关键词： Evolutionary computation   term operation   idemprimality   primal algebras  

摘要： The Deep Drilling Algorithm (DDA) is an efficient non-evolutionary algorithm, extracted from previous work with evolutionary algorithms, that takes as input a finite groupoid and an operation over its universe, and searches for a term representing that operation. We give theoretical and experimental evidence that this algorithm is successful for all idemprimal term continuous groupoids, which appear to be almost all finite groupoids, and that the DDA is seriously compromised or fails for most finite groupoids not meeting both of these conditions. See our online version of the DDA at http://***/lspector/dda.

关键词： Page segmentation   Document layout analysis   Homogeneity structure   OCR   Mathematical morphology   Recursive filter  

摘要： Document layout analysis or page segmentation is the task of decomposing document images into many different regions such as texts, images, separators, and tables. It is still a challenging problem due to the variety of document layouts. In this paper, we propose a novel hybrid method, which includes three main stages to deal with this problem. In the first stage, the text and non-text elements are classified by using minimum homogeneity algorithm. This method is the combination of connected component analysis and multilevel homogeneity structure. Then, in the second stage, a new homogeneity structure is combined with an adaptive mathematical morphology in the text document to get a set of text regions. Besides, on the non-text document, further classification of non-text elements is applied to get separator regions, table regions, image regions, etc. The final stage, in refinement region and noise detection process, all regions both in the text document and non-text document are refined to eliminate noises and get the geometric layout of each region. The proposed method has been tested with the dataset of ICDAR2009 page segmentation competition and many other databases with different languages. The results of these tests showed that our proposed method achieves a higher accuracy compared to other methods. This proves the effectiveness and superiority of our method.

关键词： Job shop scheduling   Robustness index   Disruption   Branch and Bound   Particle swarm optimization  

摘要： Job shop scheduling problem is very important one in real application of many kind of industries. In the real world applications, there exist many different kinds of disruptions with different sizes. In this situation, beyond the optimality of the final solution, its ability to absorb disruptions is vital, so that the final solution remains feasible in the case of occurring predicted disruptions. In this paper a robust job shop scheduling problem under disruptions is considered. It is intended to generate robust schedules which are able to absorb a predefined range of disruptions. For this reason, two robustness indices are proposed and the related formulas for computing the required buffer times to reach the desired robustness level are proposed. For this purpose, four methods are proposed to solve the variant defined robust job shop scheduling problem, including (1) a mathematical model, (2) a Branch and Bound algorithm, (3) a beam search algorithm, and (4) a meta-heuristic algorithm based on the particle swarm optimization (PSO) method. The first and second methods result in optimum solution. As the size of the problem increases, the required time to find the optimum solutions raises, so that no solutions can be achieved in rational amount of time, e.g. one hour. Therefore, the third and fourth methods are proposed to find good solutions even for large-scale problem in a limited amount of time. Finally, the algorithms are compared using some randomly generated instances. The results show that each algorithm can outperform the others in different conditions. (C) 2016 Published by Elsevier Ltd.

关键词： Linear   Numerical   Multilinear algebra  

关键词： 人工智能   数学   建模  

摘要： 数学建模竞赛作为一项成功的数学教学改革实践,有效的促进了学生数学实践能力的提高以及对数学思想的探索,近年来,随着计算机技术及人工智能技术的飞速发展,人工智能算法在数学建模中得到了广泛的应用,智能算法的提出为数学建模的发展起到了至关重要的推动作用.

关键词： 云模型   贝叶斯网络   参数学习   离散化  

摘要： 针对贝叶斯网络连续节点离散化后,概念知识表达存在模糊性和随机性的问题,提出一种将云模型与EM(Expectations Maximization)算法相结合的贝叶斯网络参数学习算法。首先运用启发式高斯云变换算法(Heuristic Gaussian Cloud Transformation)和云发生器将连续节点定量样本转换成定性概念,并记录下样本对所属概念的确定度,运用确定度概率转换公式将确定度转换成相应概率;随后复制扩充样本并按概率选择所属概念;样本更新后结合EM算法进行参数优化,实现贝叶斯网络的参数学习。仿真实验结果表明,通过云模型表征概念得到的参数学习结果更加符合实际情况,参数学习精度和网络推理准确性得到了提高。

关键词： 杨辉算法   经济   南宋   计量数学  

摘要： 从经济史的角度重新解读《杨辉算法》,我们会发现南宋在许多经济领域都用到了计量数学,像各种形状的山田丈量方法、日常商业活动中的秤衡与斤两制度等。由于南宋地方政府与民间在较长时期内始终没有形成统一的秤衡与斤两制度,因而给南宋商业经济的发展造成了一定负面影响,而杨辉通过算题这种特殊媒介,以灵活多样的方式讨论了正斛法和零两求分定数等问题,从而对南宋计量数学的发展产生了积极影响。作为计量数学发展演变的重要阶段,南宋正好处于由筹算向珠算转变的历史时期,杨辉不遗余力地推广乘除捷法,以不断适应计量数学发展的客观需要。《杨辉算法》中的捷法运算对于现代基础数学与实用数学的发展仍具有一定参考价值。

关键词： 数学教学   算法   算理   融合   具体策略  

摘要： 小学生的数学计算能力在今后的学习中有着重要的影响力,关系着孩子的思维能力和学习习惯等。在目前的小学数学教学中,通过情景化和生活化的教学方式有效提升了学生数学计算的学习兴趣,但计算能力明显有所下降,其速度较慢、正确率不高。归总其原因发现,由于在日常教学中并没有将算理与算法的关系处理妥当,只注重计算结果,忽视了教学的算理。为此,本文围绕计算数学的重要性,简要分析了如何使小学数学算理和算法有效融合。

关键词： 数学模型   BP神经网络   权重   低通滤波   灰色模型  

摘要： 基于BP神经网络算法建立水资源评估数学模型。首先获得大量相关的评估指标,通过主成分分析法(PCA)剔除不重要指标。对于指标赋权,先用基于蒙特卡罗的层次分析法(AHP-MCA)初步给指标赋权,由于此法具有一定主观性,因此进一步采用BP神经网络算法对所赋权重进行训练调节,过程中需要一个标准比对物,最终得到符合实际情况的权重因子。在建立预测数学模型前,针对可能的突变输入数据,采用低通滤波器将突变高频数据过滤,增加模型适用性,最后通过灰色模型GM(1,1)建立预测模型。

关键词： 数学算法   计算机编程   优化   分析研究  

摘要： 随着科学技术的不断进步,社会发展的不断加快,使得社会发展的重心由以往的工业生产向高新的计算机领域发展。计算机在当今的发展中扮演着极为重要的作用,当前计算机软件多数是通过编程实现的,计算机编程的效果将对软件工作效率有着直接的影响。而数学算法是数学学科中的一项重要的内容,可以对问题进行归纳总结后加以解决。计算机技术中科学合理的应用数学算法对计算机编程的突破以及创新有着极大的推动作用。该文就编程中运用数学算法进行优化来分析,以期对有关人士在运用、开发、研究中有所借鉴意义。