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.

scholarly journals Compressing Exact Cover Problems with Zero-suppressed Binary Decision Diagrams

2021 ◽  
Author(s):  
Masaaki Nishino ◽  
Norihito Yasuda ◽  
Kengo Nakamura
Keyword(s):  
Data Structure ◽  
State Of The Art ◽  
Linear Time ◽  
Binary Decision Diagrams ◽  
Experimental Results ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Running Time ◽  
Order Of Magnitude ◽  
Exact Cover

Exact cover refers to the problem of finding subfamily F of a given family of sets S whose universe is D, where F forms a partition of D. Knuth’s Algorithm DLX is a state-of-the-art method for solving exact cover problems. Since DLX’s running time depends on the cardinality of input S, it can be slow if S is large. Our proposal can improve DLX by exploiting a novel data structure, DanceDD, which extends the zero-suppressed binary decision diagram (ZDD) by adding links to enable efficient modifications of the data structure. With DanceDD, we can represent S in a compressed way and perform search in linear time with the size of the structure by using link operations. The experimental results show that our method is an order of magnitude faster when the problem is highly compressed.

scholarly journals Implementation of GA with Position Based Crossover-PX Technique for Size Optimization of BDD Mapped Adder Circuits

2020 ◽  
Vol 9 (3) ◽  
pp. 4215-4218
Keyword(s):  
Genetic Algorithm ◽  
Digital Circuits ◽  
Full Adder ◽  
System Optimization ◽  
Size Optimization ◽  
Variable Order ◽  
Decision Diagrams ◽  
Order Method ◽  
Binary Decision ◽  
Solution Formation

Binary Decision Diagrams or BDD are data structure used to represent single and multi-output digital circuits. BDD mapped adder circuits are used to represent different adder functions in a digital system. Optimization of adder circuits are done by optimizing the corresponding BDDs. In this work the optimization of BDD Mapped adder circuits are proposed by using genetic algorithm with position-based crossover-PX technique. The main feature of position-based crossover technique is that it is suitable for order-based solution formation. We compared our result with other existing variable order method available in BDD manipulation tool BuDDy-2.4. The result is obtained for Full Adder circuits of 1 to 8-bit size. Experimental results show the improvement of the proposed work over other techniques. The result is quite significant for large circuits i.e. full adder circuit having larger bit size.

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