An improved algorithm for solving all d-MPs in multi-state networks

Reliability is a desirable performance indicator of many real-world systems to measure the quality level. One general method for evaluating multi-state reliability is using d-minimal paths (d-MPs). However, being an NP-hard problem, searching for all d-MPs is a rather challenging task. This paper proposes an improved algorithm to solve the d-MP problem. To reduce the search space of d-MPs, a concept of lower capacity bound is introduced into the d-MP problem, and an effective technique is developed to find lower capacity bounds. Meanwhile, the fast enumeration method which is a recent improvement to the traditional enumeration method is employed to solve d-MPs. In addition, by introducing the operation of transforming undirected edges into directed edges, the proposed algorithm is applicable to solving both directed networks and undirected networks. Through numerical experiments, it is found that the proposed algorithm holds a distinct advantage over the existing methods in solving all d-MPs.

[1]  Yi-Kuei Lin,et al.  Search for All Minimal Paths in a General Large Flow Network , 2012, IEEE Transactions on Reliability.

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

[3]  Wei-Chang Yeh.  Evaluation of the one-to-all-target-subsets reliability of a novel deterioration-effect acyclic multi-state information network , 2017, Reliab. Eng. Syst. Saf..

[4]  Michael O. Ball,et al.  Computational Complexity of Network Reliability Analysis: An Overview , 1986, IEEE Transactions on Reliability.

[5]  Wei-Chang Yeh,et al.  A Simple Universal Generating Function Method to Search for All Minimal Paths in Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[6]  Yi-Kuei Lin,et al.  Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs , 2002, Reliab. Eng. Syst. Saf..

[7]  Yi-Kuei Lin,et al.  Estimated and exact system reliabilities of a maintainable computer network , 2011 .

[8]  Nezam Mahdavi-Amiri,et al.  A New Efficient Approach to Search for All Multi-State Minimal Cuts , 2014, IEEE Transactions on Reliability.

[9]  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..

[10]  Tao Jiang,et al.  Parameter inference for non-repairable multi-state system reliability models by multi-level observation sequences , 2017, Reliab. Eng. Syst. Saf..

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

[12]  Meng Qian,et al.  Improving efficiency of solving d-MC problem in stochastic-flow network , 2007, Reliab. Eng. Syst. Saf..

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

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

[15]  Ravindra K. Ahuja,et al.  Computational investigations of maximum flow algorithms , 1997 .

[16]  Wei-wei Wu,et al.  Evaluation of the reliability of transport networks based on the stochastic flow of moving objects , 2008, Reliab. Eng. Syst. Saf..

[17]  Xiu-Zhen Xu,et al.  Reliability evaluation of multi-state systems under cost consideration , 2012 .

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

[19]  Ming Jian Zuo,et al.  An improved algorithm for finding all minimal paths in a network , 2016, Reliab. Eng. Syst. Saf..

[20]  Lirong Cui,et al.  MDD-based performability analysis of multi-state linear consecutive-k-out-of-n: F systems , 2017, Reliab. Eng. Syst. Saf..

[21]  Yi-Kuei Lin,et al.  System reliability of assured accuracy rate for multi-state computer networks from service level agreements viewpoint , 2014 .

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

[23]  Gregory Levitin,et al.  Importance and sensitivity analysis of multi-state systems using the universal generating function method , 1999 .

[24]  S. G. Chen.  Efficiency improvement in explicit enumeration for integer programming problems , 2013, 2013 IEEE International Conference on Industrial Engineering and Engineering Management.

[25]  Wei-Chang Yeh.  New Method in Searching for All Minimal Paths for the Directed Acyclic Network Reliability Problem , 2016, IEEE Transactions on Reliability.

[26]  Jane Nichols Hagstrom.  Note on independence of arcs in antiparallel for network flow problems , 1984, Networks.

[27]  Yi-Kuei Lin,et al.  Searching for d-MPs with fast enumeration , 2016, J. Comput. Sci..

[28]  David W. Coit,et al.  A generalized multistate-based path vector approach to multistate two-terminal reliability , 2006 .

[29]  Jose Emmanuel Ramirez-Marquez,et al.  Element substitution algorithm for general two-terminal network reliability analyses , 2007 .

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

[31]  C. Alexopoulos.  A note on state-space decomposition methods for analyzing stochastic flow networks , 1995 .

[32]  Jose Emmanuel Ramirez-Marquez,et al.  Two-terminal reliability analyses for a mobile ad hoc wireless network , 2007, Reliab. Eng. Syst. Saf..

[33]  F. Robert.  Algorithmes tronques de découpe linéaire , 1972 .

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

[35]  Wei-Chang Yeh.  An Improved Sum-of-Disjoint-Products Technique for Symbolic Multi-State Flow Network Reliability , 2015, IEEE Transactions on Reliability.

[36]  Borut Mavko,et al.  Application of the fault tree analysis for assessment of power system reliability , 2009, Reliab. Eng. Syst. Saf..

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

[38]  Xiaojun Zhou,et al.  Reliability-centered predictive maintenance scheduling for a continuously monitored system subject to degradation , 2007, Reliab. Eng. Syst. Saf..

[39]  Chin-Chia Jane,et al.  Computing Multi-State Two-Terminal Reliability Through Critical Arc States That Interrupt Demand , 2010, IEEE Transactions on Reliability.

[40]  Rajesh Mishra,et al.  Enumeration of Minimal Cutsets for Directed Networks with Comparative Reliability Study for Paths or Cuts , 2016, Qual. Reliab. Eng. Int..

[41]  E. Jamoulle,et al.  Transportation networks with random arc capacities , 1972 .

[42]  Yi-Kuei Lin,et al.  Predecessor-set technique for reliability evaluation of a stochastic manufacturing system , 2015 .

[43]  S. Satitsatian,et al.  An algorithm for lower reliability bounds of multistate two-terminal networks , 2006, IEEE Transactions on Reliability.

[44]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[45]  Wei-Chang Yeh.  A Fast Algorithm for Searching All Multi-State Minimal Cuts , 2008, IEEE Transactions on Reliability.

[46]  Ming Jian Zuo,et al.  Ordering Heuristics for Reliability Evaluation of Multistate Networks , 2015, IEEE Transactions on Reliability.

[47]  John Yuan,et al.  Reliability evaluation of a limited-flow network in terms of minimal cutsets , 1993 .

[48]  Gregory Levitin,et al.  Multi-State System Reliability - Assessment, Optimization and Applications , 2003, Series on Quality, Reliability and Engineering Statistics.

[49]  Wei-Chang Yeh,et al.  A new cut-based algorithm for the multi-state flow network reliability problem , 2015, Reliab. Eng. Syst. Saf..

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

[51]  K. K. Aggarwal,et al.  A Simple Method for Reliability Evaluation of a Communication System , 1975, IEEE Trans. Commun..

[52]  Gregory Levitin,et al.  A universal generating function approach for the analysis of multi-state systems with dependent elements , 2004, Reliab. Eng. Syst. Saf..