决策神经网络模型及应用研究
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摘要
人工神经网络是模拟生物神经网络局部功能或机理的具有一定智能化的信息处理计算模型,可分为理论研究与硬件设计两大部分。在硬件实现方面,人类似乎还没有找到真正意义上模拟生物神经网络的材料,目前主要利用电子技术来实现;在用于求解优化计算的理论模型研究方面,目前主要是全连接的Hopfield模型。像细胞神经网络这种局域性连接网络主要应用于图像处理等领域。因此,如何构建局域性连接的、具有一定实用性的、可直接用于优化计算的人工神经网络模型仍是神经网络领域研究的一个核心内容。
本文意在建立一种局域连接的、模拟人脑决策思维模式的、可用于优化信息处理的神经网络模型。为此在建立模型前首先对多阶段决策问题利用图论方法进行了较为详细地研究,进而对网络乃至整个工程技术优化计算中过早收敛问题进行了探讨;在建立决策神经网络模型之后,将其应用到诸如TSP问题、图的同构问题等;文中也建立了图的顶点覆盖问题的人工神经网络模型,其主要贡献有如下几点:
首先,建立了多阶段决策问题的图论模型。对其中的基本理论与应用问题进行了研究,诸如现实生活中的问题直接或者间接地转化成多阶段决策问题;给出多阶段决策问题有向图方法的标准化方法;给出了多阶段决策问题中策略集的计数公式;以及求解策略集的两种计算方法;建立了最短路问题的标准化的基于图论方法的多阶段决策问题的模型;建立了旅行商问题的标准化的基于图论方法的多阶段决策问题的数学模型,此模型直接可应用于求解图的Hamilton问题的应用。
其次,建立了决策神经网络模型。作为一种局域连接网络,其优点是:不像Hopfield网络那样的全连接性,又不像细胞神经网络的“死板性”,是一种接近于人脑思维模式的局域连接问题。这种模型的特点应与人脑决策模式类似,可能得不到问题的最优解,但易于得到问题的满意解。给出了此模型机理、网络结构,以及网络的电路实现等问题;
再次,较系统地讨论了过早收敛现象,并应用置换群理论,图论等数学工具进行了行之有效的研究,这一成果可直接应用于众多的优化计算之中;
最后,将决策神经网络模型应用于TSP问题、图的同构问题等的研究。其基本的思想是将决策思维中局域思想加入在能量函数,进而加入在网络的运行方程之中;最后,建立了图的顶点覆盖问题的神经网络模型。该模型是在已有Hopfield网络模型的基础上给予了改进,将决策神经网络模型的思想加了进去。
Artificial Neural Networks serve as a intelligently computational model for signal processing which can simulate the partial function and mechanism for biological Neural Networks. The researches about the Artificial Neural Networks mainly emphasis on two fields, including theory and hardware. Although recently electronic techniques are used to realize the hardware, it seems that human being don't find out true materials all the time which can succeed in the simulation of biological Neural Networks. In addition, the solver of optimization computation in theory is dependent on the all-connected Hopfield model. However, like the molecular Neural Networks, the partial connected-networks are to a large extent applied to the field such as image processing and so on. Consequently, it is a core subject about how to construct Artificial Neural Networks that are of local-connection, of certain practice, and also can be applied to solver the optimized problems.
Therefore, this paper is aimed to establish a kind of Neural Networks model that are of local-connection, of simulation human's decision-making thinking, and also can be applied to solver the optimization for information. Thus we give detail discussions about the multi-stage decision problems by use of Graph Theory before establishment of models. Then we can continue to discuss the premature convergence of the network and even the optimized computation of the engineering technology. And then the Neural Networks model will be used to solutions of the TSP and Graph isomorphic problems and so on. Additionally, we also discuss how to apply the Artificial Neural Networks to vertex covering. There are mainly four important results in this paper.
Firstly, we construct the graphic model for the multi-stage decision problems and discuss some basic theory and application problems, for instance, it describes how to directly or indirectly change the realistic problems into multi-stage decision problems. And it shows a standard directed graphic method, and the counting formula of multi-stage decision problems. Besides these two computation method of solving the set to decision-making are given. This paper establishes the model of the most shortest problem based on multi-stage decision-making problem of theory method and constructs the mathematic model of TSP problem based on multi-phase decision-making problem of theory method, that can be directly applied to the solving the Hamiltonian problem.
Secondly, we establish the model of decision-making Neural Networks. This is a local area connection networks. Its merits is neither similar to the connected Hopfield Neural Networks, nor the "rigid" of cell neural networks, is close to the human thinking method in local area connection problem. The characteristics of the model are analogy to the modedecision-making of human, maybe we can't get the optimal solution, but are easy to obtain the satisfactory solution. This chapter gives the mechanism of the model, the framework of networks, and the circuit realization and so on.
Thirdly, the chapter systematically discusses the phenomenon of premature convergence and applied to the theory of permutation group, graph theory and other mathematics tools to make efficient researches, which can be directly used to many optimization computation.
Finally, we apply the model of decision-making Neural Networks to the research of traveling salesman problem, isomorphism of graph. The basic idea is to put the energy function to the decision-making, and then combine the equation of the networks. At last, establish the model of neural networks based on vertex coving. Based on the existed Hopfield neural networks, we combine the idea of decision-making neural networks to modify the model.
本文意在建立一种局域连接的、模拟人脑决策思维模式的、可用于优化信息处理的神经网络模型。为此在建立模型前首先对多阶段决策问题利用图论方法进行了较为详细地研究,进而对网络乃至整个工程技术优化计算中过早收敛问题进行了探讨;在建立决策神经网络模型之后,将其应用到诸如TSP问题、图的同构问题等;文中也建立了图的顶点覆盖问题的人工神经网络模型,其主要贡献有如下几点:
首先,建立了多阶段决策问题的图论模型。对其中的基本理论与应用问题进行了研究,诸如现实生活中的问题直接或者间接地转化成多阶段决策问题;给出多阶段决策问题有向图方法的标准化方法;给出了多阶段决策问题中策略集的计数公式;以及求解策略集的两种计算方法;建立了最短路问题的标准化的基于图论方法的多阶段决策问题的模型;建立了旅行商问题的标准化的基于图论方法的多阶段决策问题的数学模型,此模型直接可应用于求解图的Hamilton问题的应用。
其次,建立了决策神经网络模型。作为一种局域连接网络,其优点是:不像Hopfield网络那样的全连接性,又不像细胞神经网络的“死板性”,是一种接近于人脑思维模式的局域连接问题。这种模型的特点应与人脑决策模式类似,可能得不到问题的最优解,但易于得到问题的满意解。给出了此模型机理、网络结构,以及网络的电路实现等问题;
再次,较系统地讨论了过早收敛现象,并应用置换群理论,图论等数学工具进行了行之有效的研究,这一成果可直接应用于众多的优化计算之中;
最后,将决策神经网络模型应用于TSP问题、图的同构问题等的研究。其基本的思想是将决策思维中局域思想加入在能量函数,进而加入在网络的运行方程之中;最后,建立了图的顶点覆盖问题的神经网络模型。该模型是在已有Hopfield网络模型的基础上给予了改进,将决策神经网络模型的思想加了进去。
Artificial Neural Networks serve as a intelligently computational model for signal processing which can simulate the partial function and mechanism for biological Neural Networks. The researches about the Artificial Neural Networks mainly emphasis on two fields, including theory and hardware. Although recently electronic techniques are used to realize the hardware, it seems that human being don't find out true materials all the time which can succeed in the simulation of biological Neural Networks. In addition, the solver of optimization computation in theory is dependent on the all-connected Hopfield model. However, like the molecular Neural Networks, the partial connected-networks are to a large extent applied to the field such as image processing and so on. Consequently, it is a core subject about how to construct Artificial Neural Networks that are of local-connection, of certain practice, and also can be applied to solver the optimized problems.
Therefore, this paper is aimed to establish a kind of Neural Networks model that are of local-connection, of simulation human's decision-making thinking, and also can be applied to solver the optimization for information. Thus we give detail discussions about the multi-stage decision problems by use of Graph Theory before establishment of models. Then we can continue to discuss the premature convergence of the network and even the optimized computation of the engineering technology. And then the Neural Networks model will be used to solutions of the TSP and Graph isomorphic problems and so on. Additionally, we also discuss how to apply the Artificial Neural Networks to vertex covering. There are mainly four important results in this paper.
Firstly, we construct the graphic model for the multi-stage decision problems and discuss some basic theory and application problems, for instance, it describes how to directly or indirectly change the realistic problems into multi-stage decision problems. And it shows a standard directed graphic method, and the counting formula of multi-stage decision problems. Besides these two computation method of solving the set to decision-making are given. This paper establishes the model of the most shortest problem based on multi-stage decision-making problem of theory method and constructs the mathematic model of TSP problem based on multi-phase decision-making problem of theory method, that can be directly applied to the solving the Hamiltonian problem.
Secondly, we establish the model of decision-making Neural Networks. This is a local area connection networks. Its merits is neither similar to the connected Hopfield Neural Networks, nor the "rigid" of cell neural networks, is close to the human thinking method in local area connection problem. The characteristics of the model are analogy to the modedecision-making of human, maybe we can't get the optimal solution, but are easy to obtain the satisfactory solution. This chapter gives the mechanism of the model, the framework of networks, and the circuit realization and so on.
Thirdly, the chapter systematically discusses the phenomenon of premature convergence and applied to the theory of permutation group, graph theory and other mathematics tools to make efficient researches, which can be directly used to many optimization computation.
Finally, we apply the model of decision-making Neural Networks to the research of traveling salesman problem, isomorphism of graph. The basic idea is to put the energy function to the decision-making, and then combine the equation of the networks. At last, establish the model of neural networks based on vertex coving. Based on the existed Hopfield neural networks, we combine the idea of decision-making neural networks to modify the model.
引文
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