结点有约束的交通网络最短路径模型

结点有约束的网络是一类特殊的网络，如具有禁止通行限制信息的交通路网等，由于最短路径的求解是有后效性的，经典的Dijkstra算法等不能直接用来求解该问题，本文提出了一种结点有约束的交通网络最短路径建模方法，该方法所建模型为一般网络模型，可用任一传统高效的算法求其最短路径，从根本上降低了问题的复杂性，为很好地解决交通、通信等领域中的此类问题提供了有益的方法。     

考虑路线复杂度的应急疏散双目标路径选择模型

针对路径选择这一疏散计划中最基本的问题，考虑疏散时间以及路线复杂度因素，建立了应急疏散路径选择的双目标优化模型。模型将总疏散时间最短以及路线复杂度最低作为优化目标，同时考虑灾害扩散对疏散网络通行状况的实时影响，将各弧段上的通行速度表示为随时间的连续递减函数。设计了求解模型的蚁群优化算法，仿真结果表明了模型和算法的有效性和可行性。     

最大并流

本文根据运输问题中一类常见的情况建立了在并容量网络中求最大并流的网络模型，证明了最大并流问题的NP完全性，并给出了求解该问题的一种分枝定界算法．     

一种双层规划的光滑化目标罚函数算法

论文研究了一种双层规划的光滑化目标罚函数算法,在一些条件下,证明了光滑化罚优化问题等价于原双层规划问题,而且,当下层规划问题是凸规划问题时, 给出了一个求解算法和收敛性证明.     

一种双层规划的光滑化目标罚函数算法（英文）

论文研究了一种双层规划的光滑化目标罚函数算法,在一些条件下,证明了光滑化罚优化问题等价于原双层规划问题,而且,当下层规划问题是凸规划问题时,给出了一个求解算法和收敛性证明.     

突发事件中对嫌疑犯有效封堵的模型与算法

基于CUMCM-2011 B题中关于嫌疑犯的封堵问题的研究.通过建立描述市区交通网络图的权矩阵,采用求最短路的Dijstra算法求出市区任意两节点的最短路径及路长,构作最佳路径阵和距离矩阵,以此为基点建立封堵路口的最优调度方案模型,再在此基础上建立封堵住嫌疑犯的最优模型,并设计了模型求解的算法.将算法应用于CUMCM-2011 B题中关于嫌疑犯的封堵问题,获得最优封堵方案.     

低阶精确罚函数的一种二阶光滑逼近

给出了求解约束优化问题的低阶精确罚函数的一种二阶光滑逼近方法,证明了光滑后的罚优化问题的最优解是原约束优化问题的ε-近似最优解,基于光滑后的罚优化问题,提出了求解约束优化问题的一种新的算法,并证明了该算法的收敛性,数值例子表明该算法对于求解约束优化问题是有效的.     

加权网络结构分析

网络研究已经成为机器学习领域中的热点问题之一,近年来发展起来的随机块模型是通过建模生成网络的一种方法．本文对随机块模型加以推广,建立加权的随机块模型,在求解过程中,采用一种可以广泛的用于求解混合模型的变分EM算法．最后通过数据模拟,证明了此方法的可行性．     

带转向延误的非对称用户平衡模型与算法

为准确刻画交通网络和出行行为的复杂特征,考虑路口的转向延误及路段之间相互作用的非对称性因素,用非线性互补理论建立了带转向延误的非对称用户平衡模型,分析了用户平衡解的存在性.结合列生成算法采用有效路径集来避免枚举路网中所有路径的优点和FBLSA算法求解非线性互补问题的全局收敛性特点,提出了修正FBLSA算法.最后针对一个中等规模的交通网络进行数值实验,结果显示该算法对处理非对称网络是十分有效的.     

一种新的求解带约束的有限极大极小问题的精确罚函数

提出了一种新的精确光滑罚函数求解带约束的极大极小问题．仅仅添加一个额外的变量,利用这个精确光滑罚函数,将带约束的极大极小问题转化为无约束优化问题． 证明了在合理的假设条件下,当罚参数充分大,罚问题的极小值点就是原问题的极小值点．进一步,研究了局部精确性质．数值结果表明这种罚函数算法是求解带约束有限极大极小问题的一种有效算法．     

Comparison and hybridization of crossover operators for the nurse scheduling problem

In this paper, we present a hybrid genetic algorithm for the well-known nurse scheduling problem (NSP). The NSP involves the construction of roster schedules for nursing staff in order to maximize the quality of the roster schedule subject to various hard constraints. In the literature, several genetic algorithms have been proposed to solve the NSP under various assumptions. The contribution of this paper is twofold. First, we extensively compare the various crossover operators and test them on a standard dataset in a solitary approach. Second, we propose several options to hybridize the various crossover operators.     

Iteratively reweighted algorithm for signals recovery with coherent tight frame

We consider the problem of compressed sensing with a coherent tight frame and design an iteratively reweighted least squares algorithm to solve it. To analyze the problem, we propose a sufficient null space property under a tight frame (sufficient D‐NSP). We show that, if a measurement matrix A satisfies the sufficient D‐NSP of order s, then an s‐sparse signal under the tight frame can be exactly recovered. Furthermore, if A satisfies the restricted isometric property with tight frame D of order 2bs, then it also satisfies the sufficient D‐NSP of order as with a < b and b sufficiently large. We prove the convergence of the algorithm based on the sufficient D‐NSP and give the upper error bounds. In numerical experiments, we use the discrete cosine transform, discrete Fourier transform, and Haar wavelets to verify the effectiveness of this algorithm. With increasing measurement number, the signal‐to‐noise ratio increases monotonically.     

A global optimization method for nonconvex separable programming problems

Conventional methods of solving nonconvex separable programming (NSP) problems by mixed integer programming methods requires adding numerous 0–1 variables. In this work, we present a new method of deriving the global optimum of a NSP program using less number of 0–1 variables. A separable function is initially expressed by a piecewise linear function with summation of absolute terms. Linearizing these absolute terms allows us to convert a NSP problem into a linearly mixed 0–1 program solvable for reaching a solution which is extremely close to the global optimum.     

Quadratic Hamilton–Poisson Systems on $\mathfrak{se}(1,1)^{*}_{-}$: The Inhomogeneous Case

The blow-up of smooth solution to the isentropic compressible Navier-Stokes-Poisson (NSP) system on \(\mathbb{R}^{d}\) is studied in this paper. We obtain that if the initial density is compactly supported, the spherically symmetric smooth solution to the NSP system on \(\mathbb{R}^{d}\ (d\geq 2)\) blows up in finite time. In the case \(d=1\), if \(2\mu +\lambda >0\), then the NSP system only exits a zero smooth solution on ? for the compactly supported initial density.     

An electromagnetic meta-heuristic for the nurse scheduling problem

In this paper, we present a novel meta-heuristic technique for the nurse scheduling problem (NSP). This well-known scheduling problem assigns nurses to shifts per day maximizing the overall quality of the roster while taking various constraints into account. The problem is known to be NP-hard. Due to its complexity and relevance, many algorithms have been developed to solve practical and often case-specific models of the NSP. The huge variety of constraints and the several objective function possibilities have led to exact and meta-heuristic procedures in various guises, and hence comparison and state-of-the-art reporting of standard results seem to be a utopian idea. We present a meta-heuristic procedure for the NSP based on the framework proposed by Birbil and Fang (J. Glob. Opt. 25, 263–282, 2003). The Electromagnetic (EM) approach is based on the theory of physics, and simulates attraction and repulsion of sample points in order to move towards a promising solution. Moreover, we present computational experiments on a standard benchmark dataset, and solve problem instances under different assumptions. We show that the proposed procedure performs consistently well under many different circumstances, and hence, can be considered as robust against case-specific constraints.     

On the characterization and generation of nurse scheduling problem instances

Due to its complexity and relevance in practice, many different procedures have been proposed in the operations research literature to solve the well-known nurse scheduling problem (NSP). The NSP assigns nurses to shifts per day maximizing the overall quality of the roster while taking various constraints into account. The often highly case-specific workplace conditions in hospital departments have resulted in the development of dedicated (meta-)heuristics to find a workable schedule in an acceptable time limit. However, in spite of research community posing a growing need for benchmarking, these procedures lack any base for comparison.     

EQUIVALENCE BETWEEN NONNEGATIVE SOLUTIONS TO PARTIAL SPARSE AND WEIGHTED l1-NORM MINIMIZATIONS

Based on the range space property (RSP), the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l₁-norm minimization problem are studied in this paper. Different from other conditions based on the spark property, the mutual coherence, the null space property (NSP) and the restricted isometry property (RIP), the RSP-based conditions are easier to be verified. Moreover, the proposed conditions guarantee not only the strong equivalence, but also the equivalence between the two problems. First, according to the foundation of the strict complementarity theorem of linear programming, a sufficient and necessary condition, satisfying the RSP of the sensing matrix and the full column rank property of the corresponding sub-matrix, is presented for the unique nonnegative solution to the weighted l₁-norm minimization problem. Then, based on this condition, the equivalence conditions between the two problems are proposed. Finally, this paper shows that the matrix with the RSP of order k can guarantee the strong equivalence of the two problems.     

Asymptotical behavior of bipolar non-isentropic compressible Navier-Stokes-Poisson system

The bipolar non-isentropic compressible Navier-Stokes-Poisson (BNSP) system is investigated in R³ in the present paper, and the optimal L ² time decay rate for the global classical solution is established. It is shown that the total densities, total momenta and total temperatures of two carriers converge to the equilibrium states at the rate

$${\left( {1 + t} \right)^{ - \frac{3}{4} + \varepsilon }}$$

in L ²-norm for any small and fix ε > 0. But, both the difference of densities and the difference of temperatures of two carriers decay at the optimal rate

$${\left( {1 + t} \right)^{ - \frac{3}{4}}}$$

, and the difference of momenta decays at the optimal rate

$${\left( {1 + t} \right)^{ - \frac{1}{4}}}$$

. This phenomenon on the charge transport shows the essential difference between the non-isentropic unipolar NSP and the bipolar NSP system.

     

蚁群遗传混合算法

将蚁群遗传混合算法分别求解离散空间的和连续空间优化问题.求解旅行商问题的混合算法是以遗传算法为整个算法的框架,利用了蚁群算法中的信息素特性的进行交叉操作;根据旅行商问题的特点,给出了4种变异策略;针对遗传算法存在的过早收敛问题,加入2-0pt方法对问题求解进行了局部优化.与模拟退火算法、标准遗传算法和标准蚁群算法进行比较,4种混合算法效果都比较好,策略D的混合算法效果最好.求解连续空间优化问题是以蚁群算法为整个算法的框架,加入遗传算法的交叉操作和变异操作,用测试函数验证了混合蚁群算法的正确性.     

遗传算法的物理解释

提出了一种理想化的模拟仿生搜索算法——扰动算法 ,以此方法为基础 ,分析了遗传算法的搜索过程和效率问题 ,阐明了遗传算法作为一种次优算法的有效性 .相对于遗传算法的生物解释 ,本文给出了相应的物理解释 .同时 ,本文为遗传算法、进化策略和模拟退火算法找到了一种统一的物理解释 ,揭示了这些重要的仿生类算法实质上的相似性 .