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On the convergence rate of the inexact Levenberg-Marquardt method
Reliability optimization of component assignment problem for a multistate network in terms of minimal cuts
1. | Department of Industrial Management, National Taiwan University of Science & Technology, Taipei 106, Taiwan, Taiwan |
References:
[1] |
T. Aven, Reliability evaluation of multistate systems with multistate components, IEEE Transactions on Reliability, 34 (1985), 473-479.
doi: 10.1109/TR.1985.5222235. |
[2] |
S. T. Cheng, Topological optimization of a reliable communication network, IEEE Transactions on Reliability, 47 (1998), 225-233.
doi: 10.1109/24.740489. |
[3] |
M. L. F. Cheong, R. Bhatnagar and S. C. Graves, Logistics network design with supplier consolidation hubs and multiple shipment options, Journal of Industrial and Management Optimization, 3 (2007), 51-69. |
[4] |
P. C. Chu and J. E. Beasley, A genetic algorithm for the generalized assignment problem, Computers and Operations Research, 24 (1997), 17-23.
doi: 10.1016/S0305-0548(96)00032-9. |
[5] |
D. Coit and A. Smith, Reliability optimization of series-parallel systems using genetic algorithm, IEEE Transactions on Reliability, 45 (1996), 254-266.
doi: 10.1109/24.510811. |
[6] |
D. W. Coit and A. Smith, Penalty guided genetic search for reliability design optimization, Computers and Industrial Engineering, 30 (1996), 895-904.
doi: 10.1016/0360-8352(96)00040-X. |
[7] |
C. J. Colbourn, "The Combinatorics of network Reliability," Oxford University, New York; 1987. |
[8] |
Z. Dzalilov, I. Ouveysi and A. Rubinov, An extended lifetime measure for telecommunication network, Journal of Industrial and Management Optimization, 4 (2008), 329-337. |
[9] |
M. L. Fisher, R. Jaikumar and L. Van Wassenhove, A multiplier adjustment method for the generalised assignment problem, Management Science, 32 (1986), 1095-1103.
doi: 10.1287/mnsc.32.9.1095. |
[10] |
L. R. Ford, and D. R. Fulkerson, "Flows in Networks," Princeton University, New Jersey, 1962. |
[11] |
D. Goldberg, "Genetic Algorithms in Search, Optimization and Machine Learning," Addison-Wesley Press, Massachusetts, 1989. |
[12] |
P. R. Harper, V. De Senna, I. T. Vieira and A. K. Shahani, A genetic algorithm for the project assignment problem, Computers and Operations Research, 32 (2005), 1255-1265. |
[13] |
C. C. Hsieh and Y. T. Chen, Reliable and economic resource allocation in an unreliable flow network, Computer and Operations Research, 32 (2005), 613-628.
doi: 10.1016/j.cor.2003.08.008. |
[14] |
C. C. Hsieh and Y. T. Chen, Resource allocation decisions under various demands and cost requirements in an unreliable flow network, Computer and Operations Research, 32 (2005), 2771-2784.
doi: 10.1016/j.cor.2004.04.003. |
[15] |
C. C. Hsieh and M. H. Lin, Reliability-oriented multi-resource allocation in a stochastic-flow network, Reliability Engineering and System Safety, 81 (2003), 155-161.
doi: 10.1016/S0951-8320(03)00082-6. |
[16] |
C. C. Jane and Y. W. Laih, A practical algorithm for computing multi-state two-terminal reliability, IEEE Transactions on Reliability, 57 (2008), 295-302.
doi: 10.1109/TR.2008.920792. |
[17] |
C. C. Jane, J. S. Lin and J. Yuan, On reliability evaluation of a limited-flow network in terms of minimal cutsets, IEEE Transactions on Reliability, 42 (1993), 354-361.
doi: 10.1109/24.257817. |
[18] |
G. Levitin and A. Lisnianski, A new approach to solving problems of multi-state system reliability optimization, Quality Reliability Engineering International, 17 (2001), 93-104.
doi: 10.1002/qre.388. |
[19] |
Y. K. Lin, A simple algorithm for reliability evaluation of a stochastic-flow network with node failure, Computer and Operations Research, 28 (2001), 1277-1285.
doi: 10.1016/S0305-0548(00)00039-3. |
[20] |
Y. K. Lin, Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs, Reliability Engineering and System Safety, 75 (2002), 41-46.
doi: 10.1016/S0951-8320(01)00110-7. |
[21] |
Y. K. Lin, A stochastic model to study the system capacity for supply chains in terms of minimal cuts, International Journal of Production Economics, 124 (2010), 181-187.
doi: 10.1016/j.ijpe.2009.10.022. |
[22] |
J. S. Lin, C. C. Jane and J. Yuan, On reliability evaluation of a capacitated-flow network in terms of minimal pathsets, Network, 25 (1995), 131-138.
doi: 10.1002/net.3230250306. |
[23] |
A. Lisnianski and G. Levitin, "Multi-state System Reliability: Assessment, Optimization and Application," 6th edition, World Scientific, Singapore, 2003. |
[24] |
Q. Liu, H. Zhang, X. Ma and Q. Zhao, Genetic algorithm-based study on flow allocation in a multicommodity stochastic-flow network with unreliable nodes, in "The Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing," (2007), 576-581.
doi: 10.1109/SNPD.2007.261. |
[25] |
J. Majumdar and A. K. Bhunia, Elitist genetic algorithm for assignment problem with imprecise goal, European Journal of Operational Research, 177 (2007), 684-692.
doi: 10.1016/j.ejor.2005.11.034. |
[26] |
R. Mookherjee, B. F. Hobbs, T. L. Friesz and M. A. Rigdon, Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints, Journal of Industrial and Management Optimization, 4 (2008) 425-452. |
[27] |
L. Painton and J. Campbell, Genetic algorithms in optimization of system reliability, IEEE Transactions on Reliability, 44 (1995), 172-178.
doi: 10.1109/24.387368. |
[28] |
J. E. Ramirez-Marquez and C. M. Rocco, Stochastic network interdiction optimization via capacitated network reliability modeling and probabilistic solution discovery, Reliability Engineering and System Safety, 94 (2009), 913-921.
doi: 10.1016/j.ress.2008.10.006. |
[29] |
M. Srinivas and M. P. Lalit, Genetic algorithm: a survey, IEEE Computer, 27 (1994), 18-20. |
[30] |
Y. Z. Wang, An application of genetic algorithm methods for teacher assignment problems, Expert Systems with Applications, 22 (2002), 295-302.
doi: 10.1016/S0957-4174(02)00017-9. |
[31] |
J. M. Wilson, A genetic algorithm for the generalized assignment problem, Journal of the Operational Research Society, 48 (1997), 804-809. |
[32] |
W. Xu, S. He, R. Song and J. Li, Reliability based assignment in stochastic-flow freight network, Applied Mathematics and Computation, 211 (2009), 85-94.
doi: 10.1016/j.amc.2009.01.024. |
[33] |
J. Xue, On multistate system analysis, IEEE Transactions on Reliability, 34 (1985), 329-337.
doi: 10.1109/TR.1985.5222178. |
[34] |
M. J. Yao and W. M. Chu, A genetic algorithm for determining optimal replenishment cycles to minimize maximum warehouse space requirements, Omega, 36 (2008), 619-631.
doi: 10.1016/j.omega.2007.01.007. |
[35] |
P. Zacharia, A. Menti and Th. Zacharias, Genetic algorithm-based optimal design of shunt compensators in the presence of harmonics, Electric Power Systems Research, 78 (2008), 728-735.
doi: 10.1016/j.epsr.2007.05.016. |
[36] |
A. Zeblah, Y. Massim, S. Hadjeri,A. Benaissa and H. Hamdaoui, Optimization for series-parallel continuous power systems with buffers under reliability constraints using ant colony, Journal of Industrial and Management Optimization, 2 (2006), 467-479. |
[37] |
M. J. Zuo, Z. Tian and H. Z. Huang, An efficient method for reliability evaluation of multistate networks given all minimal path vectors, IIE Transactions, 39 (2007), 811-817.
doi: 10.1080/07408170601013653. |
show all references
References:
[1] |
T. Aven, Reliability evaluation of multistate systems with multistate components, IEEE Transactions on Reliability, 34 (1985), 473-479.
doi: 10.1109/TR.1985.5222235. |
[2] |
S. T. Cheng, Topological optimization of a reliable communication network, IEEE Transactions on Reliability, 47 (1998), 225-233.
doi: 10.1109/24.740489. |
[3] |
M. L. F. Cheong, R. Bhatnagar and S. C. Graves, Logistics network design with supplier consolidation hubs and multiple shipment options, Journal of Industrial and Management Optimization, 3 (2007), 51-69. |
[4] |
P. C. Chu and J. E. Beasley, A genetic algorithm for the generalized assignment problem, Computers and Operations Research, 24 (1997), 17-23.
doi: 10.1016/S0305-0548(96)00032-9. |
[5] |
D. Coit and A. Smith, Reliability optimization of series-parallel systems using genetic algorithm, IEEE Transactions on Reliability, 45 (1996), 254-266.
doi: 10.1109/24.510811. |
[6] |
D. W. Coit and A. Smith, Penalty guided genetic search for reliability design optimization, Computers and Industrial Engineering, 30 (1996), 895-904.
doi: 10.1016/0360-8352(96)00040-X. |
[7] |
C. J. Colbourn, "The Combinatorics of network Reliability," Oxford University, New York; 1987. |
[8] |
Z. Dzalilov, I. Ouveysi and A. Rubinov, An extended lifetime measure for telecommunication network, Journal of Industrial and Management Optimization, 4 (2008), 329-337. |
[9] |
M. L. Fisher, R. Jaikumar and L. Van Wassenhove, A multiplier adjustment method for the generalised assignment problem, Management Science, 32 (1986), 1095-1103.
doi: 10.1287/mnsc.32.9.1095. |
[10] |
L. R. Ford, and D. R. Fulkerson, "Flows in Networks," Princeton University, New Jersey, 1962. |
[11] |
D. Goldberg, "Genetic Algorithms in Search, Optimization and Machine Learning," Addison-Wesley Press, Massachusetts, 1989. |
[12] |
P. R. Harper, V. De Senna, I. T. Vieira and A. K. Shahani, A genetic algorithm for the project assignment problem, Computers and Operations Research, 32 (2005), 1255-1265. |
[13] |
C. C. Hsieh and Y. T. Chen, Reliable and economic resource allocation in an unreliable flow network, Computer and Operations Research, 32 (2005), 613-628.
doi: 10.1016/j.cor.2003.08.008. |
[14] |
C. C. Hsieh and Y. T. Chen, Resource allocation decisions under various demands and cost requirements in an unreliable flow network, Computer and Operations Research, 32 (2005), 2771-2784.
doi: 10.1016/j.cor.2004.04.003. |
[15] |
C. C. Hsieh and M. H. Lin, Reliability-oriented multi-resource allocation in a stochastic-flow network, Reliability Engineering and System Safety, 81 (2003), 155-161.
doi: 10.1016/S0951-8320(03)00082-6. |
[16] |
C. C. Jane and Y. W. Laih, A practical algorithm for computing multi-state two-terminal reliability, IEEE Transactions on Reliability, 57 (2008), 295-302.
doi: 10.1109/TR.2008.920792. |
[17] |
C. C. Jane, J. S. Lin and J. Yuan, On reliability evaluation of a limited-flow network in terms of minimal cutsets, IEEE Transactions on Reliability, 42 (1993), 354-361.
doi: 10.1109/24.257817. |
[18] |
G. Levitin and A. Lisnianski, A new approach to solving problems of multi-state system reliability optimization, Quality Reliability Engineering International, 17 (2001), 93-104.
doi: 10.1002/qre.388. |
[19] |
Y. K. Lin, A simple algorithm for reliability evaluation of a stochastic-flow network with node failure, Computer and Operations Research, 28 (2001), 1277-1285.
doi: 10.1016/S0305-0548(00)00039-3. |
[20] |
Y. K. Lin, Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs, Reliability Engineering and System Safety, 75 (2002), 41-46.
doi: 10.1016/S0951-8320(01)00110-7. |
[21] |
Y. K. Lin, A stochastic model to study the system capacity for supply chains in terms of minimal cuts, International Journal of Production Economics, 124 (2010), 181-187.
doi: 10.1016/j.ijpe.2009.10.022. |
[22] |
J. S. Lin, C. C. Jane and J. Yuan, On reliability evaluation of a capacitated-flow network in terms of minimal pathsets, Network, 25 (1995), 131-138.
doi: 10.1002/net.3230250306. |
[23] |
A. Lisnianski and G. Levitin, "Multi-state System Reliability: Assessment, Optimization and Application," 6th edition, World Scientific, Singapore, 2003. |
[24] |
Q. Liu, H. Zhang, X. Ma and Q. Zhao, Genetic algorithm-based study on flow allocation in a multicommodity stochastic-flow network with unreliable nodes, in "The Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing," (2007), 576-581.
doi: 10.1109/SNPD.2007.261. |
[25] |
J. Majumdar and A. K. Bhunia, Elitist genetic algorithm for assignment problem with imprecise goal, European Journal of Operational Research, 177 (2007), 684-692.
doi: 10.1016/j.ejor.2005.11.034. |
[26] |
R. Mookherjee, B. F. Hobbs, T. L. Friesz and M. A. Rigdon, Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints, Journal of Industrial and Management Optimization, 4 (2008) 425-452. |
[27] |
L. Painton and J. Campbell, Genetic algorithms in optimization of system reliability, IEEE Transactions on Reliability, 44 (1995), 172-178.
doi: 10.1109/24.387368. |
[28] |
J. E. Ramirez-Marquez and C. M. Rocco, Stochastic network interdiction optimization via capacitated network reliability modeling and probabilistic solution discovery, Reliability Engineering and System Safety, 94 (2009), 913-921.
doi: 10.1016/j.ress.2008.10.006. |
[29] |
M. Srinivas and M. P. Lalit, Genetic algorithm: a survey, IEEE Computer, 27 (1994), 18-20. |
[30] |
Y. Z. Wang, An application of genetic algorithm methods for teacher assignment problems, Expert Systems with Applications, 22 (2002), 295-302.
doi: 10.1016/S0957-4174(02)00017-9. |
[31] |
J. M. Wilson, A genetic algorithm for the generalized assignment problem, Journal of the Operational Research Society, 48 (1997), 804-809. |
[32] |
W. Xu, S. He, R. Song and J. Li, Reliability based assignment in stochastic-flow freight network, Applied Mathematics and Computation, 211 (2009), 85-94.
doi: 10.1016/j.amc.2009.01.024. |
[33] |
J. Xue, On multistate system analysis, IEEE Transactions on Reliability, 34 (1985), 329-337.
doi: 10.1109/TR.1985.5222178. |
[34] |
M. J. Yao and W. M. Chu, A genetic algorithm for determining optimal replenishment cycles to minimize maximum warehouse space requirements, Omega, 36 (2008), 619-631.
doi: 10.1016/j.omega.2007.01.007. |
[35] |
P. Zacharia, A. Menti and Th. Zacharias, Genetic algorithm-based optimal design of shunt compensators in the presence of harmonics, Electric Power Systems Research, 78 (2008), 728-735.
doi: 10.1016/j.epsr.2007.05.016. |
[36] |
A. Zeblah, Y. Massim, S. Hadjeri,A. Benaissa and H. Hamdaoui, Optimization for series-parallel continuous power systems with buffers under reliability constraints using ant colony, Journal of Industrial and Management Optimization, 2 (2006), 467-479. |
[37] |
M. J. Zuo, Z. Tian and H. Z. Huang, An efficient method for reliability evaluation of multistate networks given all minimal path vectors, IIE Transactions, 39 (2007), 811-817.
doi: 10.1080/07408170601013653. |
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