高级程序设计语言综述

为读者选择语言提供了总体思路,给出了高级语言的发展的趋势。     

最大面积避障矩形问题的解法

建立了在一个含有若干障碍点的矩形母域内求一个最大面积避障矩形问题的数学模型.通过分析避障矩形的几何特性,找到了求解这一含有0-1变量的非线性规划数学模型的一种特殊解法.     

Cyclic best first search: Using contours to guide branch‐and‐bound algorithms

The cyclic best‐first search (CBFS) strategy is a recent search strategy that has been successfully applied to branch‐and‐bound algorithms in a number of different settings. CBFS is a modification of best‐first search (BFS) that places search tree subproblems into contours which are collections of subproblems grouped in some way, and repeatedly cycles through all non‐empty contours, selecting one subproblem to explore from each. In this article, the theoretical properties of CBFS are analyzed for the first time. CBFS is proved to be a generalization of all other search strategies by using a contour definition that explores the same sequence of subproblems as any other search strategy. Further, a bound is proved between the number of subproblems explored by BFS and the number of children generated by CBFS, given a fixed branching strategy and set of pruning rules. Finally, a discussion of heuristic contour‐labeling functions is provided, and proof‐of‐concept computational results for mixed‐integer programming problems from the MIPLIB 2010 database are shown. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 64–82, 2017     

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.     

Exact algorithms and bounds for the dynamic assignment interdiction problem

We study a multi‐stage dynamic assignment interdiction (DAI) game in which two agents, a user and an attacker, compete in the underlying bipartite assignment graph. The user wishes to assign a set of tasks at the minimum cost, and the attacker seeks to interdict a subset of arcs to maximize the user's objective. The user assigns exactly one task per stage, and the assignment costs and interdiction impacts vary across stages. Before any stage commences in the game, the attacker can interdict arcs subject to a cardinality constraint. An interdicted arc can still be used by the user, but at an increased assignment cost. The goal is to find an optimal sequence of assignments, coupled with the attacker's optimal interdiction strategy. We prove that this problem is strongly NP‐hard, even when the attacker can interdict only one arc. We propose an exact exponential‐state dynamic‐programming algorithm for this problem as well as lower and upper bounds on the optimal objective function value. Our bounds are based on classical interdiction and robust optimization models, and on variations of the DAI game. We examine the efficiency of our algorithms and the quality of our bounds on a set of randomly generated instances. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 373–387, 2017     

舰艇防空反导自适应干扰HDP算法分析与仿真

为干扰来袭的多波次、多方向反舰导弹,提高舰艇防空反导能力,分析了自适应干扰HDP算法模型,并通过实例进行仿真。通过对结果进行分析,验证了启发式动态规划(HDP)算法在自适应电子干扰策略最优组合的生成过程中的时效性、预测精度以及适用性,为该算法的后续研究提供支持。     

使用三个数域的数域筛算法

大整数分解难题是RSA密码的数学安全基础.目前数域筛算法是分解365比特以上大整数的最有效方法,然而它的时间复杂度仍然是亚指数的.对于目前普遍使用的1024比特以上大整数,数域筛算法还不能分解,所以研究数域筛算法具有重要的意义.现有的一般数域筛算法普遍使用两个数域,对多个数域的研究极少.一般数域筛算法经过修改可以使用三个数域,即两个代数数域和一个有理数域.分析表明:修改后的数域筛算法与原来的一般数域筛算法在时间复杂度上处于同一量级.但修改后的数域筛算法有更多地方可以合并计算,所以计算速度更快了.通过两个实验也验证了这一结论.     

Determining crane areas for balancing workload among interfering and noninterfering cranes

This article treats the problem of subdividing an area for storing containers such that the workload is evenly shared among the cranes operating the resulting subareas. We consider two crane sets: while noncrossing constraints between cranes of the same set need to be observed, cranes of different sets do not interfere. Such a problem setting is, for instance, relevant for scheduling the (un‐)loading of vessels by parallel quay cranes operating on opposing berths or in container yards with cross‐over cranes. We formalize the resulting optimization problem, prove computational complexity, and present exact and heuristic solution procedures. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

一种新的装备配置优化模型

传统的装备配置优化问题一般采用确定性的数学规划方法解决,难以满足高技术条件下现代战争中需要对大量随机现象和模糊现象进行精确定量分析的实际要求。在分析了高技术条件下装备配置问题一般特性的基础上,根据机会约束规划和模糊机会约束规划的思想,提出了一种新的建立装备配置优化模型的思路和方法,并给出了基于随机模拟的遗传算法的实值算例,算例结果与实际情况基本相符,反映了模型的科学性与实用性。     

CDF9／7小波在JPEG2000中的整数变化

通过添加系数缩放值叮,使目前在JPEG2000中广泛采用的CDF9／7小波提升算法完全整数化,不仅保持了现有算法的还原度,而且简化了算法的复杂度,在图像压缩上取得了比较满意的效果。