The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decis...The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decision diagram (ADD) or variants thereof provides canonical forms to represent and manipulate Boolean functions and pseudo-Boolean functions efficiently. ADD and OBDD-based symbolic algorithms give improved results for large-scale combinatorial optimization problems by searching nodes and edges implicitly. We present novel symbolic ADD formulation and algorithm for maximum weighted matching in bipartite graphs. The symbolic algorithm implements the Hungarian algorithm in the context of ADD and OBDD formulation and manipulations. It begins by setting feasible labelings of nodes and then iterates through a sequence of phases. Each phase is divided into two stages. The first stage is building equality bipartite graphs, and the second one is finding maximum cardinality matching in equality bipartite graph. The second stage iterates through the following steps: greedily searching initial matching, building layered network, backward traversing node-disjoint augmenting paths, updating cardinality matching and building residual network. The symbolic algorithm does not require explicit enumeration of the nodes and edges, and therefore can handle many complex executions in each step. Simulation experiments indicate that symbolic algorithm is competitive with traditional algorithms.展开更多
有序二叉决策图(O rdered B inary D ec is ion D isgram-OBDD)是布尔函数表示的规范型,布尔函数的复杂运算可以基于OBDD得到极大地简化实现。在讨论基于OBDD的有界Petri网符号分析算法的基础上,对赋时位置Petri网的符号分析进行了研究...有序二叉决策图(O rdered B inary D ec is ion D isgram-OBDD)是布尔函数表示的规范型,布尔函数的复杂运算可以基于OBDD得到极大地简化实现。在讨论基于OBDD的有界Petri网符号分析算法的基础上,对赋时位置Petri网的符号分析进行了研究,构造了一种扩展标识向量,给出了赋时Petri网分析的一种符号OBDD算法,实现了赋时Petri网的隐式描述与分析。实验表明,符号算法能处理较大规模赋时Petri网问题。展开更多
This paper presents a neural network approach, based on high-order two-dimension temporal and dynamically clustering competitive activation mecha-nisms, to implement parallel searching algorithm and many other symboli...This paper presents a neural network approach, based on high-order two-dimension temporal and dynamically clustering competitive activation mecha-nisms, to implement parallel searching algorithm and many other symbolic logicalgorithms. This approach is superior in many respects to both the commonsequential algorithms of symbolic logic and the common neura.l network usedfor optimization problems. Simulations of problem solving examples prove theeffectiveness of the approach.展开更多
文摘The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decision diagram (ADD) or variants thereof provides canonical forms to represent and manipulate Boolean functions and pseudo-Boolean functions efficiently. ADD and OBDD-based symbolic algorithms give improved results for large-scale combinatorial optimization problems by searching nodes and edges implicitly. We present novel symbolic ADD formulation and algorithm for maximum weighted matching in bipartite graphs. The symbolic algorithm implements the Hungarian algorithm in the context of ADD and OBDD formulation and manipulations. It begins by setting feasible labelings of nodes and then iterates through a sequence of phases. Each phase is divided into two stages. The first stage is building equality bipartite graphs, and the second one is finding maximum cardinality matching in equality bipartite graph. The second stage iterates through the following steps: greedily searching initial matching, building layered network, backward traversing node-disjoint augmenting paths, updating cardinality matching and building residual network. The symbolic algorithm does not require explicit enumeration of the nodes and edges, and therefore can handle many complex executions in each step. Simulation experiments indicate that symbolic algorithm is competitive with traditional algorithms.
文摘有序二叉决策图(O rdered B inary D ec is ion D isgram-OBDD)是布尔函数表示的规范型,布尔函数的复杂运算可以基于OBDD得到极大地简化实现。在讨论基于OBDD的有界Petri网符号分析算法的基础上,对赋时位置Petri网的符号分析进行了研究,构造了一种扩展标识向量,给出了赋时Petri网分析的一种符号OBDD算法,实现了赋时Petri网的隐式描述与分析。实验表明,符号算法能处理较大规模赋时Petri网问题。
文摘This paper presents a neural network approach, based on high-order two-dimension temporal and dynamically clustering competitive activation mecha-nisms, to implement parallel searching algorithm and many other symbolic logicalgorithms. This approach is superior in many respects to both the commonsequential algorithms of symbolic logic and the common neura.l network usedfor optimization problems. Simulations of problem solving examples prove theeffectiveness of the approach.
