A probabilistic clustering method for data elements with normal distributed attributes

By considering uncertainty in the attributes common methods cannot be applicable in data clustering. In the recent years, many researches have been done by considering fuzzy concepts to interpolate the uncertainty. But when data elements attributes have probabilistic distributions, the uncertainty cannot be interpreted by fuzzy theory. In this article, a new concept for clustering of elements with predefined probabilistic distributions for their attributes has been proposed, so each observation will be as a member of a cluster with special probability. Two metaheuristic algorithms have been applied to deal with the problem. Squared Euclidean distance type has been considered to calculate the similarity of data elements to cluster centers. The sensitivity analysis shows that the proposed approach will converge to the classic approaches results when the variance of each point tends to be zero. Moreover, numerical analysis confirms that the proposed approach is efficient in clustering of probabilistic data.     

An evaluation of the reconstructed coefficient of determination and potential adjustments

Previously, a method was proposed for calculating a reconstructed coefficient of determination in the case of right-censored regression using the expectation–maximization (EM) algorithm. This measure is assessed via simulation study for the purpose of evaluating the utility of model fit. Further, several reconstructed adjusted coefficients of determination are proposed and compared via simulation study for the purpose of model selection. The application of these proposed measures is illustrated on a real dataset.     

Parameter estimation of a composite production function model based on improved artificial fish swarm algorithm and model application

The traditional Cobb–Douglas production function uses the compact mathematical form to describe the relationship between the production results and production factors in the production technology process. However, in macro-economic production, multi-structured production exists universally. In order to better demonstrate such input–output relation, a composite production function model is proposed in this article. In aspect of model parameter estimation, artificial fish swarm algorithm is applied. The algorithm has satisfactory performance in overcoming local extreme value and acquiring global extreme value. Moreover, realization of the algorithm does not need the gradient value of the objective function. For this reason, it is adaptive to searching space. Through the improved artificial fish swarm algorithm, convergence rate and precision are both considerably improved. In aspect of model application, the composite production function model is mainly used to calculate economic growth factor contribution rate. In this article, a relatively more accurate calculating method is proposed. In the end, empirical analysis on economic growth contribution rate of China is implemented.     

A new family of multivariate slash distributions

In this article, a new form of multivariate slash distribution is introduced and some statistical properties are derived. In order to illustrate the advantage of this distribution over the existing generalized multivariate slash distribution in the literature, it is applied to a real data set.     

基于蚁群算法参数的最优选择问题研究

蚁群算法是受现实蚂蚁群体行为启发而得出的一类仿生算法。通过对蚁群算法中影响算法性能的参数进行分析和研究,并对蚁群算法中参数的最优选择问题进行实验分析,从而给出算法参数的最佳取值范围,以利于算法在实际问题中的应用和推广.     

MAP segmentation in Bayesian hidden Markov models: a case study

We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have Dirichlet priors. We study a training set consisting of thousands of protein alignment pairs. The training data is used to set the prior hyperparameters for Bayesian MAP segmentation. Since the Viterbi algorithm is not applicable any more, there is no simple procedure to find the MAP path, and several iterative algorithms are considered and compared. The main goal of the paper is to test the Bayesian setup against the frequentist one, where the parameters of HMM are estimated using the training data.     

一种求解双目标flow shop排序问题的进化算法

提出一种求解双目标flow shop排序的递进多目标进化算法.算法采用改进的精英复制策略,在实现精英保留的前提下降低了计算复杂性;通过递进进化模式增加群体多样性,改善了算法收敛性;通过群体进化过程中对非劣解集进行竞争型可变邻域启发式搜索,增强了算法局部搜索性能.采用新算法和参照算法NSGA-II对31个标准双目标flow shop算例进行优化.研究结果表明,新算法在所有算例的求解中均获得了优于NSGA-II的非劣解集,验证了算法的有效性.     

An oracle-based algorithm for robust planning of production routing problems in closed-loop supply chains of beverage glass bottles

The demand for glass bottles is exhibiting an upward trend over time. The manufacturing of glass bottles is costlier in terms of time and resources and is associated with a higher level of heat generation and environmental pollution compared to recycling processes. In response to the aforementioned challenges, companies that use glass bottles need to implement strategies to manage their reverse supply chains in conjunction with their traditional supply chains, as the economic and environmental benefits of returned products are unquestionable. Closed-loop supply chains (CLSCs) integrate forward and reverse flows of products and information. This integration helps companies to have a broader view of the whole chain. Despite these advantages, managing CLSCs can be challenging as they are exposed to many uncertainties regarding supply and demand processes, travel times, and quantity/quality of returned products.In this study, we consider the production planning, inventory management, and vehicle routing decisions of a CLSC of beverage glass bottles. We propose an MILP model and rely on a multi-stage adjustable robust optimization (ARO) formulation to deal with the randomness in both the demand for filled bottles and the requests for pickups of empty bottles. We develop an exact oracle-based algorithm to solve the ARO problem and propose a heuristic search algorithm to reduce the solution time. Our numerical experiments not only show the incompetency of the customary method, namely the affine decision rule approach, but also illustrate how our algorithms can solve the small-size problems and significantly improve the quality of the obtained solution for large problems. Furthermore, our numerical results show that robust plans tend to be sparse, meaning the routes are chosen so that empty bottles are transported to production sites in such a way that fewer new bottles need to be ordered. Thus, robust planning makes the CLSCs more environmentally friendly.     

A note on the monotonicity of the ES algorithm

In the study of the robust nonparametric regression problem, Oh et al. [The role of pseudo data for robust smoothing with application to wavelet regression, Biometrika 94 (2007), pp. 893–904] developed and named the ES algorithm. In the event that the ES algorithm converges, the robust estimator can be obtained through a sequence of conventional penalized least-squares estimates, the computation of which is fast and straightforward. However, the convergence of the ES algorithm was not established theoretically in Oh et al. In this note, we show that under a certain simple condition, the ES algorithm is monotonic. In particular, the ES algorithm does converge globally in the setting of Oh et al.     

基于高维分步投影的多重分区聚类算法

数据分布密度划分的聚类算法是数据挖掘聚类算法的主要方法之一。针对传统密度划分聚类算法存在运算复杂、运行效率不高等缺陷，设计高维分步投影的多重分区聚类算法；以高维分布投影密度为依据，对数据集进行多重分区，产生数据集的子簇空间，并进行子簇合并，形成理想的聚类结果；依据该算法进行实验，结果证明该算法具有运算简单和运行效率高等优良性。