hacıoğlu, Model predictive control of three-axis gimbal system mounted on uav for real-time target tracking under external disturbances,, Mechanical Systems and Signal Processing, 138 (2020), 106548.  doi: 10.1016/j.ymssp.2019.106548.

[4]

J. C. Amorim, V. Alves and E. P. de Freitas, Assessing a swarm-gap based solution for the task allocation problem in dynamic scenarios,, Expert Systems with Applications, 152 (2020), 113437.  doi: 10.1016/j.eswa.2020.113437.

[5]

U. Baroudi, M. Alshaboti, A. Koubaa and S. Trigui, Dynamic multi-objective auction-based (dymo-auction) task allocation,, Applied Sciences, 10 (2020), 3264.  doi: 10.3390/app10093264.

[6]

S.-Q. Chen, Y.-M. Wang, H.-L. Shi and X.-X. Zhang, A decision-making method for uncertain matching between volunteer teams and rescue tasks,, International Journal of Disaster Risk Reduction, 58 (2021), 102138.  doi: 10.1016/j.ijdrr.2021.102138.

[7]

M. B. Dias, R. Zlot, N. Kalra and A. Stentz, Market-based multirobot coordination: A survey and analysis,, Proceedings of the IEEE, 94 (2006), 1257-1270.  doi: 10.21236/ADA526116.

[8]

P. R. Ferreira, F. Dos Santos, A. L. Bazzan, D. Epstein and S. J. Waskow, Robocup rescue as multiagent task allocation among teams: Experiments with task interdependencies,, Autonomous Agents and Multi-Agent Systems, 20 (2010), 421-443.  doi: 10.1007/s10458-009-9087-8.

[9]

P. R. Ferreira Jr, F. S. Boffo and A. L. Bazzan, A swarm based approximated algorithm to the extended generalized assignment problem (e-gap), in Proceedings of the 6th International Joint Conference on Autonomous agents and Multiagent Systems, 2007, 1–3.

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W. Han, C. Liang, B. Jiang, W. Ma and Y. Zhang, Major natural disasters in china, 1985–2014: Occurrence and damages, International Journal of Environmental Research and Public Health, 13 (2016), 1118.  doi: 10.3390/ijerph13111118.

[11]

N. Hooshangi and A. A. Alesheikh, Agent-based task allocation under uncertainties in disaster environments: An approach to interval uncertainty,, International Journal of Disaster Risk Reduction, 24 (2017), 160-171.  doi: 10.1016/j.ijdrr.2017.06.010.

[12]

N. Hooshangi and A. A. Alesheikh, Developing an agent-based simulation system for post-earthquake operations in uncertainty conditions: a proposed method for collaboration among agents,, ISPRS International Journal of Geo-Information, 7 (2018), 27.  doi: 10.3390/ijgi7010027.

[13]

B. Horling and V. Lesser, A survey of multi-agent organizational paradigms,, Knowledge Engineering Review, 19 (2004), 281-316.  doi: 10.1017/S0269888905000317.

[14]

F. Hu, S. Yang and W. Xu, A non-dominated sorting genetic algorithm for the location and districting planning of earthquake shelters,, International Journal of Geographical Information Science, 28 (2014), 1482-1501.  doi: 10.1080/13658816.2014.894638.

[15]

N. Kalra and A. Martinoli, Comparative study of market-based and threshold-based task allocation,, in Distributed Autonomous Robotic Systems, Springer, 7 (2006), 91–101. doi: 10.1007/4-431-35881-1_10.

[16]

V. A. Kazakova, A. S. Wu and G. R. Sukthankar, Respecializing swarms by forgetting reinforced thresholds, Swarm Intelligence, 14 (2020), 171-204.  doi: 10.1007/s11721-020-00181-3.

[17]

A. Khamis, A. Hussein and A. Elmogy, Multi-robot task allocation: A review of the state-of-the-art,, Cooperative Robots and Sensor Networks, 2015, 31–51. doi: 10.1007/978-3-319-18299-5_2.

[18]

M.-H. Kim, H. Baik and S. Lee, Response threshold model based uav search planning and task allocation,, Journal of Intelligent & Robotic Systems, 75 (2014), 625-640.  doi: 10.1007/s10846-013-9887-6.

[19]

H. Kitano, S. Tadokoro, I. Noda, H. Matsubara, T. Takahashi, A. Shinjou and S. Shimada, Robocup rescue: Search and rescue in large-scale disasters as a domain for autonomous agents research,, in IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No. 99CH37028), vol. 6, IEEE, 1999,739–743. doi: 10.1109/ICSMC.1999.816643.

[20]

D.-H. Lee, S. A. Zaheer and J.-H. Kim, A resource-oriented, decentralized auction algorithm for multirobot task allocation, IEEE Transactions on Automation Science and Engineering, 12 (2015), 1469-1481.  doi: 10.1109/TASE.2014.2361334.

[21]

T. Lemaire, R. Alami and S. Lacroix, A distributed tasks allocation scheme in multi-uav context,, in IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA'04. 2004, vol. 4, IEEE, 2004, 3622–3627. doi: 10.1109/ROBOT.2004.1308816.

[22]

M.-Y. Li, X.-J. Zhao, Z.-P. Fan, P.-P. Cao and X.-N. Qu, A model for assignment of rescuers considering multiple disaster areas, International Journal of Disaster Risk Reduction, 38 (2019), 101201.  doi: 10.1016/j.ijdrr.2019.101201.

[23]

S. Li and K. L. Teo, Post-disaster multi-period road network repair: Work scheduling and relief logistics optimization,, Annals of Operations Research, 283 (2019), 1345-1385.  doi: 10.1007/s10479-018-3037-2.

[24]

P. Scerri, A. Farinelli, S. Okamoto and M. Tambe, Allocating tasks in extreme teams,, in Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multiagent Systems, 2005,727–734. doi: 10.1145/1082473.1082584.

[25]

C. Schumacher, P. R. Chandler, M. Pachter and L. S. Pachter, Optimization of air vehicles operations using mixed-integer linear programming,, Journal of the Operational Research Society, 58 (2007), 516-527.  doi: 10.1057/palgrave.jors.2602176.

[26]

J. Schwarzrock, I. Zacarias, A. L. Bazzan, R. Q. de Araujo Fernandes, L. H. Moreira and E. P. de Freitas, Solving task allocation problem in multi unmanned aerial vehicles systems using swarm intelligence,, Engineering Applications of Artificial Intelligence, 72 (2018), 10-20.  doi: 10.1016/j.engappai.2018.03.008.

[27]

J. Shi, Z. Yang and J. Zhu, An auction-based rescue task allocation approach for heterogeneous multi-robot system,, Multimedia Tools and Applications, 79 (2020), 14529-14538.  doi: 10.1007/s11042-018-7080-4.

[28]

D. B. Shmoys and É. Tardos, An approximation algorithm for the generalized assignment problem,, Mathematical programming, 62 (1993), 461-474.  doi: 10.1007/BF01585178.

[29]

J. Tang, K. Zhu, H. Guo, C. Gong, C. Liao and S. Zhang, Using auction-based task allocation scheme for simulation optimization of search and rescue in disaster relief,, Simulation Modelling Practice and Theory, 82 (2018), 132-146.  doi: 10.1016/j.simpat.2017.12.014.

[30]

S. Tisue and U. Wilensky, Netlogo: A simple environment for modeling complexity, in International Conference on Complex Systems, vol. 21, Boston, MA, 2004, 16–21.

[31]

H. Wu, H. Li, R. Xiao and J. Liu, Modeling and simulation of dynamic ant colony's labor division for task allocation of uav swarm,, Physica A: Statistical Mechanics and its Applications, 491 (2018), 127-141.  doi: 10.1016/j.physa.2017.08.094.

[32]

R. Xu and D. Wunsch, Clustering, vol. 10, John Wiley & Sons, 2008.

show all references

References:
[1]

A. Altan, Ö. Aslan and R. Hacıoğlu, Model reference adaptive control of load transporting system on unmanned aerial vehicle,, in 2018 6th International Conference on Control Engineering & Information Technology (CEIT), IEEE, 2018, 1–5. doi: 10.1109/CEIT.2018.8751858.

[2]

A. Altan, Ö. Aslan and R. Hacıoğlu, Real-time control based on narx neural network of hexarotor uav with load transporting system for path tracking,, in 2018 6th International Conference On Control Engineering & information Technology (CEIT), IEEE, 2018, 1–6. doi: 10.1109/CEIT.2018.8751829.

[3]

A. Altan and R. Hacıoğlu, Model predictive control of three-axis gimbal system mounted on uav for real-time target tracking under external disturbances,, Mechanical Systems and Signal Processing, 138 (2020), 106548.  doi: 10.1016/j.ymssp.2019.106548.

[4]

J. C. Amorim, V. Alves and E. P. de Freitas, Assessing a swarm-gap based solution for the task allocation problem in dynamic scenarios,, Expert Systems with Applications, 152 (2020), 113437.  doi: 10.1016/j.eswa.2020.113437.

[5]

U. Baroudi, M. Alshaboti, A. Koubaa and S. Trigui, Dynamic multi-objective auction-based (dymo-auction) task allocation,, Applied Sciences, 10 (2020), 3264.  doi: 10.3390/app10093264.

[6]

S.-Q. Chen, Y.-M. Wang, H.-L. Shi and X.-X. Zhang, A decision-making method for uncertain matching between volunteer teams and rescue tasks,, International Journal of Disaster Risk Reduction, 58 (2021), 102138.  doi: 10.1016/j.ijdrr.2021.102138.

[7]

M. B. Dias, R. Zlot, N. Kalra and A. Stentz, Market-based multirobot coordination: A survey and analysis,, Proceedings of the IEEE, 94 (2006), 1257-1270.  doi: 10.21236/ADA526116.

[8]

P. R. Ferreira, F. Dos Santos, A. L. Bazzan, D. Epstein and S. J. Waskow, Robocup rescue as multiagent task allocation among teams: Experiments with task interdependencies,, Autonomous Agents and Multi-Agent Systems, 20 (2010), 421-443.  doi: 10.1007/s10458-009-9087-8.

[9]

P. R. Ferreira Jr, F. S. Boffo and A. L. Bazzan, A swarm based approximated algorithm to the extended generalized assignment problem (e-gap), in Proceedings of the 6th International Joint Conference on Autonomous agents and Multiagent Systems, 2007, 1–3.

[10]

W. Han, C. Liang, B. Jiang, W. Ma and Y. Zhang, Major natural disasters in china, 1985–2014: Occurrence and damages, International Journal of Environmental Research and Public Health, 13 (2016), 1118.  doi: 10.3390/ijerph13111118.

[11]

N. Hooshangi and A. A. Alesheikh, Agent-based task allocation under uncertainties in disaster environments: An approach to interval uncertainty,, International Journal of Disaster Risk Reduction, 24 (2017), 160-171.  doi: 10.1016/j.ijdrr.2017.06.010.

[12]

N. Hooshangi and A. A. Alesheikh, Developing an agent-based simulation system for post-earthquake operations in uncertainty conditions: a proposed method for collaboration among agents,, ISPRS International Journal of Geo-Information, 7 (2018), 27.  doi: 10.3390/ijgi7010027.

[13]

B. Horling and V. Lesser, A survey of multi-agent organizational paradigms,, Knowledge Engineering Review, 19 (2004), 281-316.  doi: 10.1017/S0269888905000317.

[14]

F. Hu, S. Yang and W. Xu, A non-dominated sorting genetic algorithm for the location and districting planning of earthquake shelters,, International Journal of Geographical Information Science, 28 (2014), 1482-1501.  doi: 10.1080/13658816.2014.894638.

[15]

N. Kalra and A. Martinoli, Comparative study of market-based and threshold-based task allocation,, in Distributed Autonomous Robotic Systems, Springer, 7 (2006), 91–101. doi: 10.1007/4-431-35881-1_10.

[16]

V. A. Kazakova, A. S. Wu and G. R. Sukthankar, Respecializing swarms by forgetting reinforced thresholds, Swarm Intelligence, 14 (2020), 171-204.  doi: 10.1007/s11721-020-00181-3.

[17]

A. Khamis, A. Hussein and A. Elmogy, Multi-robot task allocation: A review of the state-of-the-art,, Cooperative Robots and Sensor Networks, 2015, 31–51. doi: 10.1007/978-3-319-18299-5_2.

[18]

M.-H. Kim, H. Baik and S. Lee, Response threshold model based uav search planning and task allocation,, Journal of Intelligent & Robotic Systems, 75 (2014), 625-640.  doi: 10.1007/s10846-013-9887-6.

[19]

H. Kitano, S. Tadokoro, I. Noda, H. Matsubara, T. Takahashi, A. Shinjou and S. Shimada, Robocup rescue: Search and rescue in large-scale disasters as a domain for autonomous agents research,, in IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No. 99CH37028), vol. 6, IEEE, 1999,739–743. doi: 10.1109/ICSMC.1999.816643.

[20]

D.-H. Lee, S. A. Zaheer and J.-H. Kim, A resource-oriented, decentralized auction algorithm for multirobot task allocation, IEEE Transactions on Automation Science and Engineering, 12 (2015), 1469-1481.  doi: 10.1109/TASE.2014.2361334.

[21]

T. Lemaire, R. Alami and S. Lacroix, A distributed tasks allocation scheme in multi-uav context,, in IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA'04. 2004, vol. 4, IEEE, 2004, 3622–3627. doi: 10.1109/ROBOT.2004.1308816.

[22]

M.-Y. Li, X.-J. Zhao, Z.-P. Fan, P.-P. Cao and X.-N. Qu, A model for assignment of rescuers considering multiple disaster areas, International Journal of Disaster Risk Reduction, 38 (2019), 101201.  doi: 10.1016/j.ijdrr.2019.101201.

[23]

S. Li and K. L. Teo, Post-disaster multi-period road network repair: Work scheduling and relief logistics optimization,, Annals of Operations Research, 283 (2019), 1345-1385.  doi: 10.1007/s10479-018-3037-2.

[24]

P. Scerri, A. Farinelli, S. Okamoto and M. Tambe, Allocating tasks in extreme teams,, in Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multiagent Systems, 2005,727–734. doi: 10.1145/1082473.1082584.

[25]

C. Schumacher, P. R. Chandler, M. Pachter and L. S. Pachter, Optimization of air vehicles operations using mixed-integer linear programming,, Journal of the Operational Research Society, 58 (2007), 516-527.  doi: 10.1057/palgrave.jors.2602176.

[26]

J. Schwarzrock, I. Zacarias, A. L. Bazzan, R. Q. de Araujo Fernandes, L. H. Moreira and E. P. de Freitas, Solving task allocation problem in multi unmanned aerial vehicles systems using swarm intelligence,, Engineering Applications of Artificial Intelligence, 72 (2018), 10-20.  doi: 10.1016/j.engappai.2018.03.008.

[27]

J. Shi, Z. Yang and J. Zhu, An auction-based rescue task allocation approach for heterogeneous multi-robot system,, Multimedia Tools and Applications, 79 (2020), 14529-14538.  doi: 10.1007/s11042-018-7080-4.

[28]

D. B. Shmoys and É. Tardos, An approximation algorithm for the generalized assignment problem,, Mathematical programming, 62 (1993), 461-474.  doi: 10.1007/BF01585178.

[29]

J. Tang, K. Zhu, H. Guo, C. Gong, C. Liao and S. Zhang, Using auction-based task allocation scheme for simulation optimization of search and rescue in disaster relief,, Simulation Modelling Practice and Theory, 82 (2018), 132-146.  doi: 10.1016/j.simpat.2017.12.014.

[30]

S. Tisue and U. Wilensky, Netlogo: A simple environment for modeling complexity, in International Conference on Complex Systems, vol. 21, Boston, MA, 2004, 16–21.

[31]

H. Wu, H. Li, R. Xiao and J. Liu, Modeling and simulation of dynamic ant colony's labor division for task allocation of uav swarm,, Physica A: Statistical Mechanics and its Applications, 491 (2018), 127-141.  doi: 10.1016/j.physa.2017.08.094.

[32]

R. Xu and D. Wunsch, Clustering, vol. 10, John Wiley & Sons, 2008.

Figure 1.  Unreasonable assignment of tasks in LAL
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Figure 2.  Example of A-LAL algorithm. Task_A, task_B and task_C are assigned to agent_1 in order
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Figure 3.  Unreasonable assignment of task_A
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Figure 4.  Total reward of each algorithm for different scenarios
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Figure 5.  Quantity of completed tasks of each algorithm for different scenarios
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Figure 6.  Makespan of each algorithm for different scenarios
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Figure 7.  Quality of each algorithm for different scenarios
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Figure 8.  Total number of exchanged messages of each algorithm for different scenarios
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Figure 9.  Runtime of each algorithm in different scenarios
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Table 1.  Quality of each type of UAVs to detect the different types of task
UAV/task $ a_0 $ $ a_1 $ $ a_2 $ $ a_3 $
$ s_0 $ 1.0 0 0.3 0.5
$ s_1 $ 0 0 1.0 0
$ s_2 $ 0.2 0 0 1.0
$ s_3 $ 0 1.0 0 0.3
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UAV/task $ a_0 $ $ a_1 $ $ a_2 $ $ a_3 $
$ s_0 $ 1.0 0 0.3 0.5
$ s_1 $ 0 0 1.0 0
$ s_2 $ 0.2 0 0 1.0
$ s_3 $ 0 1.0 0 0.3
Table 2.  Experimental scenarios
scenario number of UAVs number of tasks ticks as deadline px area size
i 3 15 300 $ 100 \times 100 $
ii 6 25 300 $ 150 \times 150 $
iii 9 35 300 $ 200 \times 200 $
iv 15 100 300 $ 250 \times 250 $
v 30 200 300 $ 400 \times 400 $
vi 50 300 300 $ 500 \times 500 $
vii 60 400 300 $ 600 \times 600 $
viii 100 500 300 $ 750 \times 750 $
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scenario number of UAVs number of tasks ticks as deadline px area size
i 3 15 300 $ 100 \times 100 $
ii 6 25 300 $ 150 \times 150 $
iii 9 35 300 $ 200 \times 200 $
iv 15 100 300 $ 250 \times 250 $
v 30 200 300 $ 400 \times 400 $
vi 50 300 300 $ 500 \times 500 $
vii 60 400 300 $ 600 \times 600 $
viii 100 500 300 $ 750 \times 750 $
Table 3.  The mean (St. dev.) of total reward, makespan, quantity and quality of the completed tasks, number of exchanged messages and algorithm's runtime with deadline of 300 ticks for 1000 runs of each algorithm in less-tasks scenarios (scenarios i, ii and iii)
LAL A-LAL DA-LAL AA-LAL
3 UAVs and 15 tasks in area of 100 $ \times $ 100 pixels
Total reward 6.81 ($ \pm $1.96) $ 7.21 (\pm2.02)^{**} $ $ 7.10 (\pm1.95)^{**} $ $ 7.26 (\pm1.98)^{**} $
Elapsed time 0.82 ($ \pm $0.12) $ 0.82 (\pm0.12) $ $ 0.84 (\pm0.11)^{**} $ $ 0.84 (\pm0.11)^{**} $
Comp. tasks $ 0.79 (\pm0.15) $ $ 0.78 (\pm0.16) $ $ 0.79 (\pm0.16) $ $ 0.79 (\pm0.16) $
Quality $ 0.74 (\pm0.19) $ $ 0.76 (\pm0.20) $ $ 0.79 (\pm0.20)^{**} $ $ 0.78 (\pm0.21)^{**} $
Sending token $ 16.48 (\pm5.14) $ $ 12.45 (\pm4.13)^{**} $ $ 16.21 (\pm4.63) $ $ 13.07 (\pm4.32)^{**} $
Total runtime $ 0.39 (\pm0.10) $ $ 0.35 (\pm0.10)^{**} $ $ 0.55 (\pm0.25)^{**} $ $ 0.39 (\pm0.12)^{**} $
6 UAVs and 25 tasks in area of 150 $ \times $ 150 pixels
Total reward $ 15.53 (\pm2.31) $ $ 16.50 (\pm2.24)^{**} $ $ 15.81 (\pm2.26)^{**} $ $ 16.80 (\pm2.23)^{**} $
Elapsed time $ 0.90 (\pm0.06) $ $ 0.91 (\pm0.06) $ $ 0.93 (\pm0.04)^{**} $ $ 0.92 (\pm0.05)^{**} $
Comp. tasks $ 0.87 (\pm0.11) $ $ 0.88 (\pm0.10) $ $ 0.88 (\pm0.10)^* $ $ 0.89 (\pm0.10)^{**} $
Quality $ 0.82 (\pm0.13) $ $ 0.83 (\pm0.13)^{**} $ $ 0.86 (\pm0.12)^{**} $ $ 0.86 (\pm0.12)^{**} $
Sending token $ 26.83 (\pm3.61) $ $ 19.02 (\pm3.31)^{**} $ $ 27.88 (\pm3.67)^{**} $ $ 19.53 (\pm3.42)^{**} $
Total runtime $ 0.72 (\pm0.10) $ $ 0.59 (\pm0.10)^{**} $ $ 0.84 (\pm0.20)^{**} $ $ 0.63 (\pm0.12)^{**} $
9 UAVs and 35 tasks in area of 200 $ \times $ 200 pixels
Total reward $ 24.25 (\pm2.59) $ $ 25.81 (\pm2.40)^{**} $ $ 24.83 (\pm2.48)^{**} $ $ 25.96 (\pm2.35)^{**} $
Elapsed time $ 0.94 (\pm0.03) $ $ 0.95 (\pm0.03) $ $ 0.96 (\pm0.02)^{**} $ $ 0.95 (\pm0.02)^{**} $
Comp. tasks $ 0.90 (\pm0.07) $ $ 0.91 (\pm0.07)^{**} $ $ 0.91 (\pm0.07)^* $ $ 0.91 (\pm0.07)^{**} $
Quality $ 0.85 (\pm0.10) $ $ 0.87 (\pm0.09)^{**} $ $ 0.88 (\pm0.10)^{**} $ $ 0.89 (\pm0.09)^{**} $
Sending token $ 36.84 (\pm3.10) $ $ 23.95 (\pm3.07)^{**} $ $ 38.37 (\pm3.43)^{**} $ $ 24.73 (\pm3.46) ^{**} $
Total runtime $ 1.18 (\pm0.14) $ $ 0.91 (\pm0.12)^{**} $ $ 1.23 (\pm0.17)^{**} $ $ 0.94 (\pm0.14) ^{**} $
a The ‘*’ or ‘**’ in the table indicates the result of the t-Test between LAL and the other three algorithms, of which ‘**’ means p-value < 0.01 and ‘*’ means 0.01 ≤ p-value < 0.05. The same as ‘*’ or ‘**’ in the Table 4.
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LAL A-LAL DA-LAL AA-LAL
3 UAVs and 15 tasks in area of 100 $ \times $ 100 pixels
Total reward 6.81 ($ \pm $1.96) $ 7.21 (\pm2.02)^{**} $ $ 7.10 (\pm1.95)^{**} $ $ 7.26 (\pm1.98)^{**} $
Elapsed time 0.82 ($ \pm $0.12) $ 0.82 (\pm0.12) $ $ 0.84 (\pm0.11)^{**} $ $ 0.84 (\pm0.11)^{**} $
Comp. tasks $ 0.79 (\pm0.15) $ $ 0.78 (\pm0.16) $ $ 0.79 (\pm0.16) $ $ 0.79 (\pm0.16) $
Quality $ 0.74 (\pm0.19) $ $ 0.76 (\pm0.20) $ $ 0.79 (\pm0.20)^{**} $ $ 0.78 (\pm0.21)^{**} $
Sending token $ 16.48 (\pm5.14) $ $ 12.45 (\pm4.13)^{**} $ $ 16.21 (\pm4.63) $ $ 13.07 (\pm4.32)^{**} $
Total runtime $ 0.39 (\pm0.10) $ $ 0.35 (\pm0.10)^{**} $ $ 0.55 (\pm0.25)^{**} $ $ 0.39 (\pm0.12)^{**} $
6 UAVs and 25 tasks in area of 150 $ \times $ 150 pixels
Total reward $ 15.53 (\pm2.31) $ $ 16.50 (\pm2.24)^{**} $ $ 15.81 (\pm2.26)^{**} $ $ 16.80 (\pm2.23)^{**} $
Elapsed time $ 0.90 (\pm0.06) $ $ 0.91 (\pm0.06) $ $ 0.93 (\pm0.04)^{**} $ $ 0.92 (\pm0.05)^{**} $
Comp. tasks $ 0.87 (\pm0.11) $ $ 0.88 (\pm0.10) $ $ 0.88 (\pm0.10)^* $ $ 0.89 (\pm0.10)^{**} $
Quality $ 0.82 (\pm0.13) $ $ 0.83 (\pm0.13)^{**} $ $ 0.86 (\pm0.12)^{**} $ $ 0.86 (\pm0.12)^{**} $
Sending token $ 26.83 (\pm3.61) $ $ 19.02 (\pm3.31)^{**} $ $ 27.88 (\pm3.67)^{**} $ $ 19.53 (\pm3.42)^{**} $
Total runtime $ 0.72 (\pm0.10) $ $ 0.59 (\pm0.10)^{**} $ $ 0.84 (\pm0.20)^{**} $ $ 0.63 (\pm0.12)^{**} $
9 UAVs and 35 tasks in area of 200 $ \times $ 200 pixels
Total reward $ 24.25 (\pm2.59) $ $ 25.81 (\pm2.40)^{**} $ $ 24.83 (\pm2.48)^{**} $ $ 25.96 (\pm2.35)^{**} $
Elapsed time $ 0.94 (\pm0.03) $ $ 0.95 (\pm0.03) $ $ 0.96 (\pm0.02)^{**} $ $ 0.95 (\pm0.02)^{**} $
Comp. tasks $ 0.90 (\pm0.07) $ $ 0.91 (\pm0.07)^{**} $ $ 0.91 (\pm0.07)^* $ $ 0.91 (\pm0.07)^{**} $
Quality $ 0.85 (\pm0.10) $ $ 0.87 (\pm0.09)^{**} $ $ 0.88 (\pm0.10)^{**} $ $ 0.89 (\pm0.09)^{**} $
Sending token $ 36.84 (\pm3.10) $ $ 23.95 (\pm3.07)^{**} $ $ 38.37 (\pm3.43)^{**} $ $ 24.73 (\pm3.46) ^{**} $
Total runtime $ 1.18 (\pm0.14) $ $ 0.91 (\pm0.12)^{**} $ $ 1.23 (\pm0.17)^{**} $ $ 0.94 (\pm0.14) ^{**} $
a The ‘*’ or ‘**’ in the table indicates the result of the t-Test between LAL and the other three algorithms, of which ‘**’ means p-value < 0.01 and ‘*’ means 0.01 ≤ p-value < 0.05. The same as ‘*’ or ‘**’ in the Table 4.
Table 4.  The mean (St.dev.) of total reward (T.r.), elapsed time (E.t.), quantity (C.t.) and quality (Q.) of the completed tasks, number of exchanged messages (S.t.) and algorithm's runtime (R.t.) with deadline of 300 ticks for 200 runs of each algorithm in more-tasks scenarios (scenarios iv, v, vi, vii and viii)
LAL A-LAL DA-LAL AA-LAL
15 UAVs and 100 tasks in area of 250 $ \times $ 250 pixels
T.r. $ 70.95 (\pm5.43) $ $ 76.03 (\pm4.44)^{**} $ $ 71.56 (\pm5.68) $ $ 76.09 (\pm4.82)^{**} $
E.t. $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $
C.t. $ 0.81 (\pm0.05) $ $ 0.85 (\pm0.04)^{**} $ $ 0.82 (\pm0.05) $ $ 0.85 (\pm0.05)^{**} $
Q. $ 0.90 (\pm0.06) $ $ 0.91 (\pm0.05)^{**} $ $ 0.92 (\pm0.06)^{**} $ $ 0.92 (\pm0.06)^{**} $
S.t. $ 86.81 (\pm5.27) $ $ 42.80 (\pm4.27)^{**} $ $ 88.86 (\pm6.35)^{**} $ $ 43.34 (\pm5.55)^{**} $
R.t. $ 7.09 (\pm0.71) $ $ 4.41 (\pm0.54)^{**} $ $ 7.47 (\pm1.17)^{**} $ $ 4.54 (\pm0.63)^{**} $
30 UAVs and 200 tasks in area of 400 $ \times $ 400 pixels
T.r. $ 147.09 (\pm7.81) $ $ 155.81 (\pm6.57) ^{**} $ $ 145.82 (\pm8.16) $ $ 154.81 (\pm7.38) ^{} $
E.t. $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $
C.t. $ 0.80 (\pm0.04) $ $ 0.84 (\pm0.03) ^{**} $ $ 0.80 (\pm0.04) $ $ 0.83 (\pm0.03) ^{**} $
Q. $ 0.92 (\pm0.05) $ $ 0.94 (\pm0.04) ^{**} $ $ 0.94 (\pm0.05) $ $ 0.94 (\pm0.04) ^{**} $
S.t. $ 169.40 (\pm8.19) $ $ 73.69 (\pm6.15) ^{**} $ $ 170.18 (\pm8.54) $ $ 73.69 (\pm6.33) ^{**} $
R.t. $ 31.83 (\pm4.78) $ $ 17.10 (\pm2.70) ^{**} $ $ 31.84 (\pm4.24) $ $ 17.40 (\pm2.81) ^{**} $
50 UAVs and 300 tasks in area of 500 $ \times $ 500 pixels
T.r. $ 237.02 (\pm10.12) $ $ 248.77 (\pm8.36) ^{**} $ $ 238.00 (\pm9.84) $ $ 250.18 (\pm8.42) ^{**} $
E.t. $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) ^{**} $ $ 0.99 (\pm0.01) ^{**} $
C.t. $ 0.85 (\pm0.03) $ $ 0.88 (\pm0.02) ^{**} $ $ 0.85 (\pm0.03) $ $ 0.89 (\pm0.02) ^{**} $
Q. $ 0.93 (\pm0.04) $ $ 0.95 (\pm0.03) ^{**} $ $ 0.94 (\pm0.04) ^{**} $ $ 0.95 (\pm0.03) ^{**} $
S.t. $ 273.05 (\pm10.39) $ $ 114.91 (\pm7.12) ^{**} $ $ 277.85 (\pm9.38) ^{**} $ $ 116.66 (\pm7.76) ^{**} $
R.t. $ 81.92 (\pm15.51) $ $ 43.72 (\pm5.77) ^{**} $ $ 83.41 (\pm8.27) $ $ 43.01 (\pm5.84) ^{**} $
60 UAVs and 400 tasks in area of 600 $ \times $ 600 pixels
T.r. $ 303.29 (\pm11.09) $ $ 315.07 (\pm10.91) ^{**} $ $ 303.45 (\pm10.97) $ $ 313.86 (\pm10.44) ^{**} $
E.t. $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $
C.t. $ 0.80 (\pm0.02) $ $ 0.83 (\pm0.02) ^{**} $ $ 0.80 (\pm0.02) $ $ 0.83 (\pm0.02) ^{**} $
Q. $ 0.94 (\pm0.03) $ $ 0.95 (\pm0.03) ^{**} $ $ 0.95 (\pm0.03) ^{**} $ $ 0.96 (\pm0.03) ^{**} $
S.t. $ 339.74 (\pm10.52) $ $ 135.63 (\pm6.96) ^{**} $ $ 344.07 (\pm10.64) ^{**} $ $ 136.00 (\pm7.95) ^{**} $
R.t. $ 149.66 (\pm15.38) $ $ 80.99 (\pm9.61) ^{**} $ $ 153.22 (\pm17.03) $ $ 82.08 (\pm11.10) ^{**} $
100 UAVs and 500 tasks in area of 750 $ \times $ 750 pixels
T.r. $ 416.84 (\pm11.40) $ $ 434.06 (\pm11.06) ^{**} $ $ 417.13 (\pm12.08) $ $ 434.20 (\pm9.92) ^{**} $
E.t. $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $
C.t. $ 0.88 (\pm0.02) $ $ 0.91 (\pm0.02) ^{**} $ $ 0.89 (\pm0.02) $ $ 0.91 (\pm0.02) ^{**} $
Q. $ 0.94 (\pm0.02) $ $ 0.95 (\pm0.02) ^{**} $ $ 0.95 (\pm0.03) ^{**} $ $ 0.96 (\pm0.02) ^{**} $
S.t. $ 480.17 (\pm10.80) $ $ 205.26 (\pm9.56) ^{**} $ $ 489.75 (\pm12.79) ^{**} $ $ 207.83 (\pm9.33) ^{**} $
R.t. $ 309.44 (\pm35.44) $ $ 158.06 (\pm20.67) ^{**} $ $ 314.83 (\pm36.04) $ $ 161.18 (\pm20.50) ^{**} $
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LAL A-LAL DA-LAL AA-LAL
15 UAVs and 100 tasks in area of 250 $ \times $ 250 pixels
T.r. $ 70.95 (\pm5.43) $ $ 76.03 (\pm4.44)^{**} $ $ 71.56 (\pm5.68) $ $ 76.09 (\pm4.82)^{**} $
E.t. $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $
C.t. $ 0.81 (\pm0.05) $ $ 0.85 (\pm0.04)^{**} $ $ 0.82 (\pm0.05) $ $ 0.85 (\pm0.05)^{**} $
Q. $ 0.90 (\pm0.06) $ $ 0.91 (\pm0.05)^{**} $ $ 0.92 (\pm0.06)^{**} $ $ 0.92 (\pm0.06)^{**} $
S.t. $ 86.81 (\pm5.27) $ $ 42.80 (\pm4.27)^{**} $ $ 88.86 (\pm6.35)^{**} $ $ 43.34 (\pm5.55)^{**} $
R.t. $ 7.09 (\pm0.71) $ $ 4.41 (\pm0.54)^{**} $ $ 7.47 (\pm1.17)^{**} $ $ 4.54 (\pm0.63)^{**} $
30 UAVs and 200 tasks in area of 400 $ \times $ 400 pixels
T.r. $ 147.09 (\pm7.81) $ $ 155.81 (\pm6.57) ^{**} $ $ 145.82 (\pm8.16) $ $ 154.81 (\pm7.38) ^{} $
E.t. $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $ $ 0.98 (\pm0.01) $
C.t. $ 0.80 (\pm0.04) $ $ 0.84 (\pm0.03) ^{**} $ $ 0.80 (\pm0.04) $ $ 0.83 (\pm0.03) ^{**} $
Q. $ 0.92 (\pm0.05) $ $ 0.94 (\pm0.04) ^{**} $ $ 0.94 (\pm0.05) $ $ 0.94 (\pm0.04) ^{**} $
S.t. $ 169.40 (\pm8.19) $ $ 73.69 (\pm6.15) ^{**} $ $ 170.18 (\pm8.54) $ $ 73.69 (\pm6.33) ^{**} $
R.t. $ 31.83 (\pm4.78) $ $ 17.10 (\pm2.70) ^{**} $ $ 31.84 (\pm4.24) $ $ 17.40 (\pm2.81) ^{**} $
50 UAVs and 300 tasks in area of 500 $ \times $ 500 pixels
T.r. $ 237.02 (\pm10.12) $ $ 248.77 (\pm8.36) ^{**} $ $ 238.00 (\pm9.84) $ $ 250.18 (\pm8.42) ^{**} $
E.t. $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) ^{**} $ $ 0.99 (\pm0.01) ^{**} $
C.t. $ 0.85 (\pm0.03) $ $ 0.88 (\pm0.02) ^{**} $ $ 0.85 (\pm0.03) $ $ 0.89 (\pm0.02) ^{**} $
Q. $ 0.93 (\pm0.04) $ $ 0.95 (\pm0.03) ^{**} $ $ 0.94 (\pm0.04) ^{**} $ $ 0.95 (\pm0.03) ^{**} $
S.t. $ 273.05 (\pm10.39) $ $ 114.91 (\pm7.12) ^{**} $ $ 277.85 (\pm9.38) ^{**} $ $ 116.66 (\pm7.76) ^{**} $
R.t. $ 81.92 (\pm15.51) $ $ 43.72 (\pm5.77) ^{**} $ $ 83.41 (\pm8.27) $ $ 43.01 (\pm5.84) ^{**} $
60 UAVs and 400 tasks in area of 600 $ \times $ 600 pixels
T.r. $ 303.29 (\pm11.09) $ $ 315.07 (\pm10.91) ^{**} $ $ 303.45 (\pm10.97) $ $ 313.86 (\pm10.44) ^{**} $
E.t. $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $
C.t. $ 0.80 (\pm0.02) $ $ 0.83 (\pm0.02) ^{**} $ $ 0.80 (\pm0.02) $ $ 0.83 (\pm0.02) ^{**} $
Q. $ 0.94 (\pm0.03) $ $ 0.95 (\pm0.03) ^{**} $ $ 0.95 (\pm0.03) ^{**} $ $ 0.96 (\pm0.03) ^{**} $
S.t. $ 339.74 (\pm10.52) $ $ 135.63 (\pm6.96) ^{**} $ $ 344.07 (\pm10.64) ^{**} $ $ 136.00 (\pm7.95) ^{**} $
R.t. $ 149.66 (\pm15.38) $ $ 80.99 (\pm9.61) ^{**} $ $ 153.22 (\pm17.03) $ $ 82.08 (\pm11.10) ^{**} $
100 UAVs and 500 tasks in area of 750 $ \times $ 750 pixels
T.r. $ 416.84 (\pm11.40) $ $ 434.06 (\pm11.06) ^{**} $ $ 417.13 (\pm12.08) $ $ 434.20 (\pm9.92) ^{**} $
E.t. $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $ $ 0.99 (\pm0.01) $
C.t. $ 0.88 (\pm0.02) $ $ 0.91 (\pm0.02) ^{**} $ $ 0.89 (\pm0.02) $ $ 0.91 (\pm0.02) ^{**} $
Q. $ 0.94 (\pm0.02) $ $ 0.95 (\pm0.02) ^{**} $ $ 0.95 (\pm0.03) ^{**} $ $ 0.96 (\pm0.02) ^{**} $
S.t. $ 480.17 (\pm10.80) $ $ 205.26 (\pm9.56) ^{**} $ $ 489.75 (\pm12.79) ^{**} $ $ 207.83 (\pm9.33) ^{**} $
R.t. $ 309.44 (\pm35.44) $ $ 158.06 (\pm20.67) ^{**} $ $ 314.83 (\pm36.04) $ $ 161.18 (\pm20.50) ^{**} $
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