Fast Algorithm for Searching $d$ -MPs for all Possible $d$

The evaluation of the reliability of a multistate flow network (MFN) is primarily based on the <inline-formula> <tex-math notation="LaTeX">$d$</tex-math></inline-formula> minimal path (MP), which is a special state vector formed by the addition of <italic>d</italic> MPs. The existing algorithm for searching <inline-formula> <tex-math notation="LaTeX">$d$</tex-math></inline-formula>-MPs for all possible <inline-formula> <tex-math notation="LaTeX">$d$</tex-math></inline-formula> is based on the addition of MPs and <inline-formula> <tex-math notation="LaTeX">$(d-1)$</tex-math></inline-formula>-MPs to generate <italic>d</italic>-MP combinations. This algorithm always requires extra time for detecting and removing the <inline-formula><tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-MP combinations with infeasible states, redundant states, and/or duplicates. A more efficient addition-based algorithm is proposed to overcome the obstacles of the existing algorithm. Experiment shows that the proposed new algorithm is up to 14 000 faster than the existing algorithm. The time complexity and demonstration of the proposed algorithm are analyzed and provided using examples.

[1]  Gregory Levitin,et al.  The Universal Generating Function in Reliability Analysis and Optimization , 2005 .

[2]  Tongdan Jin,et al.  Unbiased Variance Estimates for System Reliability Estimate Using Block Decompositions , 2008, IEEE Transactions on Reliability.

[3]  Charles J. Colbourn,et al.  The Combinatorics of Network Reliability , 1987 .

[4]  Gregory Levitin.  Multi-State Vector-k-Out-of-n Systems , 2013, IEEE Transactions on Reliability.

[5]  W.-C. Yeh.  A novel method for the network reliability in terms of capacitated-minimum-paths without knowing minimum-paths in advance , 2005, J. Oper. Res. Soc..

[6]  Wei-Chang Yeh,et al.  Economic-based resource allocation for reliable Grid-computing service based on Grid Bank , 2012, Future Gener. Comput. Syst..

[7]  Wei-Chang Yeh,et al.  A Squeezed Artificial Neural Network for the Symbolic Network Reliability Functions of Binary-State Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Terje Aven,et al.  Availability evaluation of oil/gas production and transportation systems , 1987 .

[9]  Hong-Zhong Huang,et al.  An efficient method for reliability evaluation of multistate networks given all minimal path vectors , 2007 .

[10]  B. Sanso,et al.  COMMUNICATION AND TRANSPORTATION NETWORKS RELIABILITY USING ROUTING MODELS. REVISED EDITION , 1987 .

[11]  Terje Aven,et al.  Some considerations on reliability theory and its applications , 1988 .

[12]  Wei-Chang Yen.  A Simple Heuristic Algorithm for Generating All Minimal Paths , 2007, IEEE Transactions on Reliability.

[13]  Wei-Chang Yeh.  A Simple Method to Verify All d-Minimal Path Candidates of a Limited-Flow Network and its Reliability , 2002 .

[14]  Chin-Chia Jane,et al.  A Practical Algorithm for Computing Multi-State Two-Terminal Reliability , 2008, IEEE Transactions on Reliability.

[15]  David W. Coit,et al.  A Monte-Carlo simulation approach for approximating multi-state two-terminal reliability , 2005, Reliab. Eng. Syst. Saf..

[16]  Yantao Song,et al.  Survey on Reliability of Power Electronic Systems , 2013, IEEE Transactions on Power Electronics.

[17]  Fang-Ming Shao,et al.  A practical bounding algorithm for computing two-terminal reliability based on decomposition technique , 2011, Comput. Math. Appl..

[18]  Ziyou Gao,et al.  An improved algorithm for solving all d-MPs in multi-state networks , 2017 .

[19]  Wei Jiang,et al.  Confidence bounds for the reliability of binary capacitated two-terminal networks , 2006, Reliab. Eng. Syst. Saf..

[20]  Chin-Chia Jane,et al.  On reliability evaluation of a capacitated-flow network in terms of minimal pathsets , 1995, Networks.

[21]  Yuanlong Shen,et al.  A new simple algorithm for enumerating all minimal paths and cuts of a graph , 1995 .

[22]  D. Shier.  Network Reliability and Algebraic Structures , 1991 .

[23]  Wei-Chang Yeh,et al.  New parallel swarm algorithm for smart sensor systems redundancy allocation problems in the Internet of Things , 2016, The Journal of Supercomputing.

[24]  Tao Zhang,et al.  Capacitated stochastic coloured Petri net-based approach for computing two-terminal reliability of multi-state network , 2012 .

[25]  Yi-Kuei Lin,et al.  A simple algorithm for reliability evaluation of a stochastic-flow network with node failure , 2001, Comput. Oper. Res..

[26]  Ming Jian Zuo,et al.  Search for all d-MPs for all d levels in multistate two-terminal networks , 2015, Reliab. Eng. Syst. Saf..