Network Reliability Optimization via the Cross-Entropy Method

Consider a network of unreliable links, each of which comes with a certain price, and reliability. Given a fixed budget, which links should be purchased in order to maximize the system's reliability? We introduce a new approach, based on the cross-entropy method, which can deal effectively with the constraints, and noise introduced when estimating the reliabilities via simulation, in this difficult combinatorial optimization problem. Numerical results demonstrate the effectiveness of the proposed technique

[1]  Dirk Reichelt,et al.  Designing Reliable Communication Networks with a Genetic Algorithm Using a Repair Heuristic , 2004, EvoCOP.

[2]  Héctor Cancela,et al.  Simulated annealing for communication network :reliability improvement , 1995 .

[3]  T. Elperin,et al.  An Evolution Model for Monte Carlo Estimation of Equilibrium Network Renewal Parameters , 1992 .

[4]  E. Henley,et al.  State-Transition Monte Carlo for Evaluating Large, Repairable Systems , 1980, IEEE Transactions on Reliability.

[5]  R. Rubinstein The Cross-Entropy Method for Combinatorial and Continuous Optimization , 1999 .

[6]  Tov Elperin,et al.  Estimation of network reliability using graph evolution models , 1991 .

[7]  Miro Kraetzl,et al.  THE TREE CUT AND MERGE ALGORITHM FOR ESTIMATION OF NETWORK RELIABILITY , 2003 .

[8]  K. I. M. McKinnon,et al.  An Exact Solution Method for Reliability Optimization in Complex Systems , 2005, Ann. Oper. Res..

[9]  Kin-Ping Hui Monte Carlo Network Reliability Ranking Estimation , 2007, IEEE Transactions on Reliability.

[10]  I. Gertsbakh,et al.  Statistical Reliability Theory , 1988 .

[11]  Kathryn Dowsland,et al.  Combinatorial Optimisation , 2002 .

[12]  Dirk P. Kroese,et al.  Convergence properties of the cross-entropy method for discrete optimization , 2007, Oper. Res. Lett..

[13]  E. Henley,et al.  Dagger-Sampling Monte Carlo For System Unavailability Evaluation , 1980, IEEE Transactions on Reliability.

[14]  Ruey-Shun Chen,et al.  A Genetic Algorithm for K-node Set Reliability Optimization with Capacity Constraint of a Distributed System , 2001 .

[15]  Alice E. Smith,et al.  Estimating all-terminal network reliability using a neural network , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[16]  M. Lomonosov On Monte Carlo Estimates in Network Reliability , 1994, Probability in the Engineering and Informational Sciences.

[17]  Marshall W. Bern,et al.  The Steiner Problem with Edge Lengths 1 and 2 , 1989, Inf. Process. Lett..

[18]  Shie Mannor,et al.  A Tutorial on the Cross-Entropy Method , 2005, Ann. Oper. Res..

[19]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[20]  Dirk P. Kroese,et al.  The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning , 2004 .

[21]  Lih-Yuan Deng,et al.  The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning , 2006, Technometrics.

[22]  R. Rubinstein Combinatorial Optimization, Cross-Entropy, Ants and Rare Events , 2001 .

[23]  John N. Tsitsiklis,et al.  An Analysis of Stochastic Shortest Path Problems , 1991, Math. Oper. Res..

[24]  J. Scott Provan,et al.  The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected , 1983, SIAM J. Comput..

[25]  Gary Chartrand,et al.  Applied and algorithmic graph theory , 1992 .

[26]  Way Kuo,et al.  An annotated overview of system-reliability optimization , 2000, IEEE Trans. Reliab..

[27]  George S. Fishman A Monte Carlo Sampling Plan for Estimating Network Reliability , 1986, Oper. Res..

[28]  L. Margolin,et al.  On the Convergence of the Cross-Entropy Method , 2005, Ann. Oper. Res..

[29]  Wei-Chang Yeh,et al.  A New Monte Carlo Method for the Network Reliability , 2002 .

[30]  Dirk P. Kroese,et al.  Network reliability estimation using the tree cut and merge algorithm with importance sampling , 2003, Fourth International Workshop on Design of Reliable Communication Networks, 2003. (DRCN 2003). Proceedings..

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

[32]  Miro Kraetzl,et al.  The Cross-Entropy Method for Network Reliability Estimation , 2005, Ann. Oper. Res..

[33]  Charles J. Colbourn,et al.  Evaluating performability: Most probable states and bounds , 1993, Telecommun. Syst..

[34]  Dirk P. Kroese,et al.  Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment , 2005, Ann. Oper. Res..

[35]  Tito Homem-de-Mello,et al.  Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method , 2005, Ann. Oper. Res..

[36]  Alice E. Smith,et al.  Local search genetic algorithm for optimal design of reliable networks , 1997, IEEE Trans. Evol. Comput..

[37]  Reuven Y. Rubinstein,et al.  Optimization of computer simulation models with rare events , 1997 .