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The Glowinski–Le Tallec splitting method revisited: A general convergence and convergence rate analysis
Ambulance routing in disaster response considering variable patient condition: NSGA-II and MOPSO algorithms
1. | School of Industrial Engineering, University of Tehran, Tehran, Iran |
The shortage of relief vehicles capacity is a common issue throughout disastrous situations due to the abundance of injured people who need urgent medical aid. Hence, ambulances fleet management is highly important to save as many injured individuals as possible. In this regard, the present paper defines different patient groups based on their needs and characteristics. In order to provide the affected people with proper and timely medical aid, changes in their health status are also considered. A Mixed-integer Linear Programming (MILP) model is proposed to find the best sequence of routes for each ambulance and minimize the latest service completion time (SCT) as well as the number of patients whose condition gets worse because of receiving untimely medical services. Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are used to find high-quality solutions over a short time. In the end, Lorestan province, Iran, is considered as a case study to assess the model's performance and analyze the sensitivity of solutions with respect to the major parameters, which results in insightful managerial suggestions.
References:
[1] |
T. Andersson and P. Värbrand, Decision support tools for ambulance dispatch and relocation, in Operational Research for Emergency Planning in Healthcare: Volume 1, Palgrave Macmillan, London, 195-201.
doi: 10.1057/9781137535696_3. |
[2] |
E. Babaee Tirkolaee, A. Goli, M. Pahlevan and R. Malekalipour Kordestanizadeh,
A robust bi-objective multi-trip periodic capacitated arc routing problem for urban waste collection using a multi-objective invasive weed optimization, Waste Management & Research, 37 (2019), 1089-1101.
doi: 10.1177/0734242X19865340. |
[3] |
A. Başar, B. Çatay and T. Ünlüyurt,
A taxonomy for emergency service station location problem, Optimization Letters, 6 (2012), 1147-1160.
doi: 10.1007/s11590-011-0376-1. |
[4] |
D. Berkoune, J. Renaud, M. Rekik and A. Ruiz,
Transportation in disaster response operations, Socio-Economic Planning Sciences, 46 (2012), 23-32.
doi: 10.1016/j.seps.2011.05.002. |
[5] |
O. Berman, Z. Drezner and G. O. Wesolowsky,
The facility and transfer points location problem, International Transactions in Operational Research, 12 (2005), 387-402.
doi: 10.1111/j.1475-3995.2005.00514.x. |
[6] |
A. Bozorgi-Amiri, S. Tavakoli, H. Mirzaeipour and M. Rabbani,
Integrated locating of helicopter stations and helipads for wounded transfer under demand location uncertainty, The American Journal of Emergency Medicine, 35 (2017), 410-417.
doi: 10.1016/j.ajem.2016.11.024. |
[7] |
C. C. Branas, E. J. MacKenzie and C. S. ReVelle, A trauma resource allocation model for ambulances and hospitals, Health Services Research, 35 (2000), 489. Google Scholar |
[8] |
J.-F. Camacho-Vallejo, E. González-Rodríguez, F.-J. Almaguer and R. G. González-Ramírez, A bi-level optimization model for aid distribution after the occurrence of a disaster, Journal of Cleaner Production, 105 (2015), 134-145. Google Scholar |
[9] |
C. A. Coello Coello, G. T. Pulido and Mk Salazar Lechuga,
Handling multiple objectives with particle swarm optimization, IEEE Transactions on Evolutionary Computation, 8 (2004), 256-279.
doi: 10.1109/TEVC.2004.826067. |
[10] |
K. Deb, A. Pratap, S. Agarwal and T. Meyarivan,
A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.
doi: 10.1109/4235.996017. |
[11] |
A. E. Eiben, Z. Michalewicz, M. Schoenauer and J. E. Smith, Parameter control in evolutionary algorithms, In Parameter Setting in Evolutionary Algorithms, Springer, 2007, 19-46. Google Scholar |
[12] |
E. T. Erdemir, R. Batta, P. A. Rogerson, A. Blatt and Ma rie Flanigan,
Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach, European Journal of Operational Research, 207 (2010), 736-749.
doi: 10.1016/j.ejor.2010.05.047. |
[13] |
J. A. Fitzsimmons and B. N. Srikar,
Emergency ambulance location using the contiguous zone search routine, Journal of Operations Management, 2 (1982), 225-237.
doi: 10.1016/0272-6963(82)90011-0. |
[14] |
T. Furuta and K.-i. Tanaka,
Minisum and minimax location models for helicopter emergency medical service systems, Journal of the Operations Research Society of Japan, 56 (2013), 221-242.
doi: 10.15807/jorsj.56.221. |
[15] |
H. Garg,
An efficient biogeography based optimization algorithm for solving reliability optimization problems, Swarm and Evolutionary Computation, 24 (2015), 1-10.
doi: 10.1016/j.swevo.2015.05.001. |
[16] |
H. Garg,
A hybrid PSO-GA algorithm for constrained optimization problems, Applied Mathematics and Computation, 274 (2016), 292-305.
doi: 10.1016/j.amc.2015.11.001. |
[17] |
H. Garg,
A hybrid GSA-GA algorithm for constrained optimization problems, Information Sciences, 478 (2019), 499-523.
doi: 10.1016/j.ins.2018.11.041. |
[18] |
H. Garg and S. P. Sharma,
Multi-objective reliability-redundancy allocation problem using particle swarm optimization, Computers & Industrial Engineering, 64 (2013), 247-255.
doi: 10.1016/j.cie.2012.09.015. |
[19] |
M. Gendreau, G. Laporte and F. Semet,
A dynamic model and parallel tabu search heuristic for real-time ambulance relocation, Parallel Computing, 27 (2001), 1641-1653.
doi: 10.1016/S0167-8191(01)00103-X. |
[20] |
Z. Ghelichi, M. Saidi-Mehrabad and M. S. Pishvaee,
A stochastic programming approach toward optimal design and planning of an integrated green biodiesel supply chain network under uncertainty: A case study, Energy, 156 (2018), 661-687.
doi: 10.1016/j.energy.2018.05.103. |
[21] |
Z. Ghelichi, J. Tajik and M. S. Pishvaee,
A novel robust optimization approach for an integrated municipal water distribution system design under uncertainty: A case study of Mashhad, Computers & Chemical Engineering, 110 (2018), 13-34.
doi: 10.1016/j.compchemeng.2017.11.017. |
[22] |
A. Ghodratnama, H. R. Arbabi and A. Azaron,
Production planning in industrial townships modeled as hub location-allocation problems considering congestion in manufacturing plants, Computers & Industrial Engineering, 129 (2019), 479-501.
doi: 10.1016/j.cie.2019.01.049. |
[23] |
R. Goldberg and P. Listowsky,
Critical factors for emergency vehicle routing expert systems, Expert Systems with Applications, 7 (1994), 589-602.
doi: 10.1016/0957-4174(94)90082-5. |
[24] |
J. Holguín-Veras, M. Jaller, L. N. Van Wassenhove, N. Pérez and T. Wachtendorf, On the unique features of post-disaster humanitarian logistics, Journal of Operations Management, 30 (2012), 494-506. Google Scholar |
[25] |
S. A. Hosseinijou and M. Bashiri,
Stochastic models for transfer point location problem, The International Journal of Advanced Manufacturing Technology, 58 (2012), 211-225.
doi: 10.1007/s00170-011-3360-0. |
[26] |
A. Jotshi, Q. Gong and R. Batta,
Dispatching and routing of emergency vehicles in disaster mitigation using data fusion, Socio-Economic Planning Sciences, 43 (2009), 1-24.
doi: 10.1016/j.seps.2008.02.005. |
[27] |
H. Kalantari, A. Yousefli, M. Ghazanfari and K. Shahanaghi,
Fuzzy transfer point location problem: A possibilistic unconstrained nonlinear programming approach, The International Journal of Advanced Manufacturing Technology, 70 (2014), 1043-1051.
doi: 10.1007/s00170-013-5338-6. |
[28] |
V. A. Knight, P. R. Harper and L. Smith,
Ambulance allocation for maximal survival with heterogeneous outcome measures, Omega, 40 (2012), 918-926.
doi: 10.1016/j.omega.2012.02.003. |
[29] |
G. Mavrotas and K. Florios,
An improved version of the augmented $\varepsilon$-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems, Applied Mathematics and Computation, 219 (2013), 9652-9669.
doi: 10.1016/j.amc.2013.03.002. |
[30] |
F. Navazi, R. Tavakkoli-Moghaddam and Z. Sazvar,
A multi-period location-allocation-inventory problem for ambulance and helicopter ambulance stations: Robust possibilistic approach, IFAC-PapersOnLine, 51 (2018), 322-327.
doi: 10.1016/j.ifacol.2018.08.303. |
[31] |
L. Özdamar and M. A. Ertem,
Models, solutions and enabling technologies in humanitarian logistics, European Journal of Operational Research, 244 (2015), 55-65.
doi: 10.1016/j.ejor.2014.11.030. |
[32] |
R. S. Patwal, N. Narang and H. Garg,
A novel TVAC-PSO based mutation strategies algorithm for generation scheduling of pumped storage hydrothermal system incorporating solar units, Energy, 142 (2018), 822-837.
doi: 10.1016/j.energy.2017.10.052. |
[33] |
A. J. Pedraza-Martinez and L. N. Van Wassenhove,
Transportation and vehicle fleet management in humanitarian logistics: Challenges for future research, EURO Journal on Transportation and Logistics, 1 (2012), 185-196.
doi: 10.1007/s13676-012-0001-1. |
[34] |
M. Rabbani, S. Momen, N. Akbarian-Saravi, H. Farrokhi-Asl and Z. Ghelichi, Optimal design for sustainable bioethanol supply chain considering the bioethanol production strategies: A case study, Computers & Chemical Engineering, 134 (2020), 106720.
doi: 10.1016/j.compchemeng.2019.106720. |
[35] |
M. Sasaki, T. Furuta and A. Suzuki,
Exact optimal solutions of the minisum facility and transfer points location problems on a network, International Transactions in Operational Research, 15 (2008), 295-306.
doi: 10.1111/j.1475-3995.2008.00602.x. |
[36] |
V. Schmid,
Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming, European Journal of Operational Research, 219 (2012), 611-621.
doi: 10.1016/j.ejor.2011.10.043. |
[37] |
N. Schuurman, N. J. Bell, R. L'Heureux and S. M Hameed, Modelling optimal location for pre-hospital helicopter emergency medical services, BMC Emergency Medicine, 9 (2009), Art. No. 6.
doi: 10.1186/1471-227X-9-6. |
[38] |
N. Srinivas and K. Deb,
Muiltiobjective optimization using nondominated sorting in genetic algorithms, Evolutionary Computation, 2 (1994), 221-248.
doi: 10.1162/evco.1994.2.3.221. |
[39] |
G. Taguchi, Introduction to quality engineering: designing quality into products and processes, Technical report, 1986. Google Scholar |
[40] |
L. Talarico, F. Meisel and K. Sörensen,
Ambulance routing for disaster response with patient groups, Computers & Operations Research, 56 (2015), 120-133.
doi: 10.1016/j.cor.2014.11.006. |
[41] |
H. Tikani and M. Setak, Ambulance routing in disaster response scenario considering different types of ambulances and semi soft time windows, Journal of Industrial and Systems Engineering, 12 (2019), 95-128. Google Scholar |
[42] |
E. B. Tirkolaee, A. Goli and G.-W. Weber, Fuzzy mathematical programming and self-adaptive artificial fish swarm algorithm for just-in-time energy-aware flow shop scheduling problem with outsourcing option, IEEE Transactions on Fuzzy Systems, 2020. Google Scholar |
[43] |
E. B. Tirkolaee, S. Hadian, G.-W. Weber and I. Mahdavi,
A robust green traffic-based routing problem for perishable products distribution, Computational Intelligence, 36 (2020), 80-101.
doi: 10.1111/coin.12240. |
[44] |
T. Tlili, S. Abidi and S. Krichen,
A mathematical model for efficient emergency transportation in a disaster situation, The American Journal of Emergency Medicine, 36 (2018), 1585-1590.
doi: 10.1016/j.ajem.2018.01.039. |
[45] |
H. Toro-DíAz, M. E. Mayorga, S. Chanta and and L. A. Mclay, Joint location and dispatching decisions for emergency medical services, Computers & Industrial Engineering, 64 (2013), 917-928. Google Scholar |
[46] |
Y.-J. Zheng, S.-Y. Chen and and H.-F. Ling,
Evolutionary optimization for disaster relief operations: A survey, Applied Soft Computing, 27 (2015), 553-566.
doi: 10.1016/j.asoc.2014.09.041. |
[47] |
A. Zhou, B.-Y. Qu, H. Li, S.-Z. Zhao, P. N. Suganthan and Q. Zhang,
Multiobjective evolutionary algorithms: A survey of the state of the art, Swarm and Evolutionary Computation, 1 (2011), 32-49.
doi: 10.1016/j.swevo.2011.03.001. |
show all references
References:
[1] |
T. Andersson and P. Värbrand, Decision support tools for ambulance dispatch and relocation, in Operational Research for Emergency Planning in Healthcare: Volume 1, Palgrave Macmillan, London, 195-201.
doi: 10.1057/9781137535696_3. |
[2] |
E. Babaee Tirkolaee, A. Goli, M. Pahlevan and R. Malekalipour Kordestanizadeh,
A robust bi-objective multi-trip periodic capacitated arc routing problem for urban waste collection using a multi-objective invasive weed optimization, Waste Management & Research, 37 (2019), 1089-1101.
doi: 10.1177/0734242X19865340. |
[3] |
A. Başar, B. Çatay and T. Ünlüyurt,
A taxonomy for emergency service station location problem, Optimization Letters, 6 (2012), 1147-1160.
doi: 10.1007/s11590-011-0376-1. |
[4] |
D. Berkoune, J. Renaud, M. Rekik and A. Ruiz,
Transportation in disaster response operations, Socio-Economic Planning Sciences, 46 (2012), 23-32.
doi: 10.1016/j.seps.2011.05.002. |
[5] |
O. Berman, Z. Drezner and G. O. Wesolowsky,
The facility and transfer points location problem, International Transactions in Operational Research, 12 (2005), 387-402.
doi: 10.1111/j.1475-3995.2005.00514.x. |
[6] |
A. Bozorgi-Amiri, S. Tavakoli, H. Mirzaeipour and M. Rabbani,
Integrated locating of helicopter stations and helipads for wounded transfer under demand location uncertainty, The American Journal of Emergency Medicine, 35 (2017), 410-417.
doi: 10.1016/j.ajem.2016.11.024. |
[7] |
C. C. Branas, E. J. MacKenzie and C. S. ReVelle, A trauma resource allocation model for ambulances and hospitals, Health Services Research, 35 (2000), 489. Google Scholar |
[8] |
J.-F. Camacho-Vallejo, E. González-Rodríguez, F.-J. Almaguer and R. G. González-Ramírez, A bi-level optimization model for aid distribution after the occurrence of a disaster, Journal of Cleaner Production, 105 (2015), 134-145. Google Scholar |
[9] |
C. A. Coello Coello, G. T. Pulido and Mk Salazar Lechuga,
Handling multiple objectives with particle swarm optimization, IEEE Transactions on Evolutionary Computation, 8 (2004), 256-279.
doi: 10.1109/TEVC.2004.826067. |
[10] |
K. Deb, A. Pratap, S. Agarwal and T. Meyarivan,
A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.
doi: 10.1109/4235.996017. |
[11] |
A. E. Eiben, Z. Michalewicz, M. Schoenauer and J. E. Smith, Parameter control in evolutionary algorithms, In Parameter Setting in Evolutionary Algorithms, Springer, 2007, 19-46. Google Scholar |
[12] |
E. T. Erdemir, R. Batta, P. A. Rogerson, A. Blatt and Ma rie Flanigan,
Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach, European Journal of Operational Research, 207 (2010), 736-749.
doi: 10.1016/j.ejor.2010.05.047. |
[13] |
J. A. Fitzsimmons and B. N. Srikar,
Emergency ambulance location using the contiguous zone search routine, Journal of Operations Management, 2 (1982), 225-237.
doi: 10.1016/0272-6963(82)90011-0. |
[14] |
T. Furuta and K.-i. Tanaka,
Minisum and minimax location models for helicopter emergency medical service systems, Journal of the Operations Research Society of Japan, 56 (2013), 221-242.
doi: 10.15807/jorsj.56.221. |
[15] |
H. Garg,
An efficient biogeography based optimization algorithm for solving reliability optimization problems, Swarm and Evolutionary Computation, 24 (2015), 1-10.
doi: 10.1016/j.swevo.2015.05.001. |
[16] |
H. Garg,
A hybrid PSO-GA algorithm for constrained optimization problems, Applied Mathematics and Computation, 274 (2016), 292-305.
doi: 10.1016/j.amc.2015.11.001. |
[17] |
H. Garg,
A hybrid GSA-GA algorithm for constrained optimization problems, Information Sciences, 478 (2019), 499-523.
doi: 10.1016/j.ins.2018.11.041. |
[18] |
H. Garg and S. P. Sharma,
Multi-objective reliability-redundancy allocation problem using particle swarm optimization, Computers & Industrial Engineering, 64 (2013), 247-255.
doi: 10.1016/j.cie.2012.09.015. |
[19] |
M. Gendreau, G. Laporte and F. Semet,
A dynamic model and parallel tabu search heuristic for real-time ambulance relocation, Parallel Computing, 27 (2001), 1641-1653.
doi: 10.1016/S0167-8191(01)00103-X. |
[20] |
Z. Ghelichi, M. Saidi-Mehrabad and M. S. Pishvaee,
A stochastic programming approach toward optimal design and planning of an integrated green biodiesel supply chain network under uncertainty: A case study, Energy, 156 (2018), 661-687.
doi: 10.1016/j.energy.2018.05.103. |
[21] |
Z. Ghelichi, J. Tajik and M. S. Pishvaee,
A novel robust optimization approach for an integrated municipal water distribution system design under uncertainty: A case study of Mashhad, Computers & Chemical Engineering, 110 (2018), 13-34.
doi: 10.1016/j.compchemeng.2017.11.017. |
[22] |
A. Ghodratnama, H. R. Arbabi and A. Azaron,
Production planning in industrial townships modeled as hub location-allocation problems considering congestion in manufacturing plants, Computers & Industrial Engineering, 129 (2019), 479-501.
doi: 10.1016/j.cie.2019.01.049. |
[23] |
R. Goldberg and P. Listowsky,
Critical factors for emergency vehicle routing expert systems, Expert Systems with Applications, 7 (1994), 589-602.
doi: 10.1016/0957-4174(94)90082-5. |
[24] |
J. Holguín-Veras, M. Jaller, L. N. Van Wassenhove, N. Pérez and T. Wachtendorf, On the unique features of post-disaster humanitarian logistics, Journal of Operations Management, 30 (2012), 494-506. Google Scholar |
[25] |
S. A. Hosseinijou and M. Bashiri,
Stochastic models for transfer point location problem, The International Journal of Advanced Manufacturing Technology, 58 (2012), 211-225.
doi: 10.1007/s00170-011-3360-0. |
[26] |
A. Jotshi, Q. Gong and R. Batta,
Dispatching and routing of emergency vehicles in disaster mitigation using data fusion, Socio-Economic Planning Sciences, 43 (2009), 1-24.
doi: 10.1016/j.seps.2008.02.005. |
[27] |
H. Kalantari, A. Yousefli, M. Ghazanfari and K. Shahanaghi,
Fuzzy transfer point location problem: A possibilistic unconstrained nonlinear programming approach, The International Journal of Advanced Manufacturing Technology, 70 (2014), 1043-1051.
doi: 10.1007/s00170-013-5338-6. |
[28] |
V. A. Knight, P. R. Harper and L. Smith,
Ambulance allocation for maximal survival with heterogeneous outcome measures, Omega, 40 (2012), 918-926.
doi: 10.1016/j.omega.2012.02.003. |
[29] |
G. Mavrotas and K. Florios,
An improved version of the augmented $\varepsilon$-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems, Applied Mathematics and Computation, 219 (2013), 9652-9669.
doi: 10.1016/j.amc.2013.03.002. |
[30] |
F. Navazi, R. Tavakkoli-Moghaddam and Z. Sazvar,
A multi-period location-allocation-inventory problem for ambulance and helicopter ambulance stations: Robust possibilistic approach, IFAC-PapersOnLine, 51 (2018), 322-327.
doi: 10.1016/j.ifacol.2018.08.303. |
[31] |
L. Özdamar and M. A. Ertem,
Models, solutions and enabling technologies in humanitarian logistics, European Journal of Operational Research, 244 (2015), 55-65.
doi: 10.1016/j.ejor.2014.11.030. |
[32] |
R. S. Patwal, N. Narang and H. Garg,
A novel TVAC-PSO based mutation strategies algorithm for generation scheduling of pumped storage hydrothermal system incorporating solar units, Energy, 142 (2018), 822-837.
doi: 10.1016/j.energy.2017.10.052. |
[33] |
A. J. Pedraza-Martinez and L. N. Van Wassenhove,
Transportation and vehicle fleet management in humanitarian logistics: Challenges for future research, EURO Journal on Transportation and Logistics, 1 (2012), 185-196.
doi: 10.1007/s13676-012-0001-1. |
[34] |
M. Rabbani, S. Momen, N. Akbarian-Saravi, H. Farrokhi-Asl and Z. Ghelichi, Optimal design for sustainable bioethanol supply chain considering the bioethanol production strategies: A case study, Computers & Chemical Engineering, 134 (2020), 106720.
doi: 10.1016/j.compchemeng.2019.106720. |
[35] |
M. Sasaki, T. Furuta and A. Suzuki,
Exact optimal solutions of the minisum facility and transfer points location problems on a network, International Transactions in Operational Research, 15 (2008), 295-306.
doi: 10.1111/j.1475-3995.2008.00602.x. |
[36] |
V. Schmid,
Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming, European Journal of Operational Research, 219 (2012), 611-621.
doi: 10.1016/j.ejor.2011.10.043. |
[37] |
N. Schuurman, N. J. Bell, R. L'Heureux and S. M Hameed, Modelling optimal location for pre-hospital helicopter emergency medical services, BMC Emergency Medicine, 9 (2009), Art. No. 6.
doi: 10.1186/1471-227X-9-6. |
[38] |
N. Srinivas and K. Deb,
Muiltiobjective optimization using nondominated sorting in genetic algorithms, Evolutionary Computation, 2 (1994), 221-248.
doi: 10.1162/evco.1994.2.3.221. |
[39] |
G. Taguchi, Introduction to quality engineering: designing quality into products and processes, Technical report, 1986. Google Scholar |
[40] |
L. Talarico, F. Meisel and K. Sörensen,
Ambulance routing for disaster response with patient groups, Computers & Operations Research, 56 (2015), 120-133.
doi: 10.1016/j.cor.2014.11.006. |
[41] |
H. Tikani and M. Setak, Ambulance routing in disaster response scenario considering different types of ambulances and semi soft time windows, Journal of Industrial and Systems Engineering, 12 (2019), 95-128. Google Scholar |
[42] |
E. B. Tirkolaee, A. Goli and G.-W. Weber, Fuzzy mathematical programming and self-adaptive artificial fish swarm algorithm for just-in-time energy-aware flow shop scheduling problem with outsourcing option, IEEE Transactions on Fuzzy Systems, 2020. Google Scholar |
[43] |
E. B. Tirkolaee, S. Hadian, G.-W. Weber and I. Mahdavi,
A robust green traffic-based routing problem for perishable products distribution, Computational Intelligence, 36 (2020), 80-101.
doi: 10.1111/coin.12240. |
[44] |
T. Tlili, S. Abidi and S. Krichen,
A mathematical model for efficient emergency transportation in a disaster situation, The American Journal of Emergency Medicine, 36 (2018), 1585-1590.
doi: 10.1016/j.ajem.2018.01.039. |
[45] |
H. Toro-DíAz, M. E. Mayorga, S. Chanta and and L. A. Mclay, Joint location and dispatching decisions for emergency medical services, Computers & Industrial Engineering, 64 (2013), 917-928. Google Scholar |
[46] |
Y.-J. Zheng, S.-Y. Chen and and H.-F. Ling,
Evolutionary optimization for disaster relief operations: A survey, Applied Soft Computing, 27 (2015), 553-566.
doi: 10.1016/j.asoc.2014.09.041. |
[47] |
A. Zhou, B.-Y. Qu, H. Li, S.-Z. Zhao, P. N. Suganthan and Q. Zhang,
Multiobjective evolutionary algorithms: A survey of the state of the art, Swarm and Evolutionary Computation, 1 (2011), 32-49.
doi: 10.1016/j.swevo.2011.03.001. |




















Authors | Objective function | Problem | Modes | Variable condition | Patient groups | Solution approach |
Talarico et al. [40] | Min max response time | Routing | _ | _ | X | Heuristic |
Jotshi et al. [26] | Max demand coverage/Min coverage cost | Routing | _ | _ | X | Heuristic |
Schuurman et al. [37] | Max demand coverage | Locating | _ | _ | _ | Exact |
Erdemir et al. [12] | Min establishment cost/Max demand coverage | Locating | X | _ | _ | Heuristic |
Branas et al. [7] | Min average response time | Locating | _ | _ | _ | Heuristic |
Furuta and Tanaka [14] | Min max transfer time/Min response time | Locating | X | _ | _ | Exact |
Sasaki et al. [35] | Min transfer time | Locating | _ | _ | _ | Exact |
Berman et al. [5] | Min transfer time | Locating | _ | _ | _ | Heuristic |
Hosseinijou and Bashiri [25] | Min max distance | Locating | _ | _ | _ | Exact: analytical/numerical |
Kalantari et al. [27] | Min transfer time | Locating | _ | _ | _ | Heuristic |
Camacho et al. [8] | Min response time | Distribution | X | _ | _ | Exact |
Tikani and Setak [41] | Min max response time | Routing | _ | _ | X | Heuristic |
Fitzsimmons and Srikar [13] | Min max response time | Locating | _ | _ | _ | Heuristic |
Gendreau et al. [19] | Max demand coverage | Relocating | _ | _ | _ | Heuristic |
Knight et al. [28] | Max survival probability | Locating | _ | _ | X | Heuristic |
Toro-Díaz et al. [45] | Min response time/Max demand coverage | Locating/dispatching | _ | _ | _ | Heuristic |
Andersson and Värbrand [1] | Min max transfer time | Locating/dispatching | _ | _ | _ | Heuristic |
Schmid [36] | Min average response time | Relocating/dispatching | _ | _ | _ | Heuristic |
Goldberg and Listowsky [23] | _ | Routing | _ | _ | _ | Survey |
Tlili et al. [44] | Min travel cost | Routing | _ | _ | _ | Heuristic |
Bozorgi-Amiri et al. [6] | Min transfer time | Locating | X | _ | _ | Exact |
Navazi et al. [30] | Min establishment cost/Min response time | Locating | X | _ | _ | Exact |
This paper | Min max response time/Min number of patients | Routing | _ | X | X | Heuristic |
Authors | Objective function | Problem | Modes | Variable condition | Patient groups | Solution approach |
Talarico et al. [40] | Min max response time | Routing | _ | _ | X | Heuristic |
Jotshi et al. [26] | Max demand coverage/Min coverage cost | Routing | _ | _ | X | Heuristic |
Schuurman et al. [37] | Max demand coverage | Locating | _ | _ | _ | Exact |
Erdemir et al. [12] | Min establishment cost/Max demand coverage | Locating | X | _ | _ | Heuristic |
Branas et al. [7] | Min average response time | Locating | _ | _ | _ | Heuristic |
Furuta and Tanaka [14] | Min max transfer time/Min response time | Locating | X | _ | _ | Exact |
Sasaki et al. [35] | Min transfer time | Locating | _ | _ | _ | Exact |
Berman et al. [5] | Min transfer time | Locating | _ | _ | _ | Heuristic |
Hosseinijou and Bashiri [25] | Min max distance | Locating | _ | _ | _ | Exact: analytical/numerical |
Kalantari et al. [27] | Min transfer time | Locating | _ | _ | _ | Heuristic |
Camacho et al. [8] | Min response time | Distribution | X | _ | _ | Exact |
Tikani and Setak [41] | Min max response time | Routing | _ | _ | X | Heuristic |
Fitzsimmons and Srikar [13] | Min max response time | Locating | _ | _ | _ | Heuristic |
Gendreau et al. [19] | Max demand coverage | Relocating | _ | _ | _ | Heuristic |
Knight et al. [28] | Max survival probability | Locating | _ | _ | X | Heuristic |
Toro-Díaz et al. [45] | Min response time/Max demand coverage | Locating/dispatching | _ | _ | _ | Heuristic |
Andersson and Värbrand [1] | Min max transfer time | Locating/dispatching | _ | _ | _ | Heuristic |
Schmid [36] | Min average response time | Relocating/dispatching | _ | _ | _ | Heuristic |
Goldberg and Listowsky [23] | _ | Routing | _ | _ | _ | Survey |
Tlili et al. [44] | Min travel cost | Routing | _ | _ | _ | Heuristic |
Bozorgi-Amiri et al. [6] | Min transfer time | Locating | X | _ | _ | Exact |
Navazi et al. [30] | Min establishment cost/Min response time | Locating | X | _ | _ | Exact |
This paper | Min max response time/Min number of patients | Routing | _ | X | X | Heuristic |
Algorithm | Parameter | |||||||
NSGA-II | 75 | 100 | 0.6 | 0.2 | _ | _ | _ | _ |
MOPSO | 100 | 125 | _ | _ | 75 | 0.5 | 1.25 | 1.5 |
Algorithm | Parameter | |||||||
NSGA-II | 75 | 100 | 0.6 | 0.2 | _ | _ | _ | _ |
MOPSO | 100 | 125 | _ | _ | 75 | 0.5 | 1.25 | 1.5 |
Problem Num. | Dimension | NSGA-II | MOPSO | Optimal | ||||||||
CPU time (s) | RNI | DM | SM | GD | CPU time (s) | RNI | DM | SM | GD | CPU time (s) | ||
1 | (3, 4, 4, 3) | 124.23 | 0.31 | 2.1253 | 0.0079 | 0.005 | 136.61 | 0.16 | 1.9872 | 0.0098 | 0.005 | 15 |
2 | (5, 6, 8, 6) | 132.4 | 0.37 | 1.5231 | 0.0091 | 0.003 | 148.25 | 0.11 | 1.9865 | 0.0111 | 0.005 | 89 |
3 | (8, 10, 10, 7) | 139.87 | 0.29 | 3.2964 | 0.0082 | 0.003 | 161.2 | 0.2 | 5.2964 | 0.0109 | 0.006 | 236 |
4 | (12, 15, 13, 11) | 149.12 | 0.4 | 0.4374 | 0.011 | 0.004 | 169.59 | 0.33 | 0.1381 | 0.0147 | 0.004 | 894 |
5 | (15, 17, 15, 13) | 156.76 | 0.64 | 1.0964 | 0.0054 | 0.006 | 175.32 | 0.42 | 2.1784 | 0.0021 | 0.006 | 2601 |
6 | (20, 23, 20, 18) | 161.2 | 0.57 | 1.4384 | 0.0066 | 0.003 | 183.82 | 0.62 | 5.9824 | 0.0069 | 0.002 | 8732 |
7 | (20, 24, 22, 20) | 168.94 | 0.59 | 1.9842 | 0.0069 | 0.001 | 187.48 | 0.48 | 3.9855 | 0.0132 | 0.003 | 15000 |
8 | (25, 28, 21, 20) | 175.54 | 0.21 | 4.7337 | 0.0074 | 0.005 | 193.56 | 0.15 | 2.9156 | 0.0097 | 0.007 | 15000 |
9 | (25, 27, 25, 21) | 179.36 | 0.28 | 3.341 | 0.0043 | 0.002 | 195.7 | 0.27 | 3.4415 | 0.004 | 0.008 | 15000 |
10 | (30, 32, 24, 22) | 188.87 | 0.88 | 3.7609 | 0.0121 | 0.003 | 210.1 | 0.42 | 4.5699 | 0.0158 | 0.005 | 15000 |
11 | (40, 43, 29, 25) | 194.3 | 0.91 | 1.2745 | 0.0108 | 0.001 | 223.24 | 0.81 | 6.1801 | 0.0124 | 0.001 | 15000 |
12 | (50, 55, 41, 32) | 212.25 | 0.73 | 2.8954 | 0.0039 | 0.002 | 240.51 | 0.83 | 4.0643 | 0.0061 | 0.001 | 15000 |
13 | (75, 83, 66, 45) | 237.86 | 0.77 | 5.762 | 0.0089 | 0.006 | 271.24 | 0.5 | 5.957 | 0.009 | 0.008 | 15000 |
14 | (90, 95, 70, 51) | 264.22 | 0.86 | 3.8713 | 0.0077 | 0.005 | 284.5 | 0.46 | 3.869 | 0.0111 | 0.005 | 15000 |
15 | (100, 112, 84, 62) | 283.67 | 0.94 | 1.8751 | 0.0106 | 0.005 | 303.2 | 0.73 | 5.5147 | 0.0131 | 0.006 | 15000 |
Problem Num. | Dimension | NSGA-II | MOPSO | Optimal | ||||||||
CPU time (s) | RNI | DM | SM | GD | CPU time (s) | RNI | DM | SM | GD | CPU time (s) | ||
1 | (3, 4, 4, 3) | 124.23 | 0.31 | 2.1253 | 0.0079 | 0.005 | 136.61 | 0.16 | 1.9872 | 0.0098 | 0.005 | 15 |
2 | (5, 6, 8, 6) | 132.4 | 0.37 | 1.5231 | 0.0091 | 0.003 | 148.25 | 0.11 | 1.9865 | 0.0111 | 0.005 | 89 |
3 | (8, 10, 10, 7) | 139.87 | 0.29 | 3.2964 | 0.0082 | 0.003 | 161.2 | 0.2 | 5.2964 | 0.0109 | 0.006 | 236 |
4 | (12, 15, 13, 11) | 149.12 | 0.4 | 0.4374 | 0.011 | 0.004 | 169.59 | 0.33 | 0.1381 | 0.0147 | 0.004 | 894 |
5 | (15, 17, 15, 13) | 156.76 | 0.64 | 1.0964 | 0.0054 | 0.006 | 175.32 | 0.42 | 2.1784 | 0.0021 | 0.006 | 2601 |
6 | (20, 23, 20, 18) | 161.2 | 0.57 | 1.4384 | 0.0066 | 0.003 | 183.82 | 0.62 | 5.9824 | 0.0069 | 0.002 | 8732 |
7 | (20, 24, 22, 20) | 168.94 | 0.59 | 1.9842 | 0.0069 | 0.001 | 187.48 | 0.48 | 3.9855 | 0.0132 | 0.003 | 15000 |
8 | (25, 28, 21, 20) | 175.54 | 0.21 | 4.7337 | 0.0074 | 0.005 | 193.56 | 0.15 | 2.9156 | 0.0097 | 0.007 | 15000 |
9 | (25, 27, 25, 21) | 179.36 | 0.28 | 3.341 | 0.0043 | 0.002 | 195.7 | 0.27 | 3.4415 | 0.004 | 0.008 | 15000 |
10 | (30, 32, 24, 22) | 188.87 | 0.88 | 3.7609 | 0.0121 | 0.003 | 210.1 | 0.42 | 4.5699 | 0.0158 | 0.005 | 15000 |
11 | (40, 43, 29, 25) | 194.3 | 0.91 | 1.2745 | 0.0108 | 0.001 | 223.24 | 0.81 | 6.1801 | 0.0124 | 0.001 | 15000 |
12 | (50, 55, 41, 32) | 212.25 | 0.73 | 2.8954 | 0.0039 | 0.002 | 240.51 | 0.83 | 4.0643 | 0.0061 | 0.001 | 15000 |
13 | (75, 83, 66, 45) | 237.86 | 0.77 | 5.762 | 0.0089 | 0.006 | 271.24 | 0.5 | 5.957 | 0.009 | 0.008 | 15000 |
14 | (90, 95, 70, 51) | 264.22 | 0.86 | 3.8713 | 0.0077 | 0.005 | 284.5 | 0.46 | 3.869 | 0.0111 | 0.005 | 15000 |
15 | (100, 112, 84, 62) | 283.67 | 0.94 | 1.8751 | 0.0106 | 0.005 | 303.2 | 0.73 | 5.5147 | 0.0131 | 0.006 | 15000 |
Criteria | Optimal method | Average results | Two-sample t-test | ||
NSGA-II | MOPSO | Comparison of means | P-value | ||
CPU time (s) | Both methods | 194.5727 | 205.6213 | 0 | |
RNI | NSGA-II | 0.5833 | 0.4326 | 0.32 | |
DM | MOPSO | 2.6276 | 3.8711 | 0.212 | |
SM | NSGA-II | 0.0079 | 0.0098 | 0.901 | |
GD | NSGA-II | 0.0036 | 0.0048 | 0.625 |
Criteria | Optimal method | Average results | Two-sample t-test | ||
NSGA-II | MOPSO | Comparison of means | P-value | ||
CPU time (s) | Both methods | 194.5727 | 205.6213 | 0 | |
RNI | NSGA-II | 0.5833 | 0.4326 | 0.32 | |
DM | MOPSO | 2.6276 | 3.8711 | 0.212 | |
SM | NSGA-II | 0.0079 | 0.0098 | 0.901 | |
GD | NSGA-II | 0.0036 | 0.0048 | 0.625 |
City name | Population | % of injured people | % of GC demands | % of RC demands |
Aleshtar | 33, 132 | 30% | 88% | 12% |
Aligudarz | 89, 521 | 21% | 49% | 51% |
Azna | 41, 703 | 27% | 83% | 17% |
Borujerd | 245, 730 | 19% | 77% | 23% |
Dorud | 100, 979 | 32% | 66% | 34% |
Khorramabad | 354, 854 | 15% | 41% | 59% |
Kuhdasht | 111, 737 | 28% | 58% | 42% |
Nur Abad | 62, 195 | 34% | 71% | 29% |
Pol Dokhtar | 32, 590 | 26% | 92% | 8% |
City name | Population | % of injured people | % of GC demands | % of RC demands |
Aleshtar | 33, 132 | 30% | 88% | 12% |
Aligudarz | 89, 521 | 21% | 49% | 51% |
Azna | 41, 703 | 27% | 83% | 17% |
Borujerd | 245, 730 | 19% | 77% | 23% |
Dorud | 100, 979 | 32% | 66% | 34% |
Khorramabad | 354, 854 | 15% | 41% | 59% |
Kuhdasht | 111, 737 | 28% | 58% | 42% |
Nur Abad | 62, 195 | 34% | 71% | 29% |
Pol Dokhtar | 32, 590 | 26% | 92% | 8% |
Hospital name | RC patient capacity | Number of ambulances |
Ibn Sina | 120 | 25 |
Imam Ali | 215 | 30 |
Imam Jafar Sadegh | 148 | 28 |
Imam Khomeini | 270 | 41 |
Kuhdasht | 132 | 27 |
Shohada-ye Ashayer | 347 | 40 |
Shahid Chamran | 221 | 36 |
Shohada-ye Haftom Tir | 150 | 20 |
Hospital name | RC patient capacity | Number of ambulances |
Ibn Sina | 120 | 25 |
Imam Ali | 215 | 30 |
Imam Jafar Sadegh | 148 | 28 |
Imam Khomeini | 270 | 41 |
Kuhdasht | 132 | 27 |
Shohada-ye Ashayer | 347 | 40 |
Shahid Chamran | 221 | 36 |
Shohada-ye Haftom Tir | 150 | 20 |
[1] |
Jean-François Biasse. Improvements in the computation of ideal class groups of imaginary quadratic number fields. Advances in Mathematics of Communications, 2010, 4 (2) : 141-154. doi: 10.3934/amc.2010.4.141 |
2019 Impact Factor: 1.366
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