Genetic Algorithms for the Variable Ordering Problem of Binary Decision Diagrams

2005 ◽  
pp. 1-20 ◽  
Author(s):  
Wolfgang Lenders ◽  
Christel Baier
Keyword(s):  
Genetic Algorithms ◽  
Binary Decision Diagrams ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Variable Ordering

A Variable Ordering Heuristic Based on Zero-Suppressed Binary Decision Diagrams

2010 ◽  
Author(s):  
Ya-zhou Li ◽  
Jin Wang ◽  
Li-qin Hu ◽  
Yi-can Wu
Keyword(s):  
Nuclear Power ◽  
Safety Assessment ◽  
Large Scale ◽  
Binary Decision Diagrams ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Minimal Cut Sets ◽  
Variable Ordering ◽  
Safety And Reliability ◽  
Event Trees

Two approaches have been proposed to solve the large-scale fault trees or event trees for Probabilistic Safety Assessment in a nuclear power plant. The first one consists in MCS/ZBDD, which uses ZBDDs (Zero-suppressed Binary Decision Diagrams) to implement classical MCS (Minimal Cut Sets) algorithm. The second consists in designing heuristics and strategies to reduce the complexity of the BDDs (Binary Decision Diagrams) construction. This paper was motivated to combine the MCS/ZBDD and designing heuristics for ZBDDs together. A heuristic, which took the failure rate of basic event into account and utilized that truncation could be implemented on ZBDDs during the calculating process, was proposed. This heuristic accelerated the analysis progress by bringing forward the truncation and reducing the complexity of the intermediate ZBDDs. RiskA, a Zero-suppressed Binary Decision Diagram package extended to safety and reliability analysis, has adopted this heuristic. RiskA’s truncation strategies, which had some relations with the ordering scheme, were also introduced. The correctness and efficiency of this new heuristic were verified by some practical models’ analyses.

scholarly journals Genetic algorithm for binary and functional decision diagrams optimization

2018 ◽  
Vol 31 (2) ◽  
pp. 169-187
Author(s):  
Stojkovic Suzana ◽  
Velickovic Darko ◽  
Moraga Claudio
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Data Structure ◽  
Optimization Problems ◽  
Binary Decision Diagrams ◽  
Size Optimization ◽  
Decision Diagrams ◽  
Crossover Operator ◽  
Binary Decision ◽  
Discrete Functions

Decision diagrams (DD) are a widely used data structure for discrete functions representation. The major problem in DD-based applications is the DD size minimization (reduction of the number of nodes), because their size is dependent on the variables order. Genetic algorithms are often used in different optimization problems including the DD size optimization. In this paper, we apply the genetic algorithm to minimize the size of both Binary Decision Diagrams (BDDs) and Functional Decision Diagrams (FDDs). In both cases, in the proposed algorithm, a Bottom-Up Partially Matched Crossover (BU-PMX) is used as the crossover operator. In the case of BDDs, mutation is done in the standard way by variables exchanging. In the case of FDDs, the mutation by changing the polarity of variables is additionally used. Experimental results of optimization of the BDDs and FDDs of the set of benchmark functions are also presented.

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