Optimization of Binary Decision Diagram using Genetic algorithm

Abstract

Fault tree analysis is a widely accepted technique to assess the probability and frequency of system failure in many industries.Traditionally statistical methods and boolean reductions is employed to analyze the fault tree. Even though the fault tree approach is commonly used for system reliability analysis, there are inherent limitations in terms of accuracy and computational efficiency. For the evaluation of minimal cut-set using fault tree method, it is required to solve large number of boolean expressions which increases number of computations. At the same time these computations are based on approximations which affect the accuracy of the results. The Binary Decision Diagram (BDD) is relatively new approach employed for fault tree analysis which has better computational efficiency. But the limitations of BDD lies in the optimal ordering of basic events, because such an ordering determines the final size of BDD which in turns determines the overall efficiency of this method. Hence the choice of heuristic is very crucial to get the maximum benefit from this method. Fordetermining the optimal ordering many heuristic has been developed, but not a single heuristic is able to give minimal BDD.Hence for the determining the optimal ordering a latest approach based on "Genetic algorithm (GA)" is presented in our project. In our project we have discussed the current heuristic approaches being used for BDD size optimization and highlighted its limitations. Then we have proposed a generalized method for the selection of optimal ordering of basic events using GA, which is not based on any heuristic previously given. Main key idea in the application of GA in BDD size optimization is to define population size and representation of ordered set of variable as chromosome. I. I NTRODUCTIONFault tree analysis is a widely accepted technique to assess the probability and frequency of system failure in many industries. Limitations of fault tree method for calculating minimal cut-sets can be overcome by Binary decision diagram method. The Binary decision diagram (BDD) is relatively new approach which is based on binary logic where there is no need to solve such boolean expressions for finding minimal cut-sets. The BDD method does not analyse the fault tree directly, but converts978-1-4244-8343-3/10/$26.00 ©2010 IEEE 168 the tree to a BDD, which represents the Boolean equation for the top event and hence has better computational efficiency. To overcome these problems various techniques have been employed to reduce the number of comparisons [1]. Some methods only produce the most important minimal cut sets. One of these techniques is referred to as culling, which means that cut sets of a certain order, say 4 and above, are ignored or deleted from the expression, Rasmuson and Marshall [2] employ this technique in their paper. The justification for doing this is that cutsets of a high order tend to have low probability of occurrence and therefore do not make a significant contribution to the top event probability. However the disadvant...

Variable Ordering in Binary Decision Diagram Using Spider Monkey Optimization for Node and Path Length Optimization

“…Combining branch and bound with ordered best search which leads to exact minimization is also proposed [16]. Genetic algorithm-based approaches have been proposed by many researchers [17]- [19]. A comparison of the genetic algorithm-based approach and branch and bound-based technique with other dynamic techniques such as scatter search is also proposed which concluded that the genetic algorithm-based approaches and branch and bound techniques are superior to other dynamic techniques [20].…”

BDD algorithms based on modularization for fault tree analysis

“…But FT model and BDD structure exponentially increase along with the number of variables, and the size of BDD structure is very sensitive to variable ordering as described by Vesely, 1970and Awinash et al, 2010(Vesely, 1970Kumar et al, Dec 2010). Therefore, when solving a large FT in BDD algorithm, the high memory consumption is a limitation.…”

Test problems and representations for graph evolution

“…Another application is the location of cutsets, minimal collections of links that if deleted will disconnect a graph. Work on this problem appears in [1], [23]. The problem of clustering a graph into sets of tightly coupled subgraphs or communities is the subject of [21], [25].…”