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. For determining 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.