A MCS Based Neural Network Approach to Extract Network Approximate Reliability Function
Simulations have been applied extensively to solve complex problems in real-world. They provide reference results and support the decision candidates in quantitative attributes. This paper combines ANN with Monte Carlo Simulation (MCS) to provide a refere
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Abstract. Simulations have been applied extensively to solve complex problems in real-world. They provide reference results and support the decision candidates in quantitative attributes. This paper combines ANN with Monte Carlo Simulation (MCS) to provide a reference model of predicting reliability of a network. It suggests reduced BBD design to select the input training data and opens the black box of neural networks through constructing the limited space reliability function from ANN parameters. Besides, this paper applies a practical problem that considers both cost and reliability to evaluate the performance of the ANN based reliability function. Keywords: Reliability, Cost, Simulation, Artificial Neural Network.
1 Introduction Reliability optimization has been a popular area of research and received significant attention during the past four decades [1-11] due to reliability’s critical importance in various kinds of systems. To obtain the network reliability of a complex system analytically is a NP-hard problem [2]. Several authors [12-15] have adopted MCS to measuring the reliability for conveniences and accuracies. Yeh [15] combined statistical and simulation techniques to provide a good estimate to the reliability function in the complex network and consider the cost effect to minimize the total cost. After all, MCS is used to provide an estimator for response under specific parameter settings of a complex system. The ANN approach can be regarded as a statistical method. The feature hid within the designed experiment can be learned by ANN based on the cumulative historical data[16].This paper open the black box of neural networks through taking the network structure and weights as the limited space reliability function of complex system networks. The purposed approach can evaluate network reliability precisely using applicable amount of data. In this paper we also compare different input data selection methods and show their consequences. J.-W. Park, T.-G. Kim, and Y.-B. Kim (Eds.): AsiaSim 2007, CCIS 5, pp. 287–297, 2007. © Springer-Verlag Berlin Heidelberg 2007
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W.-C. Yeh, C.-H. Lin, and Y.-C. Lin
2 Notation, Nomenclature, and Assumptions Notation G(V, E, C)
: a network with the node set V={1,2,…,n}, the arc set E, the node cost function C, and nodes 1 and n denote the source node and sink node, respectively. ri, r : the reliability of node i and the reliability vector r=(r , r ,…, r ), 1 2 n respectively. P(•),E[•],Var[•] : the probability, expected value and variance of •, respectively. p, c : the number of nodes in the shortest path and min-cut between nodes 1 and n of G(V, E, C), respectively. N, M : the number of replications and the number of simulation runs in each replication of the proposed MCS. C(ri), C(r) : the cost of the node I under ri and of G(V, E, C) under r, respectively. c c : the lower-bounds of the reliability vector and the total reliability, r,R respectively. m A R(r),R (r),R (r) : the exact reliability function, the estimator of R(r) obtained from MCS and ANN, respectivel
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