安全约束条件下的经济调度优化模型研究

发电侧放开竞争的电力系统需要更加有效、准确的决策工具对有限的资源进行调度规划。短期经济调度优化问题是一个混合整数非线性规划问题,很难得到有效最优解,尤其是对于大规模电力系统。为了提高求解效率,本文提出了一个考虑安全约束的经济调度优化模型(Security-Constrained Economics Dispatch,SCED),主要采用线性化思想处理经济调度优化问题的模型以及各种约束,采用基于校正的交替求解方法,使得调度优化结果在运行成本最小化的前提下满足系统的安全稳定约束。同时,将本文方法运用到IEEE 30节点系统进行测试,从而验证本文方法有效性。     

关于波动方程混合问题的特征线方法

传统的求解1维波动方程混合问题的方法是分离变量法，进而解出该问题的Fourier级数解，本文将用特征线方法给出该问题在求解区域内解的显式表达式。     

无重叠区的双抓钩周期性排序问题的求解

在当今的自动化制造系统中，计算机控制的抓钩的排序直接影响系统的生产率。本文研究了产品在系统的一边装载、而在另一边卸载的电镀线周期性排序问题。工件在每个工作站的处理时间在给定时间范围内，工作站之间没有缓冲槽，相同轨道上的两个抓钩用于工作站之间工件的运送，目标是对运送进行排序以极小化生产周期。为了求解这个问题，本文提出一个求解方法，所提出的方法首先将生产线分为两个无重叠的区域，并且为每个区域分配一个抓钩，然后，提出了一个给定抓钩分配下的混合整数线性规划模型。通过求解不同抓钩分配下模型的最优解，并且选择这些解中最好的一个，以便得到最优解，一个标杆示例被运行，以表明该方法的应用。另外，给出有多重处理槽工序问题的模型和求解方法。     

A QP-FREE AND SUPERLINEARLY CONVERGENT ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATIONS

1 IntroductionConsider tl1e optimizatioll problemndn{f(x): gj(x) 5 0, j e I, x E R"}, j1)where f(x), gj(x): R" - R, j E I = {l,2,...,m}.We know tl1e quasi-Newton meth.d[1]'[9]1[5]1[1O1 is one of the most effective methods to solveproblenl (1) due to its property of superlinear convergence and is still all hot topic at presenttime, which attracts a Iot of authors to make iInprovemellt both in theory a1ld app1ication.Fechinei and Lucidi[3] in 1995 proposed a locally superlinearly convergell…     

A relaxed extragradient-like method for a generalized mixed equilibrium problem,a general system of generalized equilibria and a fixed point problem

Very recently, Takahashi and Takahashi [S. Takahashi, W. Takahashi, Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space, Nonlinear Anal. 69 (2008) 1025–1033] suggested and analyzed an iterative method for finding a common solution of a generalized equilibrium problem and a fixed point problem of a nonexpansive mapping in a Hilbert space. In this paper, based on Takahashi–Takahashi’s iterative method and well-known extragradient method we introduce a relaxed extragradient-like method for finding a common solution of a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem of a strictly pseudocontractive mapping in a Hilbert space and then obtain a strong convergence theorem. Utilizing this theorem, we establish some new strong convergence results in fixed point problems, variational inequalities, mixed equilibrium problems and systems of generalized equilibria.     

解重调和问题混合有限元方程的直接方法

§1.引言 考虑如下重调和方程的齐次边值问题: △~2w=f,在Ω中, w=?w/?v=0,在Ω上.(1.1)其中Ω是平面凸多边形区域,?Ω是Ω的边界,?/?v表示?Ω上的外法向导数.     

对角形拟线性椭圆方程组的一般特征问题

本文对拟线性椭圆方程组的一般特征问题得到极小解在L∞中的界,并利用变分方法证明了它的极小解的存在性.     

混合单调算子的不动点存在唯一性定理及其应用

本文首先讨论了一类混合单调算子方程组解的存在唯一性及非对称迭代逼近问题,得到了若干不具有连续性和紧性条件的有关混合单调算子、增算子和减算子的新不动点定理.其次研究了具有a-凹和-a-凸的不具有连续性和紧性条件的混合单调算子的不动点,并得到了一个新结果.最后,我们将所得结果应用于RN上的Hammerstein积分方程之中(参见文[1-12]).     

弹性接触问题的一种新的混合变分形式

1．引言用混合有限元方法求解弹性力学问题,其优点在于可同时求解位移和应力．力学问题的混合变分形式是混合有限元方法的基础．对于弹性接触问题,文献问给出了一种混合变分形式,以及相应的混合有限元分析（也可见[6]）．本文考虑了弹性接触问题的一种新的混合变分形式,它是构造弹性接触问题的另一种混合有限元方法的基础．对于通常的静态弹性力学方程组的边界值（等式情形）问题,熟知可以有二种不同的混合变分形式（例如见门）．第一种混合变分形式中,对位移的求解空间为H‘（刚,对应力的求解空间为L‘（刚;而第二种混合变分形式…     

A New 4× 4 AKNS Spectral Problem and Its Associated Integrable Decomposition of the AKNS Equation

A new approach to construct a new 4 × 4 matrix spectral problem from a normal 2 × 2 matrix spectral problem is presented. AKNS spectral problem is discussed as an example. The isospectral evolution equation of the new 4 × 4 matrix spectral problem is nothing but the famous AKNS equation hierarchy. With the aid of the binary nonlinoearization method, the authors get new integrable decompositions of the AKNS equation.In this process, the r-matrix is used to get the result.     

混沌优化算法在不可分稳态大系统优化中的应用

讨论了整体目标函数关于各子系统不具有可加形式的大规模稳态系统的优化问题,将混沌优化算法应用于其最优值的求解,利用混沌运动的遍历性来得到优化问题的全局最优值.仿真结果表明,该算法简单易行,求解精度和可靠性较高,是解决不可分稳态大系统优化问题的一种有效方法.     

A New 4 × 4 AKNS Spectral Problem and Its Associated Integrable Decomposition of the AKNS Equation

A new approach to construct a new 4×4 matrix spectral problem from a normal 2×2 matrix spectral problem is presented.AKNS spectral problem is discussed as an example.The isospectral evolution equation of the new 4×4 matrix spectral problem is nothing but the famous AKNS equation hierarchy.With the aid of the binary nonlino earization method,the authors get new integrable decompositions of the AKNS equation. In this process,the r-matrix is used to get the result.     

Multiple homoclinic orbits for a class of Hamiltonian systems

In this paper, we obtain the existence of at least two nontrivial homoclinic orbits for a class of second order autonomous Hamiltonian systems. This multiplicity result is obtained by a new variational method based on the relative category: to overcome the lack of compactness of the problem, we first solve perturbed nonautonomous problems and study the limit of the solutions as the nonautonomous perturbation goes to 0. This method allows to get rid of some assumptions on the potential used in the work of Ambrosetti and Coti-Zelati. Received August 9, 1999 / Accepted September 7, 1999 / Published online September 14, 2000     

Finding all solutions of separable systems of piecewise-linear equations using integer programming

Finding all solutions of nonlinear or piecewise-linear equations is an important problem which is widely encountered in science and engineering. Various algorithms have been proposed for this problem. However, the implementation of these algorithms are generally difficult for non-experts or beginners. In this paper, an efficient method is proposed for finding all solutions of separable systems of piecewise-linear equations using integer programming. In this method, we formulate the problem of finding all solutions by a mixed integer programming problem, and solve it by a high-performance integer programming software such as GLPK, SCIP, or CPLEX. It is shown that the proposed method can be easily implemented without making complicated programs. It is also confirmed by numerical examples that the proposed method can find all solutions of medium-scale systems of piecewise-linear equations in practical computation time.     

初值的导数具有紧支集的对角形双曲组Cauchy问题经典解的整体存在唯一性

本文研究了初值导数具有紧支集的对角形严格双曲组Cauchy问题在t>0上的经典解的整体存在唯一性,以及在最大特征的决定区域内的较一般的非严格双曲组的初值是在x≥0半轴上给定的,并且初值具有紧支集的Cauchy问题的经典解的整体存在唯一性.文中主要使用了特征线方法和解的一致先验估计方法.     

BLOW-UP OF THE SOLUTION FOR A KIND OF HIGHER ORDER HYPERBOLIC EVOLUTION SYSTEMS

In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher nonlinear hyperbolic evolution equation in finite time. By introducing the "blow-up factor K(u,ut)" we get some new results, which generalize the conclusions of [3] and [4].     

A post-improvement procedure for the mixed load school bus routing problem

This paper aims to develop a mixed load algorithm for the school bus routing problem (SBRP) and measure its effects on the number of required vehicles. SBRP seeks to find optimal routes for a fleet of vehicles, where each vehicle transports students from their homes and to their schools while satisfying various constraints. When mixed load is allowed, students of different schools can get on the same bus at the same time. Although many of real world SBRP allow mixed load, only a few studies have considered these cases. In this paper, we present a new mixed load improvement algorithm and compare it with the only existing algorithm from the literature. Benchmark problems are proposed to compare the performances of algorithms and to stimulate other researchers’ further study. The proposed algorithm outperforms the existing algorithm on the benchmark problem instances. It has also been successfully applied to some of real-world SBRP and could reduce the required number of vehicles compared with the current practice.     

Cauchy problem for the generalized Davey-Stewartson systems in Besov spaces and some counterexamples

In this paper, the Cauchy problem of the generalized ellipse-ellipse type Davey-Stewartson systems is discussed. When the dimension of space is greater than or equal to two, we get a unique global solution in Besov spaces by contraction mapping argument. Moreover, by using the F-expansion method, the exact periodic wave solutions for the generalized ellipse-ellipse type Davey-Stewartson systems are discussed, some counter examples are given.     

SEMI-GLOBAL $C^1$ SOLUTION TO THE MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

By means of an equivalent invariant form of boundary conditions, the authors get the existence and uniqueness of semi-global C^1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with general nonlinear boundary conditions.     

线性对流占优扩散方程的扩展特征混合有限元法

本文针对线性对流占优扩散方程提出了一种新型数值模拟方法一扩展特征混合有限元法,即对对流部分沿特征线方向离散,而对扩散部分采用扩展混合有限元方法,同时高精度逼近未知函数,未知函数的梯度及伴随向量函数,通过严格的数值分析,得到其最优L^2模误差估计。