A modified approach to cross entropy method: Elitist stepped distribution algorithm

This paper introduces a new algorithm named Elitist Stepped Distribution Algorithm (ESDA), which is inspired from the existing Cross Entropy Method (CEM) through the modification of elite sample based normal distribution used in CEM. Considering the natural behavior of normal distribution, ESDA is proposed to enhance the drawbacks of CEM through improving the efficiency in both exploration and exploitation processes when applying for complex function optimization problems. In ESDA, the elite sample percent defined in CEM is separated into two parts: (1) elite sample percent to calculate the mean value, and (2) elite sample percent to calculate standard deviation of normal distribution to construct an applicable balance between exploration and exploitation ability of the algorithm at a reasonable convergence speed. The elite sample percent parameter for the mean guides the algorithm to focus more on the better solutions and therefore improves the exploitation ability, whereas the elite sample percent parameter for the standard deviation controls the length of standard deviation to handle the exploration process more effectively. Performance of ESDA is investigated using unconstrained benchmark problems and compared with CEM, Simple Genetic Algorithm and Particle Swarm Optimization. The comparisons on unimodal and multi-modal functions confirm the efficiency of the algorithm in both exploration and exploitation process. In addition, the performance of ESDA is tested using constrained engineering problems commonly used in literature by comparing its performance with the other ones statistically. The results on engineering problems also prove that ESDA is perfectly applicable in real-world applications.     

An analysis of the GLVQ algorithm

Generalized learning vector quantization (GLVQ) has been proposed in as a generalization of the simple competitive learning (SCL) algorithm. The main argument of GLVQ proposal is its superior insensitivity to the initial values of the weights (code vectors). In this paper we show that the distinctive characteristics of the definition of GLVQ disappear outside a small domain of applications. GLVQ becomes identical to SCL when either the number of code vectors grows or the size of the input space is large. Besides that, the behavior of GLVQ is inconsistent for problems defined on very small scale input spaces. The adaptation rules fluctuate between performing descent and ascent searches on the gradient of the distortion function.     

一种基于遗传算法的最小交叉熵阈值选择方法

最小交叉熵阈值法(MCET) 在二级阈值中是有效的, 但在多极阈值的穷尽搜索中却要付出昂贵的时间代价. 鉴于此, 提出一种基于遗传算法(GA) 的MCET选择方法: 在执行图像分割(IS) 任务之前, 先将IS 转化为在一定约束 条件下待优化的问题; 在寻找待优化问题最优解的计算过程中引入一种回归设计技巧以存储中间结果; 使用这种回 归设计技巧, 在一组标准测试图像上利用GA搜索待优化问题的最优解. 实验结果表明, 利用所提出的方法获得的多 个阈值非常接近于穷尽搜索获得的结果.

     

鲁棒的交叉熵模糊聚类算法

针对模糊C-均值聚类(FCM)算法对噪声敏感、容易收敛到局部极小值的问题,提出一种基于交叉熵的模糊聚类算法。通过引入交叉熵重新定义了传统FCM算法的目标函数,利用交叉熵度量样本隶属度之间的差异性,并采用拉格朗日求解方法和朗伯W函数解决了目标函数的优化问题,此外,分析了样本划分矩阵的分布情况,依据分布特性对噪声样本进行识别。人工数据集合和标准数据集加噪的实验结果表明,该算法提高了传统FCM算法的抗干扰能力,具有更强的鲁棒性,噪声样本识别的准确率较高。     

基于对称交叉熵的属性约简算法

针对交叉熵用来度量两个随机变量的差异程度时不满足对称性的问题,提出对称交叉熵的概念．研究在决策表的属性约简过程中决策属性集相对条件属性集对称交叉熵的变化规律,提出基于对称交叉熵的属性约简算法,同时还对其复杂度进行简单分析．实验分析表明,在多数情况下该算法能够得到决策表的最小相对约简．     

A cross entropy algorithm for the Knapsack problem with setups

In this article we propose a new metaheuristic-based algorithm for the Integer Knapsack Problem with Setups. This problem is a generalization of the standard Integer Knapsack Problem, complicated by the presence of setup costs in the objective function as well as in the constraints. We propose a cross entropy based algorithm, where the metaheuristic scheme allows to relax the original problem to a series of well chosen standard Knapsack problems, solved through a dynamic programming algorithm. To increase the computational effectiveness of the proposed algorithm, we use a turnpike theorem, which sensibly reduces the number of iterations of the dynamic algorithm. Finally, to testify the robustness of the proposed scheme, we present extensive computational results. First, we illustrate the step-by-step behavior of the algorithm on a smaller, yet difficult, problem. Subsequently, to test the solution quality of the algorithm, we compare the results obtained on very large scale instances with the output of a branch and bound scheme. We conclude that the proposed algorithm is effective in terms of solution quality as well as computational time.     

基于交叉熵算法的PID 控制器设计

交叉熵优化方法是一种新型高效的随机优化算法,算法控制参数简单,鲁棒性强.将交叉熵优化算法用于PID控制器的参数设计,并与基于遗传算法的PID控制器设计进行对比,结果表明,交叉熵优化算法不仅所获结果较优,而且计算复杂度也明显小于遗传算法.     

Multilevel minimum cross entropy threshold selection based on the firefly algorithm

The minimum cross entropy thresholding (MCET) has been widely applied in image thresholding. The search mechanism of firefly algorithm inspired by the social behavior of the swarms of firefly and the phenomenon of bioluminescent communication, is used to search for multilevel thresholds for image segmentation in this paper. This new multilevel thresholding algorithm is called the firefly-based minimum cross entropy thresholding (FF-based MCET) algorithm. Four different methods that are the exhaustive search, the particle swarm optimization (PSO), the quantum particle swarm optimization (QPSO) and honey bee mating optimization (HBMO) methods are implemented for comparison with the results of the proposed method. The experimental results show that the proposed FF-based MCET algorithm can efficiently search for multiple thresholds which are very close to the optimal ones examined by the exhaustive search method when the number of thresholds is less than 5. The need of computation time of using the FF-based MCET algorithm is the least, meanwhile, the results using the FF-based MCET algorithm is superior to the ones of PSO-based and QPSO-based MCET algorithms but is not significantly different to the HBMO-based MCET algorithm.     

基于改进型GLVQ算法的车型分类研究

学习向量量化（LVQ）和泛化学习向量量化（GLVQ）算法都是采用欧氏距离作为相似性度量函数, 忽视了向量各维属性的数据取值范围,从而不能区分各维属性在分类中的不同作用。针对该问题,使用一种面向特征取值范围的向量相似性度量函数,对GLVQ进行改进,提出了GLVQ-FR算法。使用视频车型分类数据进行改进型GLVQ和LVQ2.1、GLVQ、GRLVQ、GMLVQ等算法的对比实验,结果表明：GLVQ-FR算法在车型分类中具有较高的分类准确性、运算速度和真实生产环境中的可用性。     

基于BBO算法的二维交叉熵多阈值图像分割*

针对复杂图像的分割问题,提出一种基于生物地理学优化算法(BBO,Biogeography-Based Optimization)的二维交叉熵多阈值图像分割方法。首先,根据二维直方图斜分法得出交叉熵阈值选取公式,并将此推广到多阈值分割,以求得多个极值提高分割效果,由于二维交叉熵法在多阈值分割时计时长、复杂性高等问题,然后引入BBO算法的思想,实现对多个阈值快速精确地寻优,最后,对标准图像进行分割以验证该算法。结果表明此算法比二维交叉熵穷举法计算效率高。     

基于改进交叉熵算法的伺服电机参数优化设计

针对伺服电机变负载控制问题,提出了一种对自适应模糊PID控制器初始参数优化的改进交叉熵算法。通过运用此方法对伺服电机模糊PID控制器在控制过程中的参数进行优化,证明了该算法在模糊PID控制器应用的过程中具有较好的鲁棒性和兼容性。通过实验,同时与基于ZN算法、遗传算法和交叉熵算法的模糊PID控制结果进行对比,证明改进交叉熵优化算法不但具有较快的响应速度、较好的稳定性、较小的超调和较优的ITASE性能指标,而且其优化过程更为精确简便。     

An efficient method for multilevel color image thresholding using cuckoo search algorithm based on minimum cross entropy

Among various thresholding methods, minimum cross entropy is implemented for its effectiveness and simplicity. Although it is efficient and gives excellent result in case of bi-level thresholding, but its evaluation becomes computationally costly when extended to perform multilevel thresholding owing to the exhaustive search performed for the optimum threshold values. Therefore, in this paper, an efficient multilevel thresholding technique based on cuckoo search algorithm is adopted to render multilevel minimum cross entropy more practical and reduce the complexity. Experiments have been conducted over different color images including natural and satellite images exhibiting low resolution, complex backgrounds and poor illumination. The feasibility and efficiency of proposed approach is investigated through an extensive comparison with multilevel minimum cross entropy based methods that are optimized using artificial bee colony, bacterial foraging optimization, differential evolution, and wind driven optimization. In addition, the proposed approach is compared with thresholding techniques depending on between-class variance (Otsu) method and Tsalli’s entropy function. Experimental results based on qualitative results and different fidelity parameters depicts that the proposed approach selects optimum threshold values more efficiently and accurately as compared to other compared techniques and produces high quality of the segmented images.     

基于交叉熵的改进NPE间歇过程故障检测算法

针对具有复杂动态特性的间歇过程进行故障检测,邻域保持嵌入(neighborhood preserving embedding,NPE)算法在保持数据局部几何结构时因忽略全局信息而造成检测率较低的问题,提出一种基于交叉熵(cross entropy,CE)的邻域保持嵌入(CEGLNPE)算法.首先,将交叉熵保持全局结构的...     

基于熵权的K最临近算法改进

维度灾难直接影响到K最临近算法（KNN）的效率和准确率,将信息论中的信息熵理论与KNN算法结合起来,用信息熵理论进行属性约简,并根据特征属性与分类的相关度来确定各属性的权限,从而建立相关度与权重的内在联系。仿真实验表明,与传统的KNN相比,基于熵权的KNN改进方法在保持分类效率的情况下,使分类器的准确率得到了极大的提高。     

二维类内最小交叉熵的图像分割快速方法

熵是基于图像的一维灰度直方图得到的,仅利用了像素的灰度信息。最小交叉熵就是要寻找最优阈值使原始图像和分割图像之间的信息量的差异最小,在交叉熵的基础上,通过引入图像的空间信息,定义了二维类内交叉熵,并提出了基于二维类内最小交叉熵的图像分割方法。实验结果表明,充分利用图像的灰度信息和空间信息后,二维类内交叉熵取得了比交叉熵更好的分割效果。为了提高运算效率,提出了相应的快速递推算法,计算时间由从多于3小时减少到只要几秒。     

An improved scheme for minimum cross entropy threshold selection based on genetic algorithm

Image segmentation is one of the most critical tasks in image analysis. Thresholding is definitely one of the most popular segmentation approaches. Among thresholding methods, minimum cross entropy thresholding (MCET) has been widely adopted for its simplicity and the measurement accuracy of the threshold. Although MCET is efficient in the case of bilevel thresholding, it encounters expensive computation when involving multilevel thresholding for exhaustive search on multiple thresholds. In this paper, an improved scheme based on genetic algorithm is presented for fastening threshold selection in multilevel MCET. This scheme uses a recursive programming technique to reduce computational complexity of objective function in multilevel MCET. Then, a genetic algorithm is proposed to search several near-optimal multilevel thresholds. Empirically, the multiple thresholds obtained by our scheme are very close to the optimal ones via exhaustive search. The proposed method was evaluated on various types of images, and the experimental results show the efficiency and the feasibility of the proposed method on the real images.     

加工时间不确定的炼钢连铸生产调度串级交叉熵算法

针对加工时间不确定的炼钢连铸生产调度问题, 一方面考虑炉次精炼时间是运输时间和等待时间的线性增函数, 并考虑分时电价, 提出基于关键炉次的左右混合调整方法对各炉次精炼时间进行调整; 另一方面, 考虑炉次在各阶段的基本加工时间和连铸机最早开浇时间可在一定范围内选择, 提出一种串级交叉熵算法进行求解. 设计了不同的仿真实例, 并将串级交叉熵算法与改进自适应遗传算法进行比较, 验证了所提出算法的优越性.

     

A new active contour remote sensing river image segmentation algorithm inspired from the cross entropy

The CV (Chan–Vese) model is a piecewise constant approximation of the Mumford and Shah model. It assumes that the original image can be segmented into two regions such that each region can be represented as constant grayscale value. In fact, the objective functional of the CV model actually finds a segmentation of the image such that the within-class variance is minimized. This is equivalent to the Otsu image thresholding algorithm which also aims to minimize the within-class variance. Similarly to the Otsu image thresholding algorithm, cross entropy is another widely used image thresholding algorithm and it finds a segmentation such that the cross entropy of the segmented image and the original image is minimized. Inspired from the cross entropy, a new active contour image segmentation algorithm is proposed. The region term in the new objective functional is the integral of the logarithm of the ratio between the grayscale of the original image and the mean value computed from the segmented image weighted by the grayscale of the original image. The new objective functional can be solved by the level set evolution method. A distance regularized term is added to the level set evolution equation so the level set need not be reinitialized periodically. A fast global minimization algorithm of the objective functional is also proposed which incorporates the edge term originated from the geodesic active contour model. Experimental results show that, the algorithm proposed can segment images more accurately than the CV model and the implementation speed of the fast global minimization algorithm is fast.     

萤火虫算法优化最大熵的图像分割方法

为了提高图像的分割效果,提出一种萤火虫算法优化最大熵的图像分割方法。获得最大熵法的阈值优化目标函数,采用萤火虫算法对目标函数进行求解,找到图像的最佳分割阈值,根据最佳阈值对图像进行分割,通过仿真实验对分割效果进行测试。结果表明,该方法可以迅速、准确找到最佳阈值,提高图像分割的准确度和抗噪性能,可以较好地满足图像分割实时性要求。     

基于熵权法的虚拟网络映射算法

目前虚拟网络研究的一个热点是虚拟网络映射,但是传统两阶段算法中的节点映射算法着重于提高网络资源利用率,而忽略了网络的整体负载性能。为了避免现有映射算法中使用单一固有属性计算拓扑势值带来的片面性,在节点映射过程中增加了节点的另一个固有属性。但是,由于这两个固有属性之间的数量级相差较大,从而引入熵权,通过计算两个属性的熵权值来优化拓扑势值的计算,提出了一种基于熵权法的虚拟网映射算法。仿真实验结果表明,所提出的算法提高了映射接受率,并降低了网络的整体负载。