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31.
旅行商问题的基因整合算法 总被引:3,自引:0,他引:3
本文针对旅行商问题提出了基因整合算法。它是通过设置扰动矩阵构造与原商问题等价的近似问题,使用最优罚函数选择回路分枝得到一系列局部最优回路,从中提取频度高的分技——基因进行整合,得到更优的回路。该算法计算量小,对大规模问题计算效果显著。利用该算法对CHN144问题给出了目前最件的结果。 相似文献
32.
结合新提出的满意度方法和混合整数规划方法,给出了多态不确定性环境下可再生能源规划模型.该模型综合描述了多地区、多时期、多品种、多部门之间的可再生能源管理系统的复杂性、系统性、动态性和不确定性.最后的实例求解结果说明该模型能很好地反映能源安全性、系统可靠性与系统成本之间的关系,并能给出不同系统违反水平下的能源配置方式及增容计划,为决策者提供决策参考. 相似文献
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给出了函数f(x)和g(x)单调性的证明.据此,得到了著名的Minc H和Sathre L不等式最好的界. 相似文献
35.
Integral representations are considered of solutions of the Airy differential equation w
–zw=0 for computing Airy functions for complex values of z. In a first method contour integral representations of the Airy functions are written as non-oscillating integrals for obtaining stable representations, which are evaluated by the trapezoidal rule. In a second method an integral representation is evaluated by using generalized Gauss–Laguerre quadrature; this approach provides a fast method for computing Airy functions to a predetermined accuracy. Comparisons are made with well-known algorithms of Amos, designed for computing Bessel functions of complex argument. Several discrepancies with Amos' code are detected, and it is pointed out for which regions of the complex plane Amos' code is less accurate than the quadrature algorithms. Hints are given in order to build reliable software for complex Airy functions. 相似文献
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After studying Gaussian type quadrature formulae with mixed boundary conditions, we suggest a fast algorithm for computing their nodes and weights. It is shown that the latter are computed in the same manner as in the theory of the classical Gauss quadrature formulae. In fact, all nodes and weights are again computed as eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. Hence, we can adapt existing procedures for generating such quadrature formulae. Comparative results with various methods now in use are given. In the second part of this paper, new algorithms for spectral approximations for second-order elliptic problems are derived. The key to the efficiency of our algorithms is to find an appropriate spectral approximation by using the most accurate quadrature formula, which takes the boundary conditions into account in such a way that the resulting discrete system has a diagonal mass matrix. Hence, our algorithms can be used to introduce explicit resolutions for the time-dependent problems. This is the so-called lumped mass method. The performance of the approach is illustrated with several numerical examples in one and two space dimensions.
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Let Z = {Z0, Z1, Z2,…} be a martingale, with difference sequence X0 = Z0, Xi = Zi ? Zi ? 1, i ≥ 1. The principal purpose of this paper is to prove that the best constant in the inequality λP(supi |Xi| ≥ λ) ≤ C supiE |Zi|, for λ > 0, is C = (log 2)?1. If Z is finite of length n, it is proved that the best constant is . The analogous best constant Cn(z) when Z0 ≡ z is also determined. For these finite cases, examples of martingales attaining equality are constructed. The results follow from an explicit determination of the quantity Gn(z, E) = supzP(maxi=1,…,n |Xi| ≥ 1), the supremum being taken over all martingales Z with Z0 ≡ z and E|Zn| = E. The expression for Gn(z,E) is derived by induction, using methods from the theory of moments. 相似文献
40.
Recently, Gill and Chien introduced a new radial quadrature for multiexponential integrands (MultiExp grid) to deal with the radial part of the numerical integration. In this article, the MultiExp grid is studied and used to integrate the charge density. The MultiExp grid, along with an optimal pruning scheme, performed very well both in terms of accuracy and efficiency compared to other radial mappings commonly used in Density Functional Theory. 相似文献