Searching for d-MPs with fast enumeration

Abstract Network theories have been developed for decades. They are now widely applied to solve many real-life problems. An active research field is the reliability evaluation of multistate networks. The most popular methods for such evaluation often use minimal paths (MP) or minimal cuts (MC) of the network. In these approaches, three basic steps exist: (a) searching for all MPs/MCs; (b) searching for all d -MPs/ d -MCs from these MPs/MCs; (c) calculating union probability from these d -MPs/ d -MCs. When the network is live, there are several minimum path vectors with respect to system state for d , namely d -MP, can be found. Steps a and c have great advances recently. This paper focuses on the searching for d -MPs by given MPs in terms of fast enumeration (FE), which was a recent advance in the integer programming problems in the literature. This paper is a first attempt to apply FE to the reliability evaluation of multistate networks. This paper also makes comparison with the well known algorithm for benchmarking. More complicated examples are also examined for illustrative purposes.

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

[2]  Shin-Guang Chen,et al.  Optimal double-resource assignment for the robust design problem in multistate computer networks , 2014 .

[3]  Daoud Aït-Kadi,et al.  An Efficient Algorithm for Enumerating Minimal PathSets in Communication Networks , 2012, NDT.

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

[5]  Shin-Guang Chen.  Optimal network planning in robust two site's communication , 2010, 2010 International Symposium On Information Theory & Its Applications.

[6]  Wei-Chang Yeh.  A simple approach to search for all d-MCs of a limited-flow network , 2001, Reliab. Eng. Syst. Saf..

[7]  Shin-Guang Chen.  Reduced Recursive Sum of Disjoint Product in Network Reliability , 2014 .

[8]  Yen-Liang Chen,et al.  An algorithm for finding the k quickest paths in a network , 1993, Comput. Oper. Res..

[9]  Gen-Huey Chen,et al.  Algorithms for the constrained quickest path problem and the enumeration of quickest paths , 1994, Comput. Oper. Res..

[10]  Y. H. Chin,et al.  The quickest path problem , 1990, Comput. Oper. Res..

[11]  Yi-Kuei Lin,et al.  On a multicommodity stochastic-flow network with unreliable nodes subject to budget constraint , 2007, Eur. J. Oper. Res..

[12]  Wei-Chang Yeh.  A simple algorithm to search for all MCs in networks , 2006, Eur. J. Oper. Res..

[13]  D. T. Lee,et al.  The All-Pairs Quickest Path Problem , 1993, Inf. Process. Lett..

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

[15]  Shin-Guang Chen,et al.  Fuzzy-scorecard based logistics management in robust SCM , 2012, Comput. Ind. Eng..

[16]  Yi-Kuei Lin,et al.  ON RELIABILITY EVALUATION OF A STOCHASTIC-FLOW NETWORK IN TERMS OF MINIMAL CUTS , 2001 .

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

[18]  Jose Emmanuel Ramirez-Marquez,et al.  A Classification Tree Based Approach for the Development of Minimal Cut and Path Vectors of a Capacitated Network , 2007, IEEE Transactions on Reliability.

[19]  Yi-Kuei Lin.  STUDY ON LONGER AND SHORTER BOUNDARY DURATION VECTORS WITH ARBITRARY DURATION AND COST VALUES , 2007 .

[20]  J. Ben Rosen,et al.  Algorithms for the quickest path problem and the enumeration of quickest paths , 1991, Comput. Oper. Res..

[21]  Yi-Kuei Lin,et al.  Reliability Evaluation for an Information Network With Node Failure Under Cost Constraint , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[22]  T. C. Hu.  Multi-Commodity Network Flows , 1963 .

[23]  Yi-Kuei Lin,et al.  On performance evaluation of ERP systems with fuzzy mathematics , 2009, Expert Syst. Appl..

[24]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

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

[26]  Yi-Kuei Lin,et al.  Study on the multicommodity reliability of a capacitated-flow network☆ , 2001 .

[27]  Yi-Kuei Lin.  Reliability evaluation for a multi‐commodity flow model under budget constraint , 2002 .

[28]  Shin-Guang Chen,et al.  Optimal logistic planning in robust Supply Chain Management , 2010, The 40th International Conference on Computers & Indutrial Engineering.

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

[30]  U. Abel,et al.  Determination of All Minimal Cut-Sets between a Vertex Pair in an Undirected Graph , 1982, IEEE Transactions on Reliability.

[31]  Yi-Kuei Lin,et al.  AN EVALUATION METHOD FOR ENTERPRISE RESOURCE PLANNING SYSTEMS , 2008 .

[32]  Shin-Guang Chen.  Reduced Recursive Inclusion-exclusion Principle for the probability of union events , 2014, 2014 IEEE International Conference on Industrial Engineering and Engineering Management.

[33]  K.K. Aggarwal,et al.  Capacity Consideration in Reliability Analysis of Communication Systems , 1982, IEEE Transactions on Reliability.

[34]  Xue Janan,et al.  On Multistate System Analysis , 1985, IEEE Transactions on Reliability.

[35]  G. Jasmon,et al.  A Method for Evaluating All the Minimal Cuts of a Graph , 1987, IEEE Transactions on Reliability.

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

[37]  Arjang A. Assad,et al.  Multicommodity network flows - A survey , 1978, Networks.

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

[39]  Yi-Kuei Lin,et al.  System capacity for a two-commodity multistate flow network with unreliable nodes and capacity weight , 2007, Comput. Oper. Res..

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

[41]  S.H. Lee,et al.  Reliability Evaluation of a Flow Network , 1980, IEEE Transactions on Reliability.

[42]  Wei-Chang Yeh.  A simple algorithm to search for all d-MPs with unreliable nodes , 2001, Reliab. Eng. Syst. Saf..

[43]  W. J. Rueger.  Reliability Analysis of Networks with Capacity-Constraints and Failures at Branches & Nodes , 1986, IEEE Transactions on Reliability.

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

[45]  Y. L. Chen,et al.  Finding the k Quickset Simple Paths in a Network , 1994, Inf. Process. Lett..

[46]  Shin-Guang Chen.  Search for All MCs with Backtracking , 2013 .