Decomposition Method for Solving Three-Index Transportation Problems

A decomposition method based on the sequential modification of the optimality criterion is used for solving the classical three-index transportation problem. The method consists of a sequence of solutions of local problems with three constraints. A monotonic (in the optimality criterion) process that converges to the solution of the original problem is constructed. The solutions of the transportation problem with a linear and quadratic objective function are considered and the numerical results are presented.     

Denoising Stochastic Progressive Photon Mapping Renderings Using a Multi-Residual Network

Journal of Computer Science and Technology - Stochastic progressive photon mapping (SPPM) is one of the important global illumination methods in computer graphics. It can simulate caustics and...     

运输问题的神经网络解法

给出了利用Hopfield连续模型求解运输问题的数值算法,是对运筹学知识的补充和完善,是借助人工神经网络计算机原理解决组合优化问题的一个成功范例。     

流通网络中随机流动的仿真研究

堵塞流是指网络在堵塞情况下通过网络的最大流量，而网络最小流量是网络在最严重堵塞情况下通过网络的最大流量。研究表明，很难从理论上确定一个网络的最小流的准确数值，因此必须借助网络的随机流动仿真试验。本文通过建立流通网络中的随机流动仿真模型来研究一般网络中的堵塞现象及堵塞流运动规律。探索了堵塞流值的概率分布规律，提出了流通网络在随机流动情况下的流通能力的新概念，并证明了作者提出的网络最小流算法的正确性。     

A Numerical Method for Solving Stochastic Optimal Control Problems with Linear Control

We introduce a numerical method to solve stochastic optimal control problems which are linear in the control. We facilitate the idea of solving two-point boundary value problems with spline functions in order to solve the resulting dynamic programming equation. We then show how to effectively reduce the dimension in the proposed algorithm, which improves computational time and memory constraints. An example, motivated as an invest problem with uncertain cost, is provided, and the effectiveness of our method demonstrated.     

Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network

In recent years, a recurrent neural network called projection neural network was proposed for solving monotone variational inequalities and related convex optimization problems. In this paper, we show that the projection neural network can also be used to solve pseudomonotone variational inequalities and related pseudoconvex optimization problems. Under various pseudomonotonicity conditions and other conditions, the projection neural network is proved to be stable in the sense of Lyapunov and globally convergent, globally asymptotically stable, and globally exponentially stable. Since monotonicity is a special case of pseudomononicity, the projection neural network can be applied to solve a broader class of constrained optimization problems related to variational inequalities. Moreover, a new concept, called componentwise pseudomononicity, different from pseudomononicity in general, is introduced. Under this new concept, two stability results of the projection neural network for solving variational inequalities are also obtained. Finally, numerical examples show the effectiveness and performance of the projection neural network     

A Benders Decomposition Method for Solving Stochastic Complementarity Problems with an Application in Energy

In this paper we present a new Benders decomposition method for solving stochastic complementarity problems based on the work by Fuller and Chung (Comput Econ 25:303–326, 2005; Eur J Oper Res 185(1):76–91, 2007). A master and subproblem are proposed both of which are in the form of a complementarity problem or an equivalent variational inequality. These problems are solved iteratively until a certain convergence gap is sufficiently close to zero. The details of the method are presented as well as an extension of the theory from Fuller and Chung (2005, 2007). In addition, extensive numerical results are provided based on an electric power market model of Hobbs (IEEE Trans Power Syst 16(2):194–202, 2001) but for which stochastic elements have been added. These results validate the approach and indicate dramatic improvements in solution times as compared to solving the extensive form of the problem directly.     

利用串行最小优化算法求解回归估计问题

支撑矢量机是以Vapnik的统计学习理论为基础,以结构风险最小化为原则的新型学习机。目前,对它的研究是国际上的一个研究热点。针对大数据量的回归估计问题,论文提出了一种新的求解方法。为了说明该方法的有效性,给出了数值模拟的例子。     

采用分数阶动量的卷积神经网络随机梯度下降法

针对随机梯度下降法可能会收敛到局部最优的问题,文中提出采用分数阶动量的随机梯度下降法,提高卷积神经网络的识别精度和学习收敛速度.结合基于动量的随机梯度下降法和分数阶差分运算,改进参数更新方法,讨论分数阶阶次对网络参数训练效果的影响,给出阶次调整方法.在MNIST、CIFAR-10数据集上的实验表明,文中方法可以提高卷积神经网络的识别精度和学习收敛速度.     

Solving Fixed Final Time Fractional Optimal Control Problems Using the Parametric Optimization Method

In this paper, the parametric optimization method is used to find optimal control laws for fractional systems. The proposed approach is based on the use for the fractional variational iteration method to convert the original optimal control problem into a nonlinear optimization one. The control variable is parameterized by unknown parameters to be determined, then its expression is substituted into the system state‐space model. The resulting fractional ordinary differential equations are solved by the fractional variational iteration method, which provides an approximate analytical expression of the closed‐form solution of the state equations. This solution is a function of time and the unknown parameters of the control law. By substituting this solution into the performance index, the original fractional optimal control problem reduces to a nonlinear optimization problem where the unknown parameters, introduced in the parameterization procedure, are the optimization variables. To solve the nonlinear optimization problem and find the optimal values of the control parameters, the Alienor global optimization method is used to achieve the global optimal values of the control law parameters. The proposed approach is illustrated by two application examples taken from the literature.     

Adaptive Park-and-ride Choice on Time-dependent Stochastic Multimodal Transportation Network

In transportation networks with stochastic and dynamic travel times, park-and-ride decisions are often made adaptively considering the realized state of traffic. That is, users continue driving towards their destination if the congestion level is low, but may consider taking transit when the congestion level is high. This adaptive behavior determines whether and where people park-and-ride. We propose to use a Markov decision process to model the problem of commuters’ adaptive park-and-ride choice behavior in a transportation network with time-dependent and stochastic link travel times. The model evaluates a routing policy by minimizing the expected cost of travel that leverages the online information about the travel time on outgoing links in making park-and-ride decisions. We provide a case study of park-and-ride facilities located on freeway I-394 in Twin Cities, Minnesota. The results show a significant improvement in the travel time by the use of park-and-ride during congested conditions. It also reveals the time of departure, the state of the traffic, and the location from where park-and-ride becomes an attractive option to the commuters. Finally, we show the benefit of using online routing in comparison to an offline routing algorithm.

     

一种减小方差求解非光滑问题的随机优化算法

随机优化算法是求解大规模机器学习问题的高效方法之一.随机学习算法使用随机抽取的单个样本梯度代替全梯度,有效节省了计算量,但却会导致较大的方差.近期的研究结果表明:在光滑损失优化问题中使用减小方差策略,能够有效提高随机梯度算法的收敛速率.考虑求解非光滑损失问题随机优化算法COMID(compositeobjective mirror descent)的方差减小问题.首先证明了COMID具有方差形式的O(1/√T+σ²/√T)收敛速率,其中,T是迭代步数,σ²是方差.该收敛速率保证了减小方差的有效性,进而在COMID中引入减小方差的策略,得到一种随机优化算法α-MDVR(mirror descent with variance reduction).不同于Prox-SVRG(proximal stochastic variance reduced gradient),α-MDVR收敛速率不依赖于样本数目,每次迭代只使用部分样本来修正梯度.对比实验验证了α-MDVR既减小了方差,又节省了计算时间.     

A Genetic Algorithm Approach to Solving Stochastic Job-shop Scheduling Problems

This paper proposes a method for solving stochastic job-shop scheduling problems based on a genetic algorithm. The genetic algorithm was expanded for stochastic programming. In this expansion, the fitness function is regarded as representing fluctuations that may occur under stochastic circumstances specified by the distribution functions of stochastic variables. In this study, the Roulette strategy is adopted for selecting the optimum solution in terms of the expected value. Within this algorithm, it is expected that the individual that appears most frequently must give the optimum solution. The effectiveness of this approach is confimed by applying it to stochastic job-shop scheduling problems. I compare the approximately optimum solutions found by this approach with the truly or approximately optimum solutions obtained by other conventional methods, and discuss the performance and effectiveness of this approach.     

分层递进的改进聚类蚁群算法解决TSP问题*

随着旅行商问题(TSP)规模的增大,传统蚁群算法的运行时间会增大,算法的解精度也会降低,并且算法很容易陷入局部最优的情况。提出的分层递进算法的思想源于分工合作的产品线组装流程,首先利用改进的密度峰聚类算法确定拐点,从而选举出聚类中心,根据聚类中心确定包含的数据点;其次将初始的TSP问题分割成较小的簇,这些簇称为二类TSP问题;再经自适应信息素更新策略的蚁群算法运算,找出每个簇的最优解,进一步将簇与簇之间相近的节点构成的边断开;然后两簇之间断开的节点重组成全局最优解;最终通过局部优化策略对重组的优化解进一步优化,从而在保证算法解质量的前提下有效地缩短了运行时间。从TSPLIB中选取小规模、大规模基准案例,通过Matlab仿真验证了改进算法具有更好的鲁棒性,特别是在大规模基准案例中显著地减少了算法运行时间。     

用双目标加权遗传算法解决网络磁盘阵列系统下校验散布布局优化问题的研究

廉价磁盘冗余阵列(RAID)作为一种提高存储系统可靠性和性能的技术,已经得到了广泛的应用,有关磁盘阵列结构和数据布局的研究也一直很活跃,但有关网络磁盘阵列下的数据布局的研究还不太多。本文首先概述了校验散布布局的技术和遗传算法的相关知识,提出了利用双目标加权遗传算法的思想解决网络磁盘阵列系统校验散布布局优化的问题。然后以“重构负截均匀分布”和“校验均匀分布”为双目标,使用改变的NSGA来解决网络磁盘阵列系统下校验散布布局的优化问题。最后给出了实验结果。     

利用改进的随机松弛法求解旅行商问题

旅行商问题是一个典型的组合优化问题,也是多种复杂问题的一种简化形式.因此,寻求一种有效的算法来求解此问题成为研究热点.随机松弛法是一种基于Metropolis迭代法求解的启发式随机搜索算法.针对该算法在求解旅行商问题时,存在易陷入局部最优的缺点,本文提出了三种不同的改进方法.即就是说,在解变换产生新解的过程中,首先,随机选择三个城市.然后,分别给出了三种不同的随机处理方法.最后,在仿真研究中,与已有方法相比,结果表明所给的三种方法的路径更短,结果更优.     

应用罚函数求解二层线性优化问题的全局优化方法

应用罚函数原理，将二层线性优化问题转化为目标函数带有罚函数子项的非线性优化问题，当罚系数大于某一数值时，库函数项为一精确项，该非线性优化问题用渐的进外逼近算法可求出其全局最优解。     

用后继序列法解决堆栈输出问题

在实际应用中经常需要生成一些满足某种条件的数值序列，产生序列往往用递归方法．本文首先介绍一种序列生成方法一后继序列法，说明了其实现步骤．比较而言，该法更简单有效，易于理解，有通用性．然后将这种方法用于解决具有典型意义的堆栈输出问题，得到了两种精巧的算法．