重大事故规避的危险品运输车辆路径优化研究

基于重大事故规避的思想,建立以最大事故后果最小及运输成本最小为双目标,且事故后果基于实时装载量的危险品运输车辆路径优化模型。基于ε-约束法,设计可求得帕累托最优解的精确算法,该算法包含通过性质求ε下界、规避被支配解的预处理及不可行路径禁止约束3处改进。进一步设计处理大规模问题的多项式时间近似算法,并分析了算法的近似比。最后通过算例对模型和算法进行测试,并通过出灵敏度分析给出管理启示。     

关于ε不敏感损失函数推广误差的界

本文研究了学习理论中推广误差的界的问题.利用ε不敏感损失函数的性质,分别获得r逼近误差和估计(样本)误差的界,并在特定的假设空间上得到了学习算法推广误差的界.     

考虑框架协议的动态报童模型强化学习建模研究

企业为了稳定货源和供货关系,常与供应商签订一定时期的框架性协议。为了解决零售商在框架协议下采购报童产品的问题,本文运用强化学习建立库存决策模型并使用Q学习算法求取较优订货策略。通过生成样本随机数来模拟需求量,对比研究Q学习算法订货和传统方法订货的差别。通过多次数值实验,发现使用强化学习方法订货相比于传统订货方法(定量订货法、移动平均预测、指数平滑法)平均利润提高约7%~22%,且多次实验下强化学习方法订货相比于理想状态的平均利润相差约8%。这些发现验证了强化学习解决库存问题的有效性和可行性。本文还研究了相关参数变化对总利润的影响,发现利润随着贪婪率(ε)增加而降低、随着学习率(α)的增加而增加。该结论能够为解决相关库存问题提供新的思路。     

函数型数据支持向量回归

函数型数据回归是一个非常有意义的课题.已有工作都是利用平方损失来衡量误差,而本文采用ε-不敏感损失来衡量误差.本文构造基于ε-不敏感损失的逼近元,给出表示形式及其系数计算.逼近元具有鲁棒性和稀疏性等性质.本文的主要结果是,在一些常规条件下建立预测误差收敛阶.与关于平方损失工作相比,我们不要求协方差算子与积分算子之间的"对齐"关系.此外,本文还讨论了支持向量回归函数本身的逼近性质.即使对有限维数据,关于这方面的结果在文献中也尚未见到.     

基于拟凸损失的核正则化成对学习算法的收敛速度

核正则化排序算法是目前机器学习理论领域讨论的热点问题,而成对学习算法是排序算法的推广.文章给出一种基于拟凸损失的核正则化成对学习算法,利用拟凸分析理论对该算法进行误差分析,给出算法的收敛速度.分析结果表明,算法的样本误差与损失函数中的参数选择有关.数值实验结果显示,与基于最小二乘损失的排序算法相比较,该算法有更稳健的学习性能.     

装备维修器材生产路径双目标问题优化决策方法研究

在装备维修器材供应保障中,针对精确保障背景下部队用户对器材保障精度的要求,构建了最小化总成本和最大化订单精准执行率的双目标优化决策模型。在ε-约束法框架内,开发可生成近似Pareto前沿的两阶迭代启发式算法,并采用模糊逻辑决策法选择符合决策者偏好的折中最优解。随机实例测试结果表明所提出的模型和算法可以很好地应用在双目标优化问题的研究中,并在求解不同规模实例时表现出优异的性能。     

基于线性ν-支持向量回归机的异常数据检测

讨论了线性v-支持向量回归机中参数v的意义,并给出了严格的理论证明。利用v-支持向量回归机中ε-不敏感损失函数及参数v的意义,提出一种回归数据中的异常值检测方法。采用线性模型使得该方法不仅速度快而且能处理大规模数据。数值实验证明其具有可行性和有效性。     

不确定性下的一主多从博弈及其ε-平衡稳定性分析

本文对主从博弈以及不确定性等问题进行研究,建立了不确定性下的一主多从博弈模型,并利用极大值定理证明了该模型均衡点的存在性。对于不确定性下的一主多从博弈的均衡点问题建立了有限理性模型,进而得到其均衡点的稳定性,即结构稳定以及对ε-平衡是鲁棒的。     

求解双层规划的多目标布谷鸟算法

双层规划是一类具有主从递阶结构的优化问题,属于NP-hard范畴。本文利用KKT条件将双层规划问题转化为等价的单层约束规划问题,通过约束处理技术进一步转化为带偏好双目标无约束优化问题,提出多目标布谷鸟算法求解策略。该算法采用Pareto支配和ε-个体比较准则,充分利用种群中优秀不可行解的信息指导搜索过程;设置外部档案集存储迭代过程中的优秀个体并通过高斯扰动改善外部档案集的质量,周期性替换群体中的劣势个体,引导种群不断向可行域或最优解逼近。数值实验及其参数分析验证了算法的有效性。     

分维权重样条插值预测算法及应用

基于高维数据预测方法的应用,提出一种分维权重样条插值预测算法.通过高维数据的各维,建立样本各维数据与对应权重的网络结构关系,网络的结点个数与样本的个数无关.通过训练样本各维权重所满足的线性方程组得到各维的权值,再根据样本的各维数据值和所得到的对应权值进行三次样条插值,得到各维数据值的权值函数,而不是传统方法的常数,这克服了个别数据变化所带来的整体度量值发生较大变化的缺点.数值仿真实验表明:分维权重样条插值预测算法不失是一种稳定而灵活的算法,而且预测的精度较高,可以根据样条插值函数得到样本各维的权值.     

资源受限下森林火灾应急救援多目标调度优化

许多森林火灾由于救援资源受限而不能在第一时间扑灭,导致火灾扩大蔓延,进而造成更大的森林资源损失。因此,在救援资源受限情形下,如何对消防救援车辆进行合理的调度安排以快速和低成本地扑灭火灾已成为亟待解决的现实问题。本文研究了一类资源受限下森林火灾应急救援多目标调度优化问题,为该问题构建了多目标混合整数非线性规划模型,优化目标为同时最小化总灭火救援时间和救援车辆总行驶距离。为有效求解该问题,首先将上述非线性模型等价转化为线性模型。然后提出ε-约束法和模糊逻辑相结合的算法对问题进行求解。最后,以大兴安岭山发生的火灾案例和随机生成仿真算例对模型和算法有效性进行验证,结果表明所提出的模型和算法能够有效解决资源受限下森林火灾应急救援问题,并为决策者提供最优的消防调度方案。     

Robust algorithms for multiphase regression models

This paper proposes a robust procedure for solving multiphase regression problems that is efficient enough to deal with data contaminated by atypical observations due to measurement errors or those drawn from heavy-tailed distributions. Incorporating the expectation and maximization algorithm with the M-estimation technique, we simultaneously derive robust estimates of the change-points and regression parameters, yet as the proposed method is still not resistant to high leverage outliers we further suggest a modified version by first moderately trimming those outliers and then implementing the new procedure for the trimmed data. This study sets up two robust algorithms using the Huber loss function and Tukey's biweight function to respectively replace the least squares criterion in the normality-based expectation and maximization algorithm, illustrating the effectiveness and superiority of the proposed algorithms through extensive simulations and sensitivity analyses. Experimental results show the ability of the proposed method to withstand outliers and heavy-tailed distributions. Moreover, as resistance to high leverage outliers is particularly important due to their devastating effect on fitting a regression model to data, various real-world applications show the practicability of this approach.     

Low-rank elastic-net regularized multivariate Huber regression model

Heavy-tailed noise or strongly correlated predictors often go with the multivariate linear regression model. To tackle with these problems, this paper focuses on the matrix elastic-net regularized multivariate Huber regression model. This new model possesses the grouping effect property and the robustness to heavy-tailed noise. Meanwhile, it also has the ability of reducing the negative effect of outliers due to Huber loss. Furthermore, an accelerated proximal gradient algorithm is designed to solve the proposed model. Some numerical studies including a real data analysis are dedicated to show the efficiency of our method.     

Duality results and proximal solutions of the Huber M-estimator problem

We investigate the interest of solving the Huber M-estimator problem by a proximal approach combined with duality theory. Three different duality schemes are developed. The first one which only deals with estimator determination yields useful information on the geometrical structure of the set of optimal solutions. The second scheme links together estimator determination and outliers detection while the third one only focuses on outliers separation. We show that these three duality schemes can be solved by the partial inverse method, i.e., a special instance of the basic proximal point algorithm, which leads to very simple updating rules. This method which is always globally convergent enjoys nice stability properties and permits parallel computations.     

Robust support vector regression with generic quadratic nonconvex ε-insensitive loss

In this paper, we propose a robust support vector regression with a novel generic nonconvex quadratic ε-insensitive loss function. The proposed method is robust to outliers or noise since it can adaptively control the loss value and decrease the negative influence of outliers or noise on the decision function by adjusting the elastic interval parameter and adaptive robustification parameter. Given the nature of the nonconvexity of the optimization problem, a concave-convex programming procedure is employed to solve the proposed problem. Experimental results on two artificial data sets and three real-world data sets indicate that the proposed method outperforms support vector regression, L₁-norm support vector regression, least squares support vector regression, robust least squares support vector regression, and support vector regression with the Huber loss function on both robustness and generalization ability.     

Functional linear regression with Huber loss

In this paper, we consider the robust regression problem associated with Huber loss in the framework of functional linear model and reproducing kernel Hilbert spaces. We propose an Ivanov regularized empirical risk minimization estimation procedure to approximate the slope function of the linear model in the presence of outliers or heavy-tailed noises. By appropriately tuning the scale parameter of the Huber loss, we establish explicit rates of convergence for our estimates in terms of excess prediction risk under mild assumptions. Our study in the paper justifies the efficiency of Huber regression for functional data from a theoretical viewpoint.     

Linear scaling and the DIRECT algorithm

In this paper, we discuss the performance of the DIRECT global optimization algorithm on problems with linear scaling. We show with computations that the performance of DIRECT can be affected by linear scaling of the objective function. We also provide a theoretical result which shows that DIRECT does not perform well when the absolute value of the objective function is large enough. Then we present DIRECT-a, a modification of DIRECT, to eliminate the sensitivity to linear scaling of the objective function. We prove theoretically that linear scaling of the objective function does not affect the performance of DIRECT-a. Similarly, we prove that some modifications of DIRECT are also unaffected by linear scaling of the objective function, while the original DIRECT algorithm is sensitive to linear scaling. Numerical results in this paper show that DIRECT-a is more robust than the original DIRECT algorithm, which support the theoretical results. Numerical results also show that careful choices of the parameter ε can help DIRECT perform well when the objective function is poorly linearly scaled.     

Homogenization of Elliptic Problems with Neumann Boundary Conditions in Non-smooth Domains

We consider a family of second-order elliptic operators {L_ε} in divergence form with rapidly oscillating and periodic coefficients in Lipschitz and convex domains in R~n. We are able to show that the uniform W~(1,p) estimate of second order elliptic systems holds for 2n/(n+1)-δ p 2n/(n-1)+ δ where δ 0 is independent of ε and the ranges are sharp for n = 2, 3. And for elliptic equations in Lipschitz domains, the W~(1,p) estimate is true for 3/2-δ p 3 + δ if n ≥ 4, similar estimate was extended to convex domains for 1 p ∞.