A novel multi-distribution multi-state flow network and its reliability optimization problem

Abstract The traditional multi-state flow network (MFN) reliability problem is a well-known NP-hard problem, and has been an active area of research for the past four decades. In the MFN reliability problem, the state distribution, i.e. the states and the occurrence probabilities of each arc, is known and fixed. However, the notations used in the MFN problems never considered the state distribution. In addition, each arc has only one state distribution, and this limits the application of the MFN. Thus, the notations relating to the state distribution are added or redefined in this study, and a novel budget-allocation multi-distribution MFN reliability problem is defined and proposed by considering networks with more than one state distribution under different budget allocations. Furthermore, a new algorithm is proposed to solve the proposed novel NP-Hard problem. The correctness and time complexity of the proposed algorithm are analyzed, and one benchmark example is given to demonstrate how to optimize the budget-allocation multi-distribution MFN reliability under different budget constraints.

[1]  Ming Jian Zuo,et al.  Reliability and Availability Analysis of a Repairable k-out-of-n: G System With R Repairmen Subject to Shut-Off Rules , 2011, IEEE Trans. Reliab..

[2]  Qiang Feng,et al.  Availability-based engineering resilience metric and its corresponding evaluation methodology , 2018, Reliab. Eng. Syst. Saf..

[3]  Alistair G. Sutcliffe,et al.  Automating Scenario Analysis of Human and System Reliability , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[4]  David W. Coit,et al.  Reliability optimization of series-parallel systems using a genetic algorithm , 1996, IEEE Trans. Reliab..

[5]  Yi-Kuei Lin,et al.  Performance evaluation for the logistics system in case that capacity weight varies from arcs and types of commodity , 2007 .

[6]  Junlin Xiong,et al.  A study of interval analysis for cold-standby system reliability optimization under parameter uncertainty , 2016, Comput. Ind. Eng..

[7]  Wei-Chang Yeh,et al.  A Greedy Branch-and-Bound Inclusion-Exclusion Algorithm for Calculating the Exact Multi-State Network Reliability , 2008, IEEE Transactions on Reliability.

[8]  Xiaolong Wang,et al.  A Heuristic Algorithm for Reliability Modeling and Analysis of Grid Systems , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[9]  E.N. Dialynas,et al.  Reliability and cost assessment of power transmission networks in the competitive electrical energy market , 2004, IEEE Transactions on Power Systems.

[10]  M. Zuo,et al.  Optimal Reliability Modeling: Principles and Applications , 2002 .

[11]  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.

[12]  Gregory Levitin,et al.  Reliability analysis of multi-trigger binary systems subject to competing failures , 2013, Reliab. Eng. Syst. Saf..

[13]  Edoardo Patelli,et al.  A hybrid load flow and event driven simulation approach to multi-state system reliability evaluation , 2016, Reliab. Eng. Syst. Saf..

[14]  Chia-Ling Huang.  A particle-based simplified swarm optimization algorithm for reliability redundancy allocation problems , 2015, Reliab. Eng. Syst. Saf..

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

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

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

[18]  Wei-Chang Yeh,et al.  A novel node-based sequential implicit enumeration method for finding all d-MPs in a multistate flow network , 2015, Inf. Sci..

[19]  Wei-Chang Yeh,et al.  A Novel Cut-Based Universal Generating Function Method , 2013, IEEE Transactions on Reliability.

[20]  Andreas Björklund,et al.  Set Partitioning via Inclusion-Exclusion , 2009, SIAM J. Comput..

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

[22]  Gregory Levitin,et al.  Optimal resource distribution between protection and redundancy considering the time and uncertainties of attacks , 2015, Eur. J. Oper. Res..

[23]  Wei-Chang Yeh,et al.  A novel boundary swarm optimization method for reliability redundancy allocation problems , 2018, Reliab. Eng. Syst. Saf..

[24]  Way Kuo,et al.  Recent Advances in Optimal Reliability Allocation , 2007, IEEE Trans. Syst. Man Cybern. Part A.

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

[26]  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..

[27]  Wei-Chang Yeh,et al.  Two-stage simplified swarm optimization for the redundancy allocation problem in a multi-state bridge system , 2016, Reliab. Eng. Syst. Saf..

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

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

[30]  Wei-Chang Yeh,et al.  A revised layered-network algorithm to search for all d-minpaths of a limited-flow acyclic network , 1998 .

[31]  Giovanni Sansavini,et al.  Performance-based maintenance of gas turbines for reliable control of degraded power systems , 2018 .

[32]  David W. Coit,et al.  Reliability Analysis for Multi-Component Systems Subject to Multiple Dependent Competing Failure Processes , 2014, IEEE Transactions on Reliability.

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