doi: 10.3934/jimo.2022065
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A pedestrian evacuation model based on ant colony algorithm considering dynamic panic spread

College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

*Corresponding author: Longzhen Zhai

Received  July 2021 Revised  December 2021 Early access April 2022

Fund Project: The authors are supported by China Civil Aviation Administration Project (Grant Nos. ASSA2018/17 and ASSA2017/12)

To explain the evacuation behavior characteristics of people in panic, an improved cellular automata pedestrian evacuation model is proposed by combining with the SIS (Susceptible-Infected-Susceptible) epidemic model and ant colony algorithm. First, to explain the spread of panic in dynamic pedestrian evacuation, an improved SIS infection model that considers individual movement is proposed. At the same time, a quantitative formula for panic mood is given. The infection critical value of the SIS model is analyzed by mean field theory. Secondly, the ant colony algorithm is introduced based on considering exit distance, obstacles, panic, and other factors. These factors are mapped with heuristic function and pheromone concentration in the ant colony algorithm. Finally, the evacuation model and parameters such as evacuation time, pedestrian density, and panic spread are analyzed and discussed through simulation experiments. The simulation experiment results show that the evacuation model proposed in this research can better reflect the actual situation. Simultaneously, the critical rate of effective propagation is closely related to the crowd density in the evacuation area, and individual movement has a significant impact on the panic transmission behavior.

Citation: Longzhen Zhai, Shaohong Feng. A pedestrian evacuation model based on ant colony algorithm considering dynamic panic spread. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022065
References:
[1]

Y. BenoistP. Foulon and F. Labourie, Pedestrian route-choice and activity scheduling theory and models, Transportation Research Part B Methodological, 38 (2004), 169-190. 

[2]

D. ChangL. Cui and Z. Huang, A cellular-automaton agent-hybrid model for emergency evacuation of people in public places, IEEE Access, 8 (2020), 79541-79551. 

[3]

R. K. RozoJ. ArellanaA. Santander-Mercado and M. Jubiz-Diaz, Modelling building emergency evacuation plans considering the dynamic behaviour of pedestrians using agent-based simulation, Safety science, 113 (2019), 276-284. 

[4]

M. MitsopoulouN. I. Dourvas and C. G. Sirakoulis, Spatial games and memory effects on crowd evacuation behavior with cellular automata, Safety science, 32 (2019), 87-97. 

[5]

J. MaM. S. Lo and W. G. Song, Cellular automaton modeling approach for optimum ultra high-rise building evacuation design, Fire Safety Journal, 54 (2012), 57-66. 

[6]

W. WangJ. Rong and Q. Fan, Data-driven simulation of pedestrian movement with artificial neural network, Advanced Transportation, 11 (2021), 20-32. 

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D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Physical review E, 51 (1995), 4282-4286. 

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V. J. Blue and J. L. Adler, Emergent fundamental pedestrian flows from cellular automata microsimulation, Transportation Research Record: Journal of Transportation Research Board, 1644 (1998), 29-36. 

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S. LongD. Zhang and S. Li, Simulation-based model of emergency evacuation guidance in the metro stations of china, IEEE Access, 8 (2020), 62670-62688. 

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C. BursteddeK. Klauck and A. Schadschneider, Simulation of pedestrian dynamics using a 2-dimensional cellular automaton, Physica A Statistical Mechanics & Its Applications, 295 (2001), 507-525. 

[11]

A. A. PatelE. T. Gawlinski and S. K. Lemieux, A cellular automaton model of early tumor growth and invasion, Journal of Theoretical Biology, 213 (2001), 315-331.  doi: 10.1006/jtbi.2001.2385.

[12]

A. VarasM.D. Cornejo and D. Mainemer, Cellular automaton model for evacuation process with obstacles, Physica A Statal Mechanics & Its Applications, 382 (2007), 631-642. 

[13]

Y. SongK. Xie and W. Su, Mechanism and strategies of post-earthquake evacuation based on cellular automata model, Physica A Statal Mechanics & Its Applications, 34 (2019), 220-231. 

[14]

W. G. WengT. Chen and H. Y. Yuan, Cellular automaton simulation of pedestrian counter flow with different walk velocities, Physical Review E Statal Nonlinear & Soft Matter Physics, 74 (2006), 36102-36112. 

[15]

S. L. YangK. Y. Zhu and C. Fu, Simulation of the groupdecision & rmity based on cellular automata model, Systems Engineering-Theory and Practice, 29 (2009), 115-124. 

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T. N. Dawson and F. F. R, Books of Interest, Transportation Science, 6 (1972), 214-216. 

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D. HelbingI. Farkas and T. Vicsek, Simulating dynamical features of escape panic, Transportation Science, 407 (2000), 487-490. 

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C. X. WangX. Suo and S. R. Lyu, Research on panic degree model of emergency evacuation from subway, China Safety Science Journal, 25 (2015), 171-176. 

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X. WangZ. Xie and X. Guan, Micro-simulation study of crowd evacuation under panic, International Conference on Future Information Technology and Management Engineering, 2 (2010), 15-25. 

[20]

R. Neumann and F. Strack, "Mood contagion": the automatic transfer of mood between persons, Journal of personality and social psychology, 79 (2000), 211-216. 

[21]

J. H. WangS. M. Lo and J. H. Sun, Qualitative simulation of the panic spread in large-scale evacuation, Simulation, 88 (2012), 1465-1474. 

[22]

X. Yang and Q. Wang, Pedestrian evacuation under guides in a multiple-exit room via the fuzzy logic method, Communications in Nonlinear Science and Numerical Simulation, 83 (2020), 105138-105142. 

[23]

T. Liu and X. Wang, A fuzzy-theory-based cellular automata model for pedestrian evacuation from a multiple-exit room, IEEE Access, 8 (2020), 106334-106345. 

[24]

L. ZhengX. Peng and L. Wang, Simulation of pedestrian evacuation considering emergency spread and pedestrian panic, Physica A: Statistical Mechanics and its Applications, 522 (2019), 167-181. 

[25]

Q. Xiao and J. Li, Evacuation model of emotional contagion crowd based on cellular automata, Discrete Dynamics in Nature and Society, 52 (2021), 57-62.  doi: 10.1155/2021/5549188.

[26]

P. SongY. Gao and Y. Xue, Human behavior modeling for evacuation from classroom using cellular automata, IEEE Access, 7 (2019), 98694-98701. 

[27]

R. ZhouY. Ou and W. Tang, An emergency evacuation behavior simulation method combines personality traits and emotion contagion, IEEE Access, 8 (2020), 66693-66706. 

[28]

J. Dreo and P. Siarry, Continuous interacting ant colony algorithm based on dense heterarchy, Future Generation Computer Systems, 20 (2004), 841-856. 

[29]

M. ReedA. Yiannakou and R. Evering, An ant colony algorithm for the multi-compartment vehicle routing problem, Applied Soft Computing, 15 (2014), 169-176. 

[30]

Y. H. ZhangY. J. GongW. N and Ch en, A dual-colony ant algorithm for the receiving and shipping door assignments in cross-docks, IEEE Transactions on Intelligent Transportation Systems, 20 (2019), 2523-2539. 

[31]

M. A. Samad, Public health threat caused by zoonotic diseases in bangladesh, Bangladesh Journal of Veterinary Medicine, 9 (2013), 95-120. 

[32]

T. ZhouZ. Q. Fu and B. H. Wang, Epidemic dynamics on complex networks, Progress in Natural Science, 16 (2006), 452-457.  doi: 10.1080/10020070612330019.

[33]

C. K. Chen and Y. H. Tong, Study on crowd evacuation model under panic state based on cellular automata, Journal of Safety Science and Technology, 15 (2019), 12-17. 

[34]

I. GerakakisP. Gavriilidis and N. I. Dourvas, Accelerating fuzzy cellular automata for modeling crowd dynamics, Journal of Computational ence, 32 (2019), 125-140. 

[35]

Y. ZhouT. WuG. Zhang and Z. Fan, A multistory building evacuation model based on multiple-factor analysis, Advances in Civil Engineering, 22 (2019), 15-19. 

[36]

Z. ZhangC. Wang and Y. Wang, Design of emergency evacuation scheme for louvre, IOP Conference Series: Materials Science and Engineering, 0 (2020), 12025-12029. 

[37]

R. TangX. Luan and S. Xu, Analysis of evacuation of tourists based on the louvre's emergency, Open Journal of Applied Sciences, 9 (2019), 515-534. 

show all references

References:
[1]

Y. BenoistP. Foulon and F. Labourie, Pedestrian route-choice and activity scheduling theory and models, Transportation Research Part B Methodological, 38 (2004), 169-190. 

[2]

D. ChangL. Cui and Z. Huang, A cellular-automaton agent-hybrid model for emergency evacuation of people in public places, IEEE Access, 8 (2020), 79541-79551. 

[3]

R. K. RozoJ. ArellanaA. Santander-Mercado and M. Jubiz-Diaz, Modelling building emergency evacuation plans considering the dynamic behaviour of pedestrians using agent-based simulation, Safety science, 113 (2019), 276-284. 

[4]

M. MitsopoulouN. I. Dourvas and C. G. Sirakoulis, Spatial games and memory effects on crowd evacuation behavior with cellular automata, Safety science, 32 (2019), 87-97. 

[5]

J. MaM. S. Lo and W. G. Song, Cellular automaton modeling approach for optimum ultra high-rise building evacuation design, Fire Safety Journal, 54 (2012), 57-66. 

[6]

W. WangJ. Rong and Q. Fan, Data-driven simulation of pedestrian movement with artificial neural network, Advanced Transportation, 11 (2021), 20-32. 

[7]

D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Physical review E, 51 (1995), 4282-4286. 

[8]

V. J. Blue and J. L. Adler, Emergent fundamental pedestrian flows from cellular automata microsimulation, Transportation Research Record: Journal of Transportation Research Board, 1644 (1998), 29-36. 

[9]

S. LongD. Zhang and S. Li, Simulation-based model of emergency evacuation guidance in the metro stations of china, IEEE Access, 8 (2020), 62670-62688. 

[10]

C. BursteddeK. Klauck and A. Schadschneider, Simulation of pedestrian dynamics using a 2-dimensional cellular automaton, Physica A Statistical Mechanics & Its Applications, 295 (2001), 507-525. 

[11]

A. A. PatelE. T. Gawlinski and S. K. Lemieux, A cellular automaton model of early tumor growth and invasion, Journal of Theoretical Biology, 213 (2001), 315-331.  doi: 10.1006/jtbi.2001.2385.

[12]

A. VarasM.D. Cornejo and D. Mainemer, Cellular automaton model for evacuation process with obstacles, Physica A Statal Mechanics & Its Applications, 382 (2007), 631-642. 

[13]

Y. SongK. Xie and W. Su, Mechanism and strategies of post-earthquake evacuation based on cellular automata model, Physica A Statal Mechanics & Its Applications, 34 (2019), 220-231. 

[14]

W. G. WengT. Chen and H. Y. Yuan, Cellular automaton simulation of pedestrian counter flow with different walk velocities, Physical Review E Statal Nonlinear & Soft Matter Physics, 74 (2006), 36102-36112. 

[15]

S. L. YangK. Y. Zhu and C. Fu, Simulation of the groupdecision & rmity based on cellular automata model, Systems Engineering-Theory and Practice, 29 (2009), 115-124. 

[16]

T. N. Dawson and F. F. R, Books of Interest, Transportation Science, 6 (1972), 214-216. 

[17]

D. HelbingI. Farkas and T. Vicsek, Simulating dynamical features of escape panic, Transportation Science, 407 (2000), 487-490. 

[18]

C. X. WangX. Suo and S. R. Lyu, Research on panic degree model of emergency evacuation from subway, China Safety Science Journal, 25 (2015), 171-176. 

[19]

X. WangZ. Xie and X. Guan, Micro-simulation study of crowd evacuation under panic, International Conference on Future Information Technology and Management Engineering, 2 (2010), 15-25. 

[20]

R. Neumann and F. Strack, "Mood contagion": the automatic transfer of mood between persons, Journal of personality and social psychology, 79 (2000), 211-216. 

[21]

J. H. WangS. M. Lo and J. H. Sun, Qualitative simulation of the panic spread in large-scale evacuation, Simulation, 88 (2012), 1465-1474. 

[22]

X. Yang and Q. Wang, Pedestrian evacuation under guides in a multiple-exit room via the fuzzy logic method, Communications in Nonlinear Science and Numerical Simulation, 83 (2020), 105138-105142. 

[23]

T. Liu and X. Wang, A fuzzy-theory-based cellular automata model for pedestrian evacuation from a multiple-exit room, IEEE Access, 8 (2020), 106334-106345. 

[24]

L. ZhengX. Peng and L. Wang, Simulation of pedestrian evacuation considering emergency spread and pedestrian panic, Physica A: Statistical Mechanics and its Applications, 522 (2019), 167-181. 

[25]

Q. Xiao and J. Li, Evacuation model of emotional contagion crowd based on cellular automata, Discrete Dynamics in Nature and Society, 52 (2021), 57-62.  doi: 10.1155/2021/5549188.

[26]

P. SongY. Gao and Y. Xue, Human behavior modeling for evacuation from classroom using cellular automata, IEEE Access, 7 (2019), 98694-98701. 

[27]

R. ZhouY. Ou and W. Tang, An emergency evacuation behavior simulation method combines personality traits and emotion contagion, IEEE Access, 8 (2020), 66693-66706. 

[28]

J. Dreo and P. Siarry, Continuous interacting ant colony algorithm based on dense heterarchy, Future Generation Computer Systems, 20 (2004), 841-856. 

[29]

M. ReedA. Yiannakou and R. Evering, An ant colony algorithm for the multi-compartment vehicle routing problem, Applied Soft Computing, 15 (2014), 169-176. 

[30]

Y. H. ZhangY. J. GongW. N and Ch en, A dual-colony ant algorithm for the receiving and shipping door assignments in cross-docks, IEEE Transactions on Intelligent Transportation Systems, 20 (2019), 2523-2539. 

[31]

M. A. Samad, Public health threat caused by zoonotic diseases in bangladesh, Bangladesh Journal of Veterinary Medicine, 9 (2013), 95-120. 

[32]

T. ZhouZ. Q. Fu and B. H. Wang, Epidemic dynamics on complex networks, Progress in Natural Science, 16 (2006), 452-457.  doi: 10.1080/10020070612330019.

[33]

C. K. Chen and Y. H. Tong, Study on crowd evacuation model under panic state based on cellular automata, Journal of Safety Science and Technology, 15 (2019), 12-17. 

[34]

I. GerakakisP. Gavriilidis and N. I. Dourvas, Accelerating fuzzy cellular automata for modeling crowd dynamics, Journal of Computational ence, 32 (2019), 125-140. 

[35]

Y. ZhouT. WuG. Zhang and Z. Fan, A multistory building evacuation model based on multiple-factor analysis, Advances in Civil Engineering, 22 (2019), 15-19. 

[36]

Z. ZhangC. Wang and Y. Wang, Design of emergency evacuation scheme for louvre, IOP Conference Series: Materials Science and Engineering, 0 (2020), 12025-12029. 

[37]

R. TangX. Luan and S. Xu, Analysis of evacuation of tourists based on the louvre's emergency, Open Journal of Applied Sciences, 9 (2019), 515-534. 

Figure 1.  Schematic diagram of cellular automata
Figure 2.  Neighborhood domain of cell (i, j) and possible directions of motion
Figure 3.  Information area perceived by pedestrian
Figure 4.  he relationship diagram of the influence factors of the evacuation model based on the ant colony algorithm
Figure 5.  Individual movement model
Figure 6.  Schematic diagram of the infection of the SIS model
Figure 7.  Schematic diagram of the simulation environment
Figure 8.  Evacuation diagrams
Figure 9.  The curves of the percentage of people in panic under different infection rates
Figure 10.  The curves of the percentage of people in panic under different cure rates
Figure 11.  The curves of the percentage of people at different crowd densities
Figure 12.  The effect of the motion parameter P on the SIS epidemic process
Figure 13.  The relationship between pedestrian density and the number of people in panic
Figure 14.  The relationship between the ratio of calm to panic and evacuation time
Figure 15.  The relationship between average distance and the percentage of pedestrians in panic
Figure 16.  Evacuation environment under different pedestrian densities
Figure 17.  Evacuation environment under different Obstacle distribution
Figure 18.  Evacuation environment of existing commercial software
Figure 19.  Evacuation environment of Louvre in France
Table 1.  Three models of evacuation time when the pedestrian density is 0.1
Number CA CA-FL CA-ACA
1 57 51 50
2 55 55 53
3 58 56 48
4 57 54 52
5 55 55 51
6 58 58 52
7 57 43 47
8 57 55 50
9 56 52 51
10 57 56 49
Number CA CA-FL CA-ACA
1 57 51 50
2 55 55 53
3 58 56 48
4 57 54 52
5 55 55 51
6 58 58 52
7 57 43 47
8 57 55 50
9 56 52 51
10 57 56 49
Table 2.  Three models of evacuation time when the pedestrian density is 0.2
Number CA CA-FL CA-ACA
1 75 70 65
2 73 71 66
3 73 72 65
4 74 75 67
5 72 70 64
6 71 69 66
7 74 68 65
8 73 71 67
9 74 72 67
10 73 72 65
Number CA CA-FL CA-ACA
1 75 70 65
2 73 71 66
3 73 72 65
4 74 75 67
5 72 70 64
6 71 69 66
7 74 68 65
8 73 71 67
9 74 72 67
10 73 72 65
Table 3.  Three models of evacuation time when the pedestrian density is 0.3
Number CA CA-FL CA-ACA
1 108 93 83
2 105 95 82
3 107 90 83
4 110 93 85
5 108 95 80
6 104 89 85
7 105 93 82
8 105 93 81
9 107 90 83
10 106 96 83
Number CA CA-FL CA-ACA
1 108 93 83
2 105 95 82
3 107 90 83
4 110 93 85
5 108 95 80
6 104 89 85
7 105 93 82
8 105 93 81
9 107 90 83
10 106 96 83
Table 4.  Three models of evacuation time when the pedestrian density is 0.4
Number CA CA-FL CA-ACA
1 130 115 95
2 127 115 94
3 131 117 92
4 130 116 95
5 132 115 96
6 133 114 94
7 132 117 95
8 130 115 93
9 130 117 94
10 131 116 94
Number CA CA-FL CA-ACA
1 130 115 95
2 127 115 94
3 131 117 92
4 130 116 95
5 132 115 96
6 133 114 94
7 132 117 95
8 130 115 93
9 130 117 94
10 131 116 94
Table 5.  Three models of evacuation time when the number of obstacles is 1
Number CA CA-FL CA-ACA
1 75 75 70
2 73 74 71
3 78 73 72
4 77 73 72
5 76 75 70
6 77 74 72
7 78 73 73
8 77 74 71
9 77 72 71
10 76 70 72
Number CA CA-FL CA-ACA
1 75 75 70
2 73 74 71
3 78 73 72
4 77 73 72
5 76 75 70
6 77 74 72
7 78 73 73
8 77 74 71
9 77 72 71
10 76 70 72
Table 6.  Three models of evacuation time when the number of obstacles is 2
Number CA CA-FL CA-ACA
1 84 80 75
2 82 82 77
3 81 81 76
4 80 78 75
5 83 77 75
6 83 79 76
7 85 80 75
8 83 80 77
9 82 81 75
10 83 79 74
Number CA CA-FL CA-ACA
1 84 80 75
2 82 82 77
3 81 81 76
4 80 78 75
5 83 77 75
6 83 79 76
7 85 80 75
8 83 80 77
9 82 81 75
10 83 79 74
Table 7.  Three models of evacuation time when the number of obstacles is 3
Number CA CA-FL CA-ACA
1 130 99 83
2 131 98 85
3 132 97 86
4 131 98 83
5 130 93 84
6 131 90 82
7 128 94 84
8 130 95 83
9 128 95 83
10 129 94 84
Number CA CA-FL CA-ACA
1 130 99 83
2 131 98 85
3 132 97 86
4 131 98 83
5 130 93 84
6 131 90 82
7 128 94 84
8 130 95 83
9 128 95 83
10 129 94 84
Table 8.  Different algorithms of evacuation time based on Louvre
Algorithm Algorithm1 Algorithm2 Algorithm3
Time(s) 190 182 171
Algorithm Algorithm1 Algorithm2 Algorithm3
Time(s) 190 182 171
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