An Emergency Shelter Location Model Based on the Sense of Security and the Reliability Level

Abstract

Based on the value function of the prospect theory, this paper constructs a security function, which is used to describe the victims’ feelings about the distance in emergency evacuation. Since different paths between the demand points and the emergency shelters are generally of different importance degrees, they are divided into main paths and auxiliary paths. The security function values and the reliability levels of main paths and auxiliary paths are given different weights. The weighted sum of the security function values and the weighted sum of the reliability level function values of all demand points are maximized to determine the location and the number of the emergency shelters, the transfer paths, the reinforced edges and the incremental reliability level of the selected edge. In order to solve the model, a two-stage simulated annealing-particle swarm optimization algorithm is proposed. In this algorithm, the particle swarm optimization (PSO) algorithm is embedded into the simulated annealing (SA) algorithm. The cumulative probability operator and the cost probability operator are formed to determine the evolution of the particles. Considering the budget constraint, the algorithm eliminates the shelter combinations that do not meet the constraint, which greatly saves the calculation time and improves the efficiency. The proposed algorithm is applied to a case, which verifies its feasibility and stability. The model and the algorithm of this paper provide a basis for emergency management departments to make the earthquake emergency planning.

Keywords

Emergency shelter location / security function / reliability level / two-stage SA-PSO algorithm / cumulative probability operator / cost probability operator

References

[1] Caunhye A M, Aydin N Y, Duzgun H S. Robust post-disaster route restoration. OR Spectrum, 2020, 42: 1055-1087.

[2] Chen E X, Li J Q, Liu X Y. In search of the essential binary discrete particle swarm. Applied Soft Computing, 2011, 11(3): 3260-3269.

[3] Cheng M H, Frangopol D M. Life-cycle optimization of structural systems based on cumulative prospect theory: Effects of the reference point and risk attitudes. Reliability Engineering & System Safety, 2022, 218: 108100.

[4] Coutinho-Rodrigues J, Tralhão L, Alçada-Almeida L. Solving a location-routing problem with a multiobjective approach: The design of urban evacuation plans. Journal of Transport Geography, 2012, 22: 206-218.

[5] Eglese R W. Simulated annealing: A tool for operational research. European Journal of Operational Research, 1990, 46(3): 271-281.

[6] Ford L R, Fulkerson D R. Maximal flow through a network. Canadian Journal of Mathematics, 1956, 8: 399-404.

[7] Gale D. A theorem on flows in networks. Pacific Journal of Mathematics, 1957, 7(2): 1073-1082.

[8] Gao S C, Wang Y R, Cheng J J, Inazumi Y, Tang Z. Ant colony optimization with clustering for solving the dynamic location routing problem. Applied Mathematics and Computation, 2016, 285: 149-173.

[9] Gao Y, Liu W X. Cloud estimation of distribution algorithm with quasi-oppositional learning and preference order ranking for multi-objective optimization. International Journal of Grid and Utility Computing, 2016, 7(3): 200-207.

[10] Goerigk M, Grün B, Heßler P. Branch and bound algorithms for the bus evacuation problem. Computers & Operations Research, 2013, 40(12): 3010-3020.

[11] Gou X J, Xu Z S, Zhou W, Herrera-Viedma E. The risk assessment of construction project investment based on prospect theory with linguistic preference orderings. Economic Research-Ekonomska Istraživanja, 2021, 34(1): 709-731.

[12] Guo W Z, Chen G L, Huang M, Chen S L. A discrete particle swarm optimization algorithm for the multiobjective permutation flowshop sequencing problem. In Fuzzy Information and Engineering, 2007, Berlin, Heidelberg: Springer

[13] Hou Y, Hao G S, Zhang Y, Gu F, Xu W Y. A multi-objective discrete particle swarm optimization method for particle routing in distributed particle filters. Knowledge-Based Systems, 2022, 240: 108068.

[14] Hu F Y, Yang S N, Xu W. A non-dominated sorting genetic algorithm for the location and districting planning of earthquake shelters. International Journal of Geographical Information Science, 2014, 28(7): 1482-1501.

[15] Hu P, Pan J S, Chu S C, Sun C L. Multi-surrogate assisted binary particle swarm optimization algorithm and its application for feature selection. Applied Soft Computing, 2022, 121: 108736.

[16] Hu Z H, Sheu J B, Xiao L. Post-disaster evacuation and temporary resettlement considering panic and panic spread. Transportation Research Part B: Methodological, 2014, 69: 112-132.

[17] Kennedy J, Eberhart R (1995, November). Particle swarm optimization. In Proceedings of ICNN’95-international Conference on Neural Networks (4): 1942–1948. IEEE.

[18] Kennedy J, Eberhart R C (1997, October). A discrete binary version of the particle swarm algorithm. In 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation Vol. 5: 4104–4108. IEEE.

[19] Kirkpatrick S, Gelatt C D Jr, Vecchi M P. Optimization by simulated annealing. Science, 1983, 220(4598): 671-680.

[20] Lee H W, Lee K, Modiano E. Maximizing reliability in WDM networks through lightpath routing. IEEE/ACM Transactions on Networking, 2013, 22(4): 1052-1066.

[21] Lee K, Ozsen L. Tabu search heuristic for the network design model with lead time and safety stock considerations. Computers & Industrial Engineering, 2020, 148: 106717.

[22] Lin Y K, Chen S G. A maximal flow method to search for d-MPs in stochastic-flow networks. Journal of Computational Science, 2017, 22: 119-125.

[23] Metropolis N, Rosenbluth A W, Rosenbluth M N, Teller A H, Teller E. Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 1953, 21(6): 1087-1092.

[24] Nappi M M L, Souza J C. Disaster management: Hierarchical structuring criteria for selection and location of temporary shelters. Natural Hazards, 2015, 75(3): 2421-2436.

[25] Ng M, Park J, Waller S T. A hybrid bilevel model for the optimal shelter assignment in emergency evacuations. Computer-Aided Civil and Infrastructure Engineering, 2010, 25(8): 547-556.

[26] Peng D J, Ye C M, Wan M R. A multi-objective improved novel discrete particle swarm optimization for emergency resource center location problem. Engineering Applications of Artificial Intelligence, 2022, 111: 104725.

[27] Poorzahedy H, Abulghasemi F. Application of ant system to network design problem. Transportation, 2005, 32(3): 251-273.

[28] Qiang P, Nagurney A. A bi-criteria indicator to assess supply chain network performance for critical needs under capacity and demand disruptions. Transportation Research Part A: Policy and Practice, 2012, 46(5): 801-812.

[29] Samany N N, Sheybani M, Zlatanova S. Detection of safe areas in flood as emergency evacuation stations using modified particle swarm optimization with local search. Applied Soft Computing, 2021, 111: 107681.

[30] Seraji H, Tavakkoli-Moghaddam R, Asian S, Kaur H (2021). An integrative location-allocation model for humanitarian logistics with distributive injustice and dissatisfaction under uncertainty. Annals of Operations Research 1–47.

[31] Tversky A, Kahneman D. Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 1992, 5(4): 297-323.

[32] Vahdani B, Veysmoradi D, Shekari N, Mousavi S M. Multi-objective, multi-period location-routing model to distribute relief after earthquake by considering emergency roadway repair. Neural Computing and Applications, 2018, 30(3): 835-854.

[33] Wang F W, Cheng Q G, Highland L, Miyajima M, Wang H B, Yan C G. Preliminary investigation of some large landslides triggered by the 2008 Wenchuan earthquake, Sichuan Province, China. Landslides, 2009, 6(1): 47-54.

[34] Wang J, Situ C Q, Yu M Z. The post-disaster emergency planning problem with facility location and people/resource assignment. Kybernetes, 2020, 49(10): 2385-2418.

[35] Wang Y Y, Xu Z S. A multi-objective location decision making model for emergency shelters giving priority to subjective evaluation of residents. International Journal of Computers Communications & Control, 2022, 17(4): 4749.

[36] Wang Y Y, Xu Z S, Filip F G. Multi-objective model to improve network reliability level under limited budget by considering selection of facilities and total service distance in rescue operations. International Journal of Computers, Communications & Control, 2022, 17(1): 1-18.

[37] Wang Y Y, Xu Z S, Filip F G. A multi-objective model for the location of the emergency facilities and the selection of the rescue path based on the restoration of the damaged edges. Studies in Informatics and Control, 2022, 31(3): 5-20.

[38] Yang Z, Chen H X, Chu F, Wang N M. An effective hybrid approach to the two-stage capacitated facility location problem. European Journal of Operational Research, 2019, 275(2): 467-480.

[39] Yan T R, Lu F Q, Wang S X, Wang L Z, Bi H L (2022). A hybrid metaheuristic algorithm for the multi-objective location-routing problem in the early post-disaster stage. Journal of Industrial and Management Optimization. Doi: https://doi.org/10.3934/jimo.2022145.

[40] Yu WY, Liu JJ (2020). Optimization model based on reachability guarantee for emergency facility location and link reinforcement. Journal of Advanced Transportation Article ID: 4648908.