Multistate components assignment problem with optimal network reliability subject to assignment budget

Abstract The typical assignment problem for finding the optimal assignment of a set of components to a set of locations in a system has been widely studied in practical applications. However, this problem mainly focuses on maximizing the total profit or minimizing the total cost without considering component’s failure. In practice, each component should be multistate due to failure, partially failure, or maintenance. That is, each component has several capacities with a probability distribution and may fail. When a set of multistate components is assigned to a system, the system can be treated as a stochastic-flow network. The network reliability is the probability that d units of homogenous commodity can be transmitted through the network successfully. The multistate components assignment problem to maximize the network reliability is never discussed. Therefore, this paper focuses on solving this problem under an assignment budget constraint, in which each component has an assignment cost. The network reliability under a components assignment can be evaluated in terms of minimal paths and state-space decomposition. Subsequently an optimization method based on genetic algorithm is proposed. The experimental results show that the proposed algorithm can be executed in a reasonable time.

[1]  Yi-Ting Chen,et al.  Resource allocation decisions under various demands and cost requirements in an unreliable flow network , 2005, Comput. Oper. Res..

[2]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[3]  Asoke Kumar Bhunia,et al.  Elitist genetic algorithm for assignment problem with imprecise goal , 2007, Eur. J. Oper. Res..

[4]  Terje Aven,et al.  Reliability Evaluation of Multistate Systems with Multistate Components , 1985, IEEE Transactions on Reliability.

[5]  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..

[6]  D. E. Goldberg,et al.  Optimization and Machine Learning , 2022 .

[7]  David W. Pentico,et al.  Assignment problems: A golden anniversary survey , 2007, Eur. J. Oper. Res..

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

[9]  Hailin Zhang,et al.  Genetic Algorithm-based Study on Flow Allocation in a Multicommodity Stochastic-flow Network with Unreliable Nodes , 2007 .

[10]  Kailash C. Kapur,et al.  Reliability Bounds for Multistate Systems with Multistate Components , 1985, Oper. Res..

[11]  Gregory Levitin,et al.  A new approach to solving problems of multi‐state system reliability optimization , 2001 .

[12]  Chung-Chi Hsieh,et al.  Reliability-oriented multi-resource allocation in a stochastic-flow network , 2003, Reliab. Eng. Syst. Saf..

[13]  Laura Painton,et al.  Genetic algorithms in optimization of system reliability. , 1995 .

[14]  Wei-Chang Yeh.  Multistate network reliability evaluation under the maintenance cost constraint , 2004 .

[15]  Yen-Zen Wang.  An application of genetic algorithm methods for teacher assignment problems , 2002, Expert Syst. Appl..

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

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

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

[19]  Sam Kwong,et al.  Genetic algorithms: concepts and applications [in engineering design] , 1996, IEEE Trans. Ind. Electron..

[20]  John E. Beasley,et al.  A genetic algorithm for the generalised assignment problem , 1997, Comput. Oper. Res..

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

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

[23]  Sheng-Tzong Cheng.  Topological optimization of a reliable communication network , 1998 .

[24]  Paul R. Harper,et al.  A genetic algorithm for the project assignment problem , 2005, Comput. Oper. Res..

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

[27]  Lalit M. Patnaik,et al.  Genetic algorithms: a survey , 1994, Computer.

[28]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[29]  Yi-Kuei Lin,et al.  Reliability of a stochastic-flow network with unreliable branches & nodes, under budget constraints , 2004, IEEE Trans. Reliab..

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

[31]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[32]  Sam Kwong,et al.  Genetic algorithms: concepts and applications [in engineering design] , 1996, IEEE Trans. Ind. Electron..

[33]  Arie E. Kaufman.  Guest Editor's Introduction: Visualization , 1994 .

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

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

[36]  Yi-Ting Chen,et al.  Reliable and economic resource allocation in an unreliable flow network , 2005, Comput. Oper. Res..

[37]  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.

[38]  Wei-Chang Yeh.  A new approach to evaluate reliability of multistate networks under the cost constraint , 2005 .

[39]  John M. Wilson,et al.  A genetic algorithm for the generalised assignment problem , 1997 .