求解车辆路径问题的离散蝙蝠算法

根据车辆路径问题的数学模型,分析了它的具体特征,从而对BA的操作算子又进行了重新定义,设计了求解VRP问题的离散蝙蝠算法,并通过实例测试将离散蝙蝠算法与其他算法进行比较,验证了该算法求解VRP问题的有效性与可行性.     

随机并行梯度下降算法在激光束整形中的应用

为了满足高光束质量要求,校正激光束在传输过程中产生的波前畸变,改善激光位相分布,进而提高聚焦光斑的能量集中度,基于79单元微机械薄膜变形镜（MMDM）搭建了一套激光束整形实验系统。利用随机并行梯度下降（SPGD）算法,分别选择聚焦光斑半径、形心为中心的环围能量比和质心为中心的环围能量比作为算法性能指标,开展了激光束整形实验研究。3种情况下,分别经过58次、197次、133次迭代趋于收敛,但光斑半径作为性能指标时振荡严重;环围能量比从整形前的0.200 5、0.127 7、0.200 5分别增加到整形后的0.669 9、0.733 9、0.864 0。实验结果表明：MMDM用于激光束整形具有良好的效果,光斑半径作为性能指标整形速度最快,其次为质心环围能量比,形心环围能量比最慢;质心环围能量比作为性能指标整形效果最好,其次为形心环围能量比,光斑半径最差。综合比较,质心环围能量比作为性能指标时综合效果最好。     

自适应光学中扩展信标波前探测的研究与实验

讨论了一种基于Hartmann Shack (H S)传感器的扩展信标相关波前探测方法。通过在传统H S探测光路的物平面上加入视场光阑消除了子孔径像斑的重叠问题 ,并利用一种快速相关算法计算各像斑的相对位移 ,进而得到各子孔径波前的相对斜率。光学实验研究证实了该相关波前探测方法能够较精确地测算出波前像差 ,从而使目前使用最多的H S传感器具有扩展信标波前探测能力     

基于随机并行梯度下降算法的光束相干合成技术

介绍了随机并行梯度下降算法的基本原理,对算法流程进行了仿真验证,并对其中随机扰动幅度和增益系数两个关键参数进行了仿真分析。分析结果表明,这两个参数存在一个最适区间,只有在此区间内取值时算法才能有效收敛。以仿真分析为依据开展了光纤激光的相干合成实验,结果表明光束相干合成效果显著,有效地验证了仿真分析的结果。     

改进的双曲等效法用于双站合成孔径雷达前视成像

双站合成孔径雷达(SAR)前视成像有着很多的潜在应用,比如在能见度很低的天气实现飞机的导航和盲降,提高飞机飞行的安全度等.然而实现双站SAR前视成像的难点在于其距离历程的双根式性,直接采用驻定相位原理对其分解将得到复杂的解析式,从而后续算法的推导变得困难.现有的双曲等效法可以将双根式距离历程等效为单根式,但由于该方法为距离历程的二阶近似,当用于双站SAR前视成像时,由于其较大的前视角,未完全等效的距离历程高次项造成的误差已经超出可以接受的范围.针对以上问题,本文首先提出了一种改进的双曲等效法,该方法通过引入新的补偿变量来提高距离历程的等效精度;然后在此基础上推导回波信号的二维频谱解析式,并给出了一种适用于双站SAR前视成像的距离多普勒算法;最后通过仿真实验,将原双曲等效法与改进方法的等效误差以及成像结果做对比,验证了本文算法的有效性和优越性.     

一种用硬件实现的Bayer格式图像恢复算法

针对传统的双线性Bayer彩色图像恢复算法恢复效果不理想,边界部分不明显,局部图像有团块等问题,提出了一种基于硬件实现的Bayer图像快速插值算法。采用梯度算法对Bayer格式图像绿色通道进行恢复,根据像素点所属的颜色组对蓝色通道进行恢复。实验结果表明,本文算法比双线性法有更好的峰值信噪比(PSNR)值,RGB 3个通道的PSNR值均比双线性法高5 dB以上,而且算法消耗时间比双线性法少,恢复的图像视觉效果更好。实验处理一幅512×512的全彩图像仅需要9.3 ms,完全可以满足实时性的要求,因此,本文算法在对实时性要求高的场合有很好的应用前景。     

Properties of four partial orders on standard Young tableaux

Let SYTn be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYTn and some of their crucial properties, we prove three main results:

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Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer.

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The map sending a tableau to its descent set induces a homotopy equivalence of the proper parts of all of these orders on tableaux with that of the Boolean algebra ²[n−1]. In particular, the Möbius function of these orders on tableaux is (−1)ⁿ⁻³.

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For two of the four orders, one can define a more general order on skew tableaux having fixed inner boundary, and similarly analyze their homotopy type and Möbius function.

     

Genetic Algorithm for the Jump Number Scheduling Problem

This paper introduces genetic algorithms for the jump number scheduling problem. Given a set of tasks subject to precedence constraints, the problem is to construct a schedule to minimize the number of jumps. We show that genetic algorithms outperform the previously known Knuth and Szwarcfiter's exhaustive search algorithm when applied to some classes of orders in which no polynomial time algorithms exist in solving the jump number problem. Values for various parameters of genetic jump number algorithms are tested and results are discussed.     

A memetic algorithm for the multiperiod vehicle routing problem with profit

In this paper, we extend upon current research in the vehicle routing problem whereby labour regulations affect planning horizons, and therefore, profitability. We call this extension the multiperiod vehicle routing problem with profit (mVRPP). The goal is to determine routes for a set of vehicles that maximizes profitability from visited locations, based on the conditions that vehicles can only travel during stipulated working hours within each period in a given planning horizon and that the vehicles are only required to return to the depot at the end of the last period. We propose an effective memetic algorithm with a giant-tour representation to solve the mVRPP. To efficiently evaluate a chromosome, we develop a greedy procedure to partition a given giant-tour into individual routes, and prove that the resultant partition is optimal. We evaluate the effectiveness of our memetic algorithm with extensive experiments based on a set of modified benchmark instances. The results indicate that our approach generates high-quality solutions that are reasonably close to the best known solutions or proven optima, and significantly better than the solutions obtained using heuristics employed by professional schedulers.     

Continuous Contour Monte Carlo for Marginal Density Estimation With an Application to a Spatial Statistical Model

The problem of marginal density estimation for a multivariate density function f(x) can be generally stated as a problem of density function estimation for a random vector λ(x) of dimension lower than that of x. In this article, we propose a technique, the so-called continuous Contour Monte Carlo (CCMC) algorithm, for solving this problem. CCMC can be viewed as a continuous version of the contour Monte Carlo (CMC) algorithm recently proposed in the literature. CCMC abandons the use of sample space partitioning and incorporates the techniques of kernel density estimation into its simulations. CCMC is more general than other marginal density estimation algorithms. First, it works for any density functions, even for those having a rugged or unbalanced energy landscape. Second, it works for any transformation λ(x) regardless of the availability of the analytical form of the inverse transformation. In this article, CCMC is applied to estimate the unknown normalizing constant function for a spatial autologistic model, and the estimate is then used in a Bayesian analysis for the spatial autologistic model in place of the true normalizing constant function. Numerical results on the U.S. cancer mortality data indicate that the Bayesian method can produce much more accurate estimates than the MPLE and MCMLE methods for the parameters of the spatial autologistic model.