混合量子优化算法理论及应用研究
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摘要
20世纪90年代迅速发展起来的以量子计算机为基础的量子计算方法以其在理论上证实具有超强的计算速度、指数级的存储容量、更好的稳定性和有效性等特征,被誉为未来计算科学发展的方向之一。量子计算的研究充分利用量子相干性的独特性质(量子叠加、量子纠缠和量子测量),探索以全新的方式进行计算、编码和信息传输的可能性,是一种探索突破芯片极限的新途径。
量子优化方法是借鉴量子理论的思想来解决某些特定问题的一种新方法。以量子计算理论为基础的量子优化算法,可以在一定程度上提高计算效率和克服陷入局部极值。本文提出的混合量子优化方法将量子计算方法与神经网络、进化算法、蚁群算法相融合,以期达到改进算法性能、拓宽算法应用领域、完善算法体系的目的。
本文对量子优化算法的相关问题进行研究,主要工作如下:
研究了量子进化算法原理及改进策略,首先概述了进化算法的研究概况,分析了传统进化算法存在的缺陷,然后提出将量子优化方法与进化方法融合起来形成量子进化算法,并提出量子进化算法改进策略。
研究了基于改进量子进化方法的BP神经网络权值优化模型,提出了一种将改进量子进化算法(IQEA)与BP算法相融合共同完成反向传播神经网络训练的方法,即IQEA-BP算法。首先对传统量子进化算法进行改进,然后采用改进量子进化算法对网络权值进行整体寻优,克服BP算法容易陷入局部最优的不足;再以找到的较优权值为初值,采用BP算法做进一步的寻优,以提高网络的训练和预报精度。本文将IQEA-BP神经网络应用于高炉铁水硅含量预测问题中,并与BP神经网络和QEA-BP神经网络的预测结果进行了比较,结果验证了该算法的有效性得到了较高的预测精度。
针对蚁群算法在求解连续空间优化问题时易于陷入局部最优和收敛速度慢的问题,本文提出了一种新的基于量子进化的蚁群优化算法。该算法采用量子比特的概率幅表示蚂蚁当前位置信息;设计了一种新的量子旋转门更新蚂蚁位置,完成蚂蚁的移动;最后采用量子非门实现蚂蚁所在位置的变异,增加位置的多样性。本文不仅从理论上证明了所提出量子蚁群算法的收敛性,而且从时间复杂性的角度分析了QACO具有较快的运行速度,仿真实验表明该算法可使搜索空间加倍,比传统的蚁群算法具有更好的种群多样性,更快的收敛速度和全局寻优能力。在此基础上讨论了量子进化蚁群优化算法的应用,主要研究了基于量子蚁群优化算法的板形识别。在分析研究板形信号识别的数学模型的基础上,将板形识别问题归结为板形应力误差函数寻优问题。进而在前面研究的量子蚁群优化算法的基础上探讨算法在应用于板形识别问题中的若干具体问题,仿真实验结果与参考文献中给出的其它板形识别方法的对比表明,该方法比文献中的方法识别精度高,具有具有一定的工程应用价值。
针对高炉冶炼行程炉况故障分类边界的模糊性和故障模式之间存在交叉数据的诊断不确定性问题,提出应用量子神经网络识别高炉炉况故障。本文将量子理论与神经网络融合形成量子神经网络,其隐含层神经元采用量子化的多级阶梯形传输函数,通过量子神经网络的量子间隔和权值学习算法,能够根据所提供的样本信息建立起分级的神经网络内部结构。量子神经网络借鉴量子叠加态测量坍缩原理,对不确定的输入向量给出一个近似的分类和类属概率,成功地解决了前馈神经网络模糊分类的局限性问题。为进一步提高炉况识别精度,针对高炉冶炼行程中样本数据非线性、大噪声的特点,提出了基于独立分量分析方法的特征提取算法。即采用独立分量分析方法,对原始样本进行分析处理,分离高炉炉况故障时的状态信号以提取其状态特征向量,产生新的维数降低、分量间相关性小的最能反映系统本质的特征样本空间;最后将这些特征向量作为输入向量通过量子神经网络对高炉故障进行识别,实验结果表明,基于独立分量分析的量子神经网络算法可以有效、准确地识别高炉炉况的故障模式,同时也为高炉炉况诊断提供了一种新型的方法。
Quantum computation method, developed rapidly in 1990s, is known as one of the developing trends of computing science in the future, which is based on quantum computer and proved theoretically to have prominent computing speed, storage capability with exponential level, and more stabile and effective characteristics. The studies of quantum computation make full use of unique properties of quantum Coherence state, such as the superposition of quantum state and the entanglement of qubit, and explore probabilities of a new method to compute, code and transmit the information, which is a new approach to grope for breaking through the limit of CMOS chip.
Quantum optimization algorithm is a new methods created by borrowing fundamental conception and principles from quantum theory to resolve certain problems. Quantum optimization algorithms, based on quantum computation theoey, can improve computing efficiency and prevent from dropping into a local optimum in a certain extent. In this dissertation, the proposed hybrid quantum optimization algorithms combine quantum computation with neural network, evolutionary algorithm and ant colony optimization algorithm to improve the performance of the algorithms, extend the application area of the algorithms and perfect the system of the algorithms.
This dissertation makes some researches on the problems concerned in quantum optimization algorithms, the main tasks are stated as follow.
The principle and improved measures of quantum evolutionary algorithm are researched. Firstly, this dissertation summarize the general situation survey of evolutionary algorithm and analyse the defects existed in evolutionary algorithm; and then combined it with quantum optimization algorithms and propose a quantum evolutionary algorithm. Meanwhile, several improved measures are also proposed.
A model of BP neural network, based on improved quantum evolutionary (IQEA) algorithms, is researched, and then a new neural network (NN) training algorithm, IQEA-BP algorithm, is proposed. Firstly, the traditional QEA is improved; Secondly, the improved QEA is adopted to search the optimal combinations of weights in the solution space to conquer the defect that BP neural network is easy to fall into local optimal, then regards the finded quite optimal weight as the first value, and uses BP algorithm to obtain the accurate optimal solutions quickly, which can increase the training and prediction precision of the network.This dissertation applied IQEA-BP algorithm to predict the silicon content in hot metal of blast furnace, The test results show that IQEA-BP can obtain better forecasting results, compared with BP and QEA-BP model.
Aiming at the shortcoming of optimization problems in continuous space based on ant colony optimization which is easy to fall into local optimums and has a slow convergence rate, a novel ant colony optimization algorithm based on quantum evolutionary is presented. In this algorithm, each ant position is represented by a group of quantum bits; a new quantum rotation gates are designed to update the position of the ant so as to enable the ant to move. Finally, some quantum bits are mutated by quantum non-gate so as to increase the variety of ant positions. It not only proves the convergence of the proposed algorithms through theoretical analysis, but also shows that QACO possess the more quickly speed from the angle of the time complexity. simulation experiments demonstrate that QACO can double searching space, gain better population diversity and accelerate the convergence speed and global optimal search ability, compared with the classical ant colony algorithm. Then this dissertation discusses the application based on the QACO. It mainly discussed QACO applied in the cold-rolled strip flatness recognition. On the basis of analysising the mathematical model of strip flatness signal, the flatness recognition can be attributed to a problem that the function search for the optimum. Fourthmore, this dissertation discusses some problems about QACO applied in the flatness recognition. Simulink tests demonstrate that the flatness recognition method based on QACO possesses greater accuracy, compared with the method in literature.It has some certain engineering merit.
Focusing on the fuzziness problem of fault classification borders, and on the diagnostic uncertainty of overlapping data, a fault diagnosis method for furnace state based on quantum neural network(QNN) was presented. This dissertation combines quantum theory with neural network and forms into a new model namely quantum neural network.Its hidden layer nerve cell adopts multi-level transition function.By use of the learning algorithms of quantum interval and weights, it can build grade inside structure of neural network according to the sample information.Quantum neural network can give an approximate class or category probability for uncertain input. In order to improve the recognition accuracy of abnormal blast furnace fourthmore, an independent component analyze method is proposed to extract their state features focused on the nonlinear and big yawp in the process of blast furnace.namely, by use of the ICA, original data is analyzed , disposaled, and separate the state signals of fault blast furnace and extract their state eigenvector. and then generate some new low dimension and few correlations among production parameters, which can reflect the essence of the system mostly. Finally, these state eigenvectors are regarded as input vector of QNN, the experimental results demonstrate that the ICA-QNN algorithms can recognize the fault pattern of furnace state effectively and accurately.meanwhile,it also provides a new method with fault diagnosis for blast furnace state.
量子优化方法是借鉴量子理论的思想来解决某些特定问题的一种新方法。以量子计算理论为基础的量子优化算法,可以在一定程度上提高计算效率和克服陷入局部极值。本文提出的混合量子优化方法将量子计算方法与神经网络、进化算法、蚁群算法相融合,以期达到改进算法性能、拓宽算法应用领域、完善算法体系的目的。
本文对量子优化算法的相关问题进行研究,主要工作如下:
研究了量子进化算法原理及改进策略,首先概述了进化算法的研究概况,分析了传统进化算法存在的缺陷,然后提出将量子优化方法与进化方法融合起来形成量子进化算法,并提出量子进化算法改进策略。
研究了基于改进量子进化方法的BP神经网络权值优化模型,提出了一种将改进量子进化算法(IQEA)与BP算法相融合共同完成反向传播神经网络训练的方法,即IQEA-BP算法。首先对传统量子进化算法进行改进,然后采用改进量子进化算法对网络权值进行整体寻优,克服BP算法容易陷入局部最优的不足;再以找到的较优权值为初值,采用BP算法做进一步的寻优,以提高网络的训练和预报精度。本文将IQEA-BP神经网络应用于高炉铁水硅含量预测问题中,并与BP神经网络和QEA-BP神经网络的预测结果进行了比较,结果验证了该算法的有效性得到了较高的预测精度。
针对蚁群算法在求解连续空间优化问题时易于陷入局部最优和收敛速度慢的问题,本文提出了一种新的基于量子进化的蚁群优化算法。该算法采用量子比特的概率幅表示蚂蚁当前位置信息;设计了一种新的量子旋转门更新蚂蚁位置,完成蚂蚁的移动;最后采用量子非门实现蚂蚁所在位置的变异,增加位置的多样性。本文不仅从理论上证明了所提出量子蚁群算法的收敛性,而且从时间复杂性的角度分析了QACO具有较快的运行速度,仿真实验表明该算法可使搜索空间加倍,比传统的蚁群算法具有更好的种群多样性,更快的收敛速度和全局寻优能力。在此基础上讨论了量子进化蚁群优化算法的应用,主要研究了基于量子蚁群优化算法的板形识别。在分析研究板形信号识别的数学模型的基础上,将板形识别问题归结为板形应力误差函数寻优问题。进而在前面研究的量子蚁群优化算法的基础上探讨算法在应用于板形识别问题中的若干具体问题,仿真实验结果与参考文献中给出的其它板形识别方法的对比表明,该方法比文献中的方法识别精度高,具有具有一定的工程应用价值。
针对高炉冶炼行程炉况故障分类边界的模糊性和故障模式之间存在交叉数据的诊断不确定性问题,提出应用量子神经网络识别高炉炉况故障。本文将量子理论与神经网络融合形成量子神经网络,其隐含层神经元采用量子化的多级阶梯形传输函数,通过量子神经网络的量子间隔和权值学习算法,能够根据所提供的样本信息建立起分级的神经网络内部结构。量子神经网络借鉴量子叠加态测量坍缩原理,对不确定的输入向量给出一个近似的分类和类属概率,成功地解决了前馈神经网络模糊分类的局限性问题。为进一步提高炉况识别精度,针对高炉冶炼行程中样本数据非线性、大噪声的特点,提出了基于独立分量分析方法的特征提取算法。即采用独立分量分析方法,对原始样本进行分析处理,分离高炉炉况故障时的状态信号以提取其状态特征向量,产生新的维数降低、分量间相关性小的最能反映系统本质的特征样本空间;最后将这些特征向量作为输入向量通过量子神经网络对高炉故障进行识别,实验结果表明,基于独立分量分析的量子神经网络算法可以有效、准确地识别高炉炉况的故障模式,同时也为高炉炉况诊断提供了一种新型的方法。
Quantum computation method, developed rapidly in 1990s, is known as one of the developing trends of computing science in the future, which is based on quantum computer and proved theoretically to have prominent computing speed, storage capability with exponential level, and more stabile and effective characteristics. The studies of quantum computation make full use of unique properties of quantum Coherence state, such as the superposition of quantum state and the entanglement of qubit, and explore probabilities of a new method to compute, code and transmit the information, which is a new approach to grope for breaking through the limit of CMOS chip.
Quantum optimization algorithm is a new methods created by borrowing fundamental conception and principles from quantum theory to resolve certain problems. Quantum optimization algorithms, based on quantum computation theoey, can improve computing efficiency and prevent from dropping into a local optimum in a certain extent. In this dissertation, the proposed hybrid quantum optimization algorithms combine quantum computation with neural network, evolutionary algorithm and ant colony optimization algorithm to improve the performance of the algorithms, extend the application area of the algorithms and perfect the system of the algorithms.
This dissertation makes some researches on the problems concerned in quantum optimization algorithms, the main tasks are stated as follow.
The principle and improved measures of quantum evolutionary algorithm are researched. Firstly, this dissertation summarize the general situation survey of evolutionary algorithm and analyse the defects existed in evolutionary algorithm; and then combined it with quantum optimization algorithms and propose a quantum evolutionary algorithm. Meanwhile, several improved measures are also proposed.
A model of BP neural network, based on improved quantum evolutionary (IQEA) algorithms, is researched, and then a new neural network (NN) training algorithm, IQEA-BP algorithm, is proposed. Firstly, the traditional QEA is improved; Secondly, the improved QEA is adopted to search the optimal combinations of weights in the solution space to conquer the defect that BP neural network is easy to fall into local optimal, then regards the finded quite optimal weight as the first value, and uses BP algorithm to obtain the accurate optimal solutions quickly, which can increase the training and prediction precision of the network.This dissertation applied IQEA-BP algorithm to predict the silicon content in hot metal of blast furnace, The test results show that IQEA-BP can obtain better forecasting results, compared with BP and QEA-BP model.
Aiming at the shortcoming of optimization problems in continuous space based on ant colony optimization which is easy to fall into local optimums and has a slow convergence rate, a novel ant colony optimization algorithm based on quantum evolutionary is presented. In this algorithm, each ant position is represented by a group of quantum bits; a new quantum rotation gates are designed to update the position of the ant so as to enable the ant to move. Finally, some quantum bits are mutated by quantum non-gate so as to increase the variety of ant positions. It not only proves the convergence of the proposed algorithms through theoretical analysis, but also shows that QACO possess the more quickly speed from the angle of the time complexity. simulation experiments demonstrate that QACO can double searching space, gain better population diversity and accelerate the convergence speed and global optimal search ability, compared with the classical ant colony algorithm. Then this dissertation discusses the application based on the QACO. It mainly discussed QACO applied in the cold-rolled strip flatness recognition. On the basis of analysising the mathematical model of strip flatness signal, the flatness recognition can be attributed to a problem that the function search for the optimum. Fourthmore, this dissertation discusses some problems about QACO applied in the flatness recognition. Simulink tests demonstrate that the flatness recognition method based on QACO possesses greater accuracy, compared with the method in literature.It has some certain engineering merit.
Focusing on the fuzziness problem of fault classification borders, and on the diagnostic uncertainty of overlapping data, a fault diagnosis method for furnace state based on quantum neural network(QNN) was presented. This dissertation combines quantum theory with neural network and forms into a new model namely quantum neural network.Its hidden layer nerve cell adopts multi-level transition function.By use of the learning algorithms of quantum interval and weights, it can build grade inside structure of neural network according to the sample information.Quantum neural network can give an approximate class or category probability for uncertain input. In order to improve the recognition accuracy of abnormal blast furnace fourthmore, an independent component analyze method is proposed to extract their state features focused on the nonlinear and big yawp in the process of blast furnace.namely, by use of the ICA, original data is analyzed , disposaled, and separate the state signals of fault blast furnace and extract their state eigenvector. and then generate some new low dimension and few correlations among production parameters, which can reflect the essence of the system mostly. Finally, these state eigenvectors are regarded as input vector of QNN, the experimental results demonstrate that the ICA-QNN algorithms can recognize the fault pattern of furnace state effectively and accurately.meanwhile,it also provides a new method with fault diagnosis for blast furnace state.
引文
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