量子衍生和禁忌微分进化算法研究
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摘要
进化算法已经成功地应用到与优化任务相关的许多问题中。微分进化(DE)是一种比较新颖的进化算法,最近5-7年的发展非常迅速,得到许多研究人员的关注。DE算法与遗传算法、遗传规划、进化策略和进化规划相似,具有变异、交叉和选择等操作;而它的变异操作成为最具特点的执行方式,选择操作则采用“择优选取”的策略。
DE算法是一种基于种群的优化方法,一般与问题无关,执行比较容易。它是针对实数表达的优化问题而提出的,已经广泛用于约束优化、动态优化和多目标优化等方面。研究人员在DE算法上做了许多改进研究,改进和结合的技术包括多种群、邻域搜索、小生境、模糊调节、混沌搜索、自适应策略、局部搜索和协同搜索等方面。在工程应用方面,DE算法已经用于过程控制、制造系统、调度问题、路径优化问题、知识发现和滤波等方面。
本文在介绍DE算法的改进和应用研究现状的基础上,首先关注如何增强DE算法的全局搜索能力。这里,采用量子位表达的量子衍生微分进化算法,每个个体含有更多的可用信息,增加了种群多样性,进而提高了搜索能力。其次,在分类问题和模糊建模问题的改进研究中,量子衍生微分进化算法的使用改进了搜索过程,由此求解这两种问题的结果也得以改善。最后,针对含有多个局部极小值的约束问题,研究如何提高DE算法跳出局部最优的能力。这里,提出了禁忌微分进化算法。下面介绍本文的主要研究内容:
1.为了提高微分进化算法的全局搜索能力,引入量子位的概念,提出量子衍生微分进化算法(QDE)。使用微分进化的相关搜索机制,实现量子位个体的进化;提出一个新的选择算子,有利于量子位个体的快速收敛。实验结果显示,与其它版本的二进制微分进化相比,QDE的性能突出。因此,量子衍生微分进化算法可以成为二进制微分进化新的研究方向。
2.在分类问题中,数据集的属性类型包括连续属性和名义属性,而对于其它许多方法,则需要在数据预处理阶段增加连续属性离散化的步骤。本文提出的基于DE/QDE的分类方法采用微分进化的进化机制,可以同时处理这两种属性。因此,这种方法可以方便地求解更多的含有混合属性类型的分类问题。
3.针对T-S模糊模型的辨识问题,设计了基于减法聚类和DE算法的辨识方法,以及基于MDE/QDE的T-S模糊模型的辨识方法。在基于减法聚类和DE算法的辨识方法中,先进行结构辨识,再进行参数辨识;在基于MDE/QDE的T-S模糊模型的辨识方法中,使用MDE/QDE对模型的结构和参数同时进行辨识。其中的MDE是一种改进的微分进化,用于处理编码中的实数部分,QDE用于处理编码中的二进制数部分。
4.针对含有多个局部极小值的约束问题,提出禁忌微分进化算法。禁忌搜索允许接受非优解,具有跳出局部最优的能力;本文将禁忌搜索中的邻域移动方式、禁忌列表、希望列表、特赦准则等引入微分进化中;另外引入动态的调节禁忌搜索的步长,以实现自适应搜索的过程。实验结果表明,这种算法能够有效地增强跳出局部最优的能力。
Evolutionary algorithms have been successfully applied in many types ofproblems, mainly related to optimization tasks. Di?erential evolution (DE),which is a novel kind of the evolutionary algorithms, has developed fast for 5-7years, and has attracted great attention of a large number of researchers. DEwith the mutation, crossover and selection operators is similar to genetic algo-rithm, genetic programming, evolution strategy and evolution programming.Its mutation operator is the most special operation manner, and its selectionoperator is a“selecting the better”strategy.
DE is a population-based optimization technique, which is independentof the problems and can be easily carried out. DE, which was proposed forsolving numerical optimization problems at first, has been extensively appliedto constrained optimization, dynamic optimization, multi-objective optimiza-tion, and so on. Researchers have proposed many modified versions of DEwhich include multi-population, neighboring search, niche, fuzzy adjusting,chaos search, self-adaptive strategy, local search and cooperative search. Inengineering applications, DE has been used in the process control, schedulingproblems, routing problems, knowledge discovery, and filter design.
After the current modifications and applications of DE are introduced,the work of the thesis firstly focuses on how to enhance the global search-ing ability of DE. Here, the quantum bits as a representation are used in thequantum-inspired di?erential evolution algorithm. Each individual, which in-cludes more available information, enhances the diversity of the population,and then improve the searching ability. Next, for classification and fuzzy mod-eling, the searching process is accelerated owing to the quantum-inspired dif-ferential evolution algorithm. Thus, the results are improved. The search-ing ability is enhanced for classification and fuzzy model problems by usingthe quantum-inspired di?erential evolution algorithm. Finally, for constrainedproblems with many local minima, the thesis pays attention to how to enhance the ability of escaping from the local minima. Thus the tabu-based di?erentialevolution algorithm is proposed. The main research tasks are summarized asfollows:
1. For enhancing the global searching ability, the quantum bit is introducedto propose the quantum-inspired di?erential evolution algorithm (QDE)is proposed. Some search procedures of DE are used to evolve the Q-bit individuals. A new selection operator is introduced to accelerate theconvergence of the Q-bit individuals. Compared to other versions of thebinary di?erential evolution algorithms, the experimental results showthat QDE is excellent. Thus QDE will be a new aspect of the binarydi?erential evolution algorithms.
2. In classification problems, the types of the attribute of the data set in-clude the continuous and nominal attributes. For some exiting methods,discretization is necessary to deal with the continuous attribute in thepreprocessing stage. It is proposed a classification algorithm based onDE/QDE. DE/QDE, with the basic procedures of DE, can deal withthe continuous and nominal attributes. Hence, it can easily solve moreclassification problems with mixed attributes.
3. For designing T-S fuzzy model, it is proposed two identification method:the one is based on subtractive clustering and DE; the other is based onMDE/QDE. In the identification method based on subtractive cluster-ing and DE, the structure is identified firstly, and then the parametersare calculated. In the identification method based on MDE/QDE, thestructure and parameters are identified and calculated synchronously byusing MDE/QDE. MDE is a modified di?erential algorithm for dealingwith the numerical part of the encoding scheme, and QDE is used fordealing with the binary part of that.
4. For constrained optimization problem with the local minima, the tabu-based di?erential evolution is proposed. Tabu search compromises toaccept non-improved solutions, and can escape from the local minima. It is introduced the moving strategy in the neighboring area, tabu list,comprising list and aspiration criterion of tabu search to di?erential evo-lution. Moreover, the step length of tabu search adjusted dynamically isused in order to realize the self-adaptive search process. The experimen-tal results verifies that the proposed algorithm can enhance the ability ofescaping from the local minima.
DE算法是一种基于种群的优化方法,一般与问题无关,执行比较容易。它是针对实数表达的优化问题而提出的,已经广泛用于约束优化、动态优化和多目标优化等方面。研究人员在DE算法上做了许多改进研究,改进和结合的技术包括多种群、邻域搜索、小生境、模糊调节、混沌搜索、自适应策略、局部搜索和协同搜索等方面。在工程应用方面,DE算法已经用于过程控制、制造系统、调度问题、路径优化问题、知识发现和滤波等方面。
本文在介绍DE算法的改进和应用研究现状的基础上,首先关注如何增强DE算法的全局搜索能力。这里,采用量子位表达的量子衍生微分进化算法,每个个体含有更多的可用信息,增加了种群多样性,进而提高了搜索能力。其次,在分类问题和模糊建模问题的改进研究中,量子衍生微分进化算法的使用改进了搜索过程,由此求解这两种问题的结果也得以改善。最后,针对含有多个局部极小值的约束问题,研究如何提高DE算法跳出局部最优的能力。这里,提出了禁忌微分进化算法。下面介绍本文的主要研究内容:
1.为了提高微分进化算法的全局搜索能力,引入量子位的概念,提出量子衍生微分进化算法(QDE)。使用微分进化的相关搜索机制,实现量子位个体的进化;提出一个新的选择算子,有利于量子位个体的快速收敛。实验结果显示,与其它版本的二进制微分进化相比,QDE的性能突出。因此,量子衍生微分进化算法可以成为二进制微分进化新的研究方向。
2.在分类问题中,数据集的属性类型包括连续属性和名义属性,而对于其它许多方法,则需要在数据预处理阶段增加连续属性离散化的步骤。本文提出的基于DE/QDE的分类方法采用微分进化的进化机制,可以同时处理这两种属性。因此,这种方法可以方便地求解更多的含有混合属性类型的分类问题。
3.针对T-S模糊模型的辨识问题,设计了基于减法聚类和DE算法的辨识方法,以及基于MDE/QDE的T-S模糊模型的辨识方法。在基于减法聚类和DE算法的辨识方法中,先进行结构辨识,再进行参数辨识;在基于MDE/QDE的T-S模糊模型的辨识方法中,使用MDE/QDE对模型的结构和参数同时进行辨识。其中的MDE是一种改进的微分进化,用于处理编码中的实数部分,QDE用于处理编码中的二进制数部分。
4.针对含有多个局部极小值的约束问题,提出禁忌微分进化算法。禁忌搜索允许接受非优解,具有跳出局部最优的能力;本文将禁忌搜索中的邻域移动方式、禁忌列表、希望列表、特赦准则等引入微分进化中;另外引入动态的调节禁忌搜索的步长,以实现自适应搜索的过程。实验结果表明,这种算法能够有效地增强跳出局部最优的能力。
Evolutionary algorithms have been successfully applied in many types ofproblems, mainly related to optimization tasks. Di?erential evolution (DE),which is a novel kind of the evolutionary algorithms, has developed fast for 5-7years, and has attracted great attention of a large number of researchers. DEwith the mutation, crossover and selection operators is similar to genetic algo-rithm, genetic programming, evolution strategy and evolution programming.Its mutation operator is the most special operation manner, and its selectionoperator is a“selecting the better”strategy.
DE is a population-based optimization technique, which is independentof the problems and can be easily carried out. DE, which was proposed forsolving numerical optimization problems at first, has been extensively appliedto constrained optimization, dynamic optimization, multi-objective optimiza-tion, and so on. Researchers have proposed many modified versions of DEwhich include multi-population, neighboring search, niche, fuzzy adjusting,chaos search, self-adaptive strategy, local search and cooperative search. Inengineering applications, DE has been used in the process control, schedulingproblems, routing problems, knowledge discovery, and filter design.
After the current modifications and applications of DE are introduced,the work of the thesis firstly focuses on how to enhance the global search-ing ability of DE. Here, the quantum bits as a representation are used in thequantum-inspired di?erential evolution algorithm. Each individual, which in-cludes more available information, enhances the diversity of the population,and then improve the searching ability. Next, for classification and fuzzy mod-eling, the searching process is accelerated owing to the quantum-inspired dif-ferential evolution algorithm. Thus, the results are improved. The search-ing ability is enhanced for classification and fuzzy model problems by usingthe quantum-inspired di?erential evolution algorithm. Finally, for constrainedproblems with many local minima, the thesis pays attention to how to enhance the ability of escaping from the local minima. Thus the tabu-based di?erentialevolution algorithm is proposed. The main research tasks are summarized asfollows:
1. For enhancing the global searching ability, the quantum bit is introducedto propose the quantum-inspired di?erential evolution algorithm (QDE)is proposed. Some search procedures of DE are used to evolve the Q-bit individuals. A new selection operator is introduced to accelerate theconvergence of the Q-bit individuals. Compared to other versions of thebinary di?erential evolution algorithms, the experimental results showthat QDE is excellent. Thus QDE will be a new aspect of the binarydi?erential evolution algorithms.
2. In classification problems, the types of the attribute of the data set in-clude the continuous and nominal attributes. For some exiting methods,discretization is necessary to deal with the continuous attribute in thepreprocessing stage. It is proposed a classification algorithm based onDE/QDE. DE/QDE, with the basic procedures of DE, can deal withthe continuous and nominal attributes. Hence, it can easily solve moreclassification problems with mixed attributes.
3. For designing T-S fuzzy model, it is proposed two identification method:the one is based on subtractive clustering and DE; the other is based onMDE/QDE. In the identification method based on subtractive cluster-ing and DE, the structure is identified firstly, and then the parametersare calculated. In the identification method based on MDE/QDE, thestructure and parameters are identified and calculated synchronously byusing MDE/QDE. MDE is a modified di?erential algorithm for dealingwith the numerical part of the encoding scheme, and QDE is used fordealing with the binary part of that.
4. For constrained optimization problem with the local minima, the tabu-based di?erential evolution is proposed. Tabu search compromises toaccept non-improved solutions, and can escape from the local minima. It is introduced the moving strategy in the neighboring area, tabu list,comprising list and aspiration criterion of tabu search to di?erential evo-lution. Moreover, the step length of tabu search adjusted dynamically isused in order to realize the self-adaptive search process. The experimen-tal results verifies that the proposed algorithm can enhance the ability ofescaping from the local minima.
引文
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