改进的接触算法及其在光滑粒子流体动力学中的应用

采用以黎曼解描述粒子间相互作用的接触算法,模拟一维情况下包含间断的流场。在弱间断的条件下,采用弱波近似的黎曼解来描述粒子间的相互作用;在强间断的条件下,则引入非迭代黎曼解来描述粒子间的相互作用。并引入Taylor展开思想,提高了接触算法在自由边界的计算精度。该算法无需引入人为粘性,程序结构简洁。数值计算表明,改进后的接触算法能很好地描述强间断,并有效改善了原始接触算法在自由面的计算缺陷。     

Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel

We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP‐hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two‐phase heuristics and dynamic two‐phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Maximizing project cash availability

Consider a project during the life cycle of which there are cash payouts and in‐flows. To better meet his financial commitments, the project owner would like to meet all deadlines without running out of cash. We show that the cash availability objective is similar to the total weighted flowtime used to measure work‐in‐progress performance in the scheduling and inventory control literatures. In this article we provide several specialized solution methods for the problem of minimizing total weighted flowtime in an arbitrary acyclic project network, subject to activity release times and due dates, where the activity weights may be positive or negative and represent cash in‐ and out‐flows. We describe the structure of an optimal solution and provide several efficient algorithms and their complexity based on mincost and maxflow formulations. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

On efficient algorithms for finding efficient salvo policies

We consider the salvo policy problem, in which there are k moments, called salvos, at which we can fire multiple missiles simultaneously at an incoming object. Each salvo is characterized by a probability p_i: the hit probability of a single missile. After each salvo, we can assess whether the incoming object is still active. If it is, we fire the missiles assigned to the next salvo. In the salvo policy problem, the goal is to assign at most n missiles to salvos in order to minimize the expected number of missiles used. We consider three problem versions. In Gould's version, we have to assign all n missiles to salvos. In the Big Bomb version, a cost of B is incurred when all salvo's are unsuccessful. Finally, we consider the Quota version in which the kill probability should exceed some quota Q. We discuss the computational complexity and the approximability of these problem versions. In particular, we show that Gould's version and the Big Bomb version admit pseudopolynomial time exact algorithms and fully polynomial time approximation schemes. We also present an iterative approximation algorithm for the Quota version, and show that a related problem is NP-complete.     

导弹结构热防护一体化设计与优化

针对导弹面临的严酷气动热力环境,基于传统波纹夹芯结构,为导弹设计了一种兼具承载和热防护功能的一体化结构。建立热-结构耦合计算模型,对一体化结构进行结构承载与热防护性能分析,结果表明:一体化结构在高温下具有较好的承载能力;增加一体化结构隔热层与内壁厚度有助于提高导弹的热防护效率。以一体化结构热防护效率最高和质量最小为目标,采用第二代非支配排序遗传算法实现了多目标优化,并认识到:一体化结构热防护效率与质量相互影响,设计时需要需综合考虑。     

目标宽频带RCS的快速算法研究

目标宽带RCS预估算法一直是计算电磁学的一个研究热点,本文分别研究了渐近波形估计技术（AWE）与最佳一致逼近技术在宽频带RCS预估领域内的应用。首先,介绍了传统矩量法计算RCS的原理,并分析了两种快速算法的计算过程。然后,采用这两种技术,分别计算了简易飞机模型的RCS值,并对这两种方法进行比较。计算结果表明相比传统的矩量法,这两种方法在不影响精度的前提下大大提高了计算效率。同时,相比渐近波形估计技术,最佳一致逼近技术在节省内存,节约时间方面更具优势。最后,采用最佳一致逼近理论,结合电磁计算软件,实现较大尺寸目标的宽频带RCS的计算。     

Single‐machine scheduling with deadlines to minimize the total weighted late work

We consider scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due date and before its deadline. This is the first study on scheduling with the late work criterion under the deadline restriction. In this paper, we show that (i) the problem is unary NP‐hard even if all the jobs have a unit weight, (ii) the problem is binary NP‐hard and admits a pseudo‐polynomial‐time algorithm and a fully polynomial‐time approximation scheme if all the jobs have a common due date, and (iii) some special cases of the problem are polynomially solvable.     

Simple paths with exact and forbidden lengths

We study new decision and optimization problems of finding a simple path between two given vertices in an arc weighted directed multigraph such that the path length is equal to a given number or it does not fall into the given forbidden intervals (gaps). A fairly complete computational complexity classification is provided and exact and approximation algorithms are suggested.     

A multi‐stage stochastic programming approach for network capacity expansion with multiple sources of capacity

In networks, there are often more than one sources of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity, and contract capacity. We use a scenario tree to model the uncertainty, and build a multi‐stage stochastic integer program that can incorporate multiple sources and multiple types of capacities in a general network. We propose two solution methodologies for the problem. Firstly, we design an asymptotically convergent approximation algorithm. Secondly, we design a cutting plane algorithm based on Benders decomposition to find tight bounds for the problem. The numerical experiments show superb performance of the proposed algorithms compared with commercial software. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 600–614, 2017     

Approximation results for min‐max path cover problems in vehicle routing

This article studies a min‐max path cover problem, which is to determine a set of paths for k capacitated vehicles to service all the customers in a given weighted graph so that the largest path cost is minimized. The problem has wide applications in vehicle routing, especially when the minimization of the latest service completion time is a critical performance measure. We have analyzed four typical variants of this problem, where the vehicles have either unlimited or limited capacities, and they start from either a given depot or any depot of a given depot set. We have developed approximation algorithms for these four variants, which achieve approximation ratios of max{3 ‐ 2/k,2}, 5, max{5 ‐ 2/k,4}, and 7, respectively. We have also analyzed the approximation hardness of these variants by showing that, unless P = NP , it is impossible for them to achieve approximation ratios less than 4/3, 3/2, 3/2, and 2, respectively. We have further extended the techniques and results developed for this problem to other min‐max vehicle routing problems.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010