Isomorphism Identification Of Graphs Research Articles

A new method for isomorphism identification of planetary gear trains

Abstract. Planetary gear trains (PGTs) are widely used in machinery such as vehicles, pulley blocks, wrist watches, machine tools, and robots. During the process of structural synthesis of PGTs using graph theory, isomorphism identification of graphs is an important and complicated problem. The reliability of the isomorphism detection method directly determines the accuracy of the synthesis result. In this paper, a novel isomorphism identification method for PGTs is proposed. First, a new weighted adjacent matrix is presented to describe the topological graph of PGTs, which has is unique in describing the structure of PGTs. Then, the weighted distance matrix is proposed and the sum of the matrix is obtained, which can determine whether the planetary gear trains is isomorphic or not. Eventually, the examples demonstrate that this new method can be accurately and effectively performed.

An Improved Genetic Algorithm Approach on Mechanism Kinematic Structure Enumeration with Intelligent Manufacturing

During the process of mechanism kinematic structure enumeration, isomorphism identification of graphs is an important and complicated problem. The problem is known to be a NP-complete problem. In this paper, according to the mechanism kinematic chain isomorphism identification criteria, a highly efficient hybrid genetic algorithm model is proposed for isomorphism identification. The model method is coupled with genetic algorithm, optimal choice, and optimal crossover operation. It shows a quick convergence rate of the late operation and can avoid convergence to local optimum. Simulation results show that the hybrid algorithm is more rapid and effective compared with simple genetic algorithm and the improved neural network algorithm.

Intelligent Design of Mechanism Kinematic Chains by Advanced Optimal Methods

When using graph theory to conduct intelligent design for kinematic structure enumeration, the isomorphism identification of graphs is an important and complicated problem. In this paper, the methodology of transferring isomorphism identification into optimization issue was introduced. Then the recent development of applying advanced optimal methods for isomorphism identification was reviewed, the advantages and disadvantages of there methods were discussed.

A review on graph isomorphism identification of mechanism kinematic chain for intelligent and digital manufacturing

The graph theory is an important method to achieve conceptual design for mechanism. During the process of kinematic structures enumeration using graph theory, isomorphism identification of graphs is an NP-complete problem. So, the graph isomorphism identification is a crucial problem in mechanism creative design. In this paper, some recent literatures are introduced to demonstrate some method to solve this NP-hard problem. These approaches are all proved to be effective in some cases. The purpose of this paper is to provide references and helps for researchers.

A high-performance approach on mechanism isomorphism identification based on an adaptive hybrid genetic algorithm for digital intelligent manufacturing

The graph theory is an important method to achieve conceptual design for mechanism. During the process of kinematic structures enumeration using graph theory, isomorphism identification of graphs is an NP complete problem. It is important to improve the isomorphism identification efficiency and reliability. To solve the problem, an adaptive hybrid genetic algorithm is presented by mixing the improved genetic algorithm and local search algorithm. The crossover rate and mutation rate can be designed as adaptive parameters. Hence, the crossover rate and mutation rate can sustain the variety of the population and adjust the evolution. In the meantime, the pseudo-crossover operator is introduced to improve the search efficiency. In the last, some examples are illustrated to show the high efficiency of the algorithm by comparing with the results in other literatures.

Isomorphism identification of graphs: Especially for the graphs of kinematic chains

Isomorphism identification of graphs is one of the most important and challenging problems in the fields of mathematics, computer science and mechanisms, etc. This paper attempts to solve the problem by finding a unique representation of graphs. First, the perimeter loop of a graph is identified from all the loops of the graph obtained through a new algorithm. From the perimeter loop a corresponding perimeter graph is derived, which renders the forms of the graph canonical. Then by relabelling the perimeter graph the canonical perimeter graph is obtained, reducing the adjacency matrices of a graph from hundreds of thousands to several or even just one. On the basis of canonical adjacency matrix set, the unique representation of the graph, the characteristic adjacency matrix, is obtained. In such a way, isomorphism identification, sketching, and establishment of the database of common graphs, including the graphs of kinematic chains, all become easy to realize. Computational complexity analysis shows that, in the field of kinematic chains the approach is much more efficient than McKay’s algorithm which is considered the fastest so far. It remains efficient even when the links of kinematic chains increase into the thirties.

Isomorphism identification for epicyclic gear mechanism based on mapping property and ant algorithm

To achieve computer-aided design for mechanism, one method that can be applied is graph theory. During the process of kinematic structure enumeration using graph theory, isomorphism identification of graphs is an important and complicated problem. The problem is known to be NP-complete problem. It is very important to improve the isomorphism identification efficiency and reliability. The objective of this research work is to use ant algorithm to improve the isomorphism identification efficiency and reliability for epicyclic gear mechanism. Based on mapping property between graphs, the isomorphism identification problem can be changed into a matrix operation problem. Two graphs must be isomorphism if the two matrixes of the two graphs can be exactly by exchanging their certain rows and columns, whereas show the two graphs must be non-isomorphic. A mixed model was developed for isomorphism identification by integrating the ant algorithm and mapping property between graphs. The gratifying results can be achieved while parameters are selected in appropriate situation by using the model. Finally, a computer program has been developed in Visual C++. Some examples confirm the validity of the model. The work will be a reliable isomorphism identification algorithm for intelligent CAD of epicyclic gear mechanism.

A mixed isomorphism approach for kinematic structure enumeration graphs based on intelligent design and manufacturing

When using graph theory for kinematic structure enumeration, the isomorphism identification of graphs is an important and complicated problem. The problem is known to be an NP-complete problem. This paper presents a mixed algorithm based on a mapping property, a genetic algorithm, and a simulated annealing algorithm for the isomorphism identification problem. A validity encoding scheme was developed by considering the mapping relationship between two graphs, and some reset measures for the crossover and mutation operators were developed based on the characteristics in which the encoding cell could not be reiterated. A simulated annealing algorithm was introduced into the mixed algorithm to prevent premature convergence in resolution, and some other measures were developed for improving the efficiency, based on the parameter selection. An example shows that the mixed algorithm is a valid algorithm for the isomorphism identification of kinematic structure graphs in mechanism design. It will be a reliable isomorphism identification algorithm for intelligent computer-aided design (CAD) and manufacturing (CAM).