Decomposition Method for Solving a Three-Index Planar Assignment Problem

Journal of Computer and Systems Sciences International - The classical assignment problem is considered. A third index is introduced, which can characterize, for example, the location of the work...     

Decomposition Algorithm for the Linear Three-Index Transportation Problem

Journal of Computer and Systems Sciences International - The method of sequential modification of an objective function, which was earlier used for the classical transportation problem, is extended...     

Solving Stochastic Transportation Network Protection Problems Using the Progressive Hedging-based Method

This research focuses on pre-disaster transportation network protection against uncertain future disasters. Given limited resources, the goal of the central planner is to choose the best set of network components to protect while allowing the network users to follow their own best-perceived routes in any resultant network configuration. This problem is formulated as a two-stage stochastic programming problem with equilibrium constraints, where the objective is to minimize the total expected physical and social losses caused by potential disasters. Developing efficient solution methods for such a problem can be challenging. In this work, we will demonstrate the applicability of progressive hedging-based method for solving large scale stochastic network optimization problems with equilibrium constraints. In the proposed solution procedure, we solve each modified scenario sub-problem as a mathematical program with complementary constraints and then gradually aggregate scenario-dependent solutions to the final optimal solution.     

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.     

The Decomposition Method For Solving Of A Class Of Singular Two-Point Boundary Value Problems

In this paper, a class of nonlinear singular two-point boundary value problems are solved by using Adomian's decomposition methods. The approximate solution of this problem is calculated in the form of series with easily computable components. Finally, we give a nonlinear numerical example.     

一种求解3-SAT问题的新方法

可满足性问题(SatisfiabilityProblem,SAT)是计算科学的典型问题之一,目前有DP算法、SAT1.3算法和遗传算法等多种求解方法。文章根据Kennedy和Eberhart提出的二进制粒子群优化算法(BinaryParticleSwarmOptimizers),基于局部随机搜索策略,给出了一种求解3-SAT问题的新方法:基于局部随机搜索的改进二进制粒子群优化算法(ModifedBinaryParticleSwarmOptimizersBasedonlocalstochasticsearch,简称MBPSO)。数值实验表明,对于随机产生的3-SAT问题测试实例,该算法是一种高效实用的新方法。     

A Mixed Closure-CSP Method for Solving Scheduling Problems

Scheduling problems can be viewed as a set of temporal metric and disjunctive constraints and so they can be formulated in terms of CSP techniques. In the literature, there are CSP-based methods which sequentially interleave search efforts with the application of consistency enforcing mechanisms and variable/ordering heuristics. Therefore, the number of backtrackings needed to obtain a solution is reduced. In this paper, we propose a new method that effectively integrates the CSP process into a limited closure process: not by interleaving them but rather as a part of the same process. Such an integration allows us to define more informed heuristics. These heuristics are used to limit the complete closure process to a maximum number of disjunctions, thereby reducing its complexity while at the same time reducing the search space. Some open disjunctive solutions can be maintained in the CSP process, limiting the number of backtrackings necessary, and avoiding having to know all the problem constraints in advance. Our experiments with flow-shop and job-shop instances show that this approach obtains a feasible solution/optimal solution without having to use backtracking in most cases. We also analyze the behaviour of our algorithm when some constraints are known dynamically and we demonstrate that it can provide better results than a pure CSP process.     

基于遗传算法求解约束优化问题的一种算法

在用遗传算法求解约束优化问题时,处理好约束条件是取得好的优化效果的关键.通过考虑遗传算法和约束优化问题的某些特点,提出将直接比较方法和在进化群体中自适应地保持不可行解比例的策略相结合来处理约束条件的一种新方法,并将该方法结合到通用的遗传算法中.数值实验显示了这种方法的有效性.     

Proper Generalized Decomposition Method for Solving Fisher-Type Equation and Heat Equation

A model reduction technique—the Proper Generalized Decomposition (PGD) for solving time dependent and multidimensional parameters is reviewed and applied to both the Fisher-type equations and the heat equation. Space-time discretization and separated representation technique for obtaining fast convergence computation while maintaining real time is detailed. Three situations of the Fisher-type equation are solved by the PGD and the results show a perfect agreement with the exact solutions. The source term of the heat equation is given a Huxley source and the thermal diffusivity is taken to be linearly dependent of the spatial parameter. The results show how the Fisher-type equation finds application to the heat equation and that the PGD method allows a perfect representation of the temperature distribution defined in a 5-D tensorial product space and time.     

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。     

A Multiquadric Interpolation Method for Solving Initial Value Problems

In this paper, an interpolation method for solving linear differential equations was developed using multiquadric scheme. Unlike most iterative formula, this method provides a global interpolation formula for the solution. Numerical examples show that this method offers a higher degree of accuracy than Runge-Kutta formula and the iterative multistep methods developed by Hyman (1978).     

Generalized Equivalence Set Method for Solving Multiobjective Optimization Problems

Journal of Computer and Systems Sciences International - Various aspects of solving multiobjective discrete optimization problems are considered. Advantages of the equivalence set method are shown...     

利用网格直接求解几何问题的方法

本文提出表示网格上图形的绝对方向法和相对方向法及其性质与转换。给出甩掉解析式直接用计算机检索以任意所需精度求解几何问题的方法,并解出任意曲线上的连杆曲线。     

求解最优控制问题的Chebyshev-Gauss伪谱法

提出了一种求解最优控制问题的Chebyshev-Gauss伪谱法, 配点选择为Chebyshev-Gauss点. 通过比较非线性规划问题的Kaursh-Kuhn-Tucker条件和伪谱离散化的最优性条件, 导出了协态和Lagrange乘子的估计公式. 在状态逼近中, 采用了重心Lagrange插值公式, 并提出了一种简单有效的计算状态伪谱微分矩阵的方法. 该法的独特优势是具有良好的数值稳定性和计算效率. 仿真结果表明, 该法能够高精度地求解带有约束的复杂最优控制问题.     

求解大规模非凸优化问题的多阶段MM方法

机器学习的主要目的是让计算机系统具有类似于人的学习能力,而数值优化方法对提高其效率,增强其效果有着举足轻重的作用.在L1-SVM优化问题中,可以利用截断Hinge损失剔除过多的支持向量,提高模型的鲁棒性.但却导致了棘手的非凸优化问题.MM(Majorization-Minimization,MM)是一种求解非凸问题的有...     

对基于稀疏矩阵分解求解约束系统方法的改进

采用基于稀疏矩阵分解的方法,可以把约束系统分解成依次求解的子约束集合,但有时并不能顺利求解,其子约束集合的雅可比矩阵非满秩。本文分析了出现这种状况的几种原因,提出可以采用对雅可比矩阵进行下三角化求秩的方法来消除冗余约束和冗余自由度,然后再使用基于稀疏矩阵分解的方法进行求解。     

A Nonoverlapping Domain Decomposition Method for Legendre Spectral Collocation Problems

We consider the Dirichlet boundary value problem for Poisson’s equation in an L-shaped region or a rectangle with a cross-point. In both cases, we approximate the Dirichlet problem using Legendre spectral collocation, that is, polynomial collocation at the Legendre–Gauss nodes. The L-shaped region is partitioned into three nonoverlapping rectangular subregions with two interfaces and the rectangle with the cross-point is partitioned into four rectangular subregions with four interfaces. In each rectangular subregion, the approximate solution is a polynomial tensor product that satisfies Poisson’s equation at the collocation points. The approximate solution is continuous on the entire domain and its normal derivatives are continuous at the collocation points on the interfaces, but continuity of the normal derivatives across the interfaces is not guaranteed. At the cross point, we require continuity of the normal derivative in the vertical direction. The solution of the collocation problem is first reduced to finding the approximate solution on the interfaces. The discrete Steklov–Poincaré operator corresponding to the interfaces is self-adjoint and positive definite with respect to the discrete inner product associated with the collocation points on the interfaces. The approximate solution on the interfaces is computed using the preconditioned conjugate gradient method. A preconditioner is obtained from the discrete Steklov–Poincaré operators corresponding to pairs of the adjacent rectangular subregions. Once the solution of the discrete Steklov–Poincaré equation is obtained, the collocation solution in each rectangular subregion is computed using a matrix decomposition method. The total cost of the algorithm is O(N ³), where the number of unknowns is proportional to N ².      

求解一类不可微优化问题的拟Powell方法

针对具有可微非线性约束的不可微非线性优化问题，分别定义一个子优化问题和相容非线性方程组求解问题，并利用相应的求解方法提供搜索方向，更新Ｐｏｗｅｌ方法的搜索方向，以极大地提高Ｐｏｗｅｌ方法的优化效率。算例表明了该方法的有效法。     

异构计算——求解超级问题的新途径

异构计算是近年来并行处理领域中新的研究热点。它的思想是充分利用一组汪同结构的高性能计算机求解含有不同并行性的超级问题。文中分析了异构计算的背景及特点，讨论了当前存在的问题。