Rendezvous search when marks are left at the starting points

Leaving marks at the starting points in a rendezvous search problem may provide the players with important information. Many of the standard rendezvous search problems are investigated under this new framework which we call markstart rendezvous search. Somewhat surprisingly, the relative difficulties of analysing problems in the two scenarios differ from problem to problem. Symmetric rendezvous on the line seems to be more tractable in the new setting whereas asymmetric rendezvous on the line when the initial distance is chosen by means of a convex distribution appears easier to analyse in the original setting. Results are also obtained for markstart rendezvous on complete graphs and on the line when the players' initial distance is given by an unknown probability distribution. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 722–731, 2001     

Many‐player rendezvous search: Stick together or split and meet?

Rendezvous search finds the strategies that players should use in order to find one another when they are separated in a region. Previous papers have concentrated on the case where there are two players searching for one another. This paper looks at the problem when there are more than two players and concentrates on what they should do if some but not all of them meet together. It looks at two strategies—the stick together one and the split up and meet again one. This paper shows that the former is optimal among the class of strategies which require no memory and are stationary, and it gives a method of calculating the expected rendezvous time under it. However, simulation results comparing both strategies suggest that in most situations the split up and meet again strategy which requires some memory leads to faster expected rendezvous times. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:710–721, 2001     

Rendezvous search on labeled networks

Two players are independently placed on a commonly labelled network X. They cannot see each other but wish to meet in least expected time. We consider continuous and discrete versions, in which they may move at unit speed or between adjacent distinct nodes, respectively. There are two versions of the problem (asymmetric or symmetric), depending on whether or not we allow the players to use different strategies. After obtaining some optimality conditions for general networks, we specialize to the interval and circle networks. In the first setting, we extend the work of J. V. Howard; in the second we prove a conjecture concerning the optimal symmetric strategy. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 256–274, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10011     

Rendezvous of three agents on the line

This paper considers a three‐person rendezvous problem on the line which was introduced earlier by the authors. Three agents are placed at three consecutive integer value points on the real line, say 1, 2, and 3. Each agent is randomly faced towards the right or left. Agents are blind and have a maximum speed of 1. Their common aim is to gather at a common location as quickly as possible. The main result is the proof that a strategy given by V. Baston is the unique minimax strategy. Baston's strategy ensures a three way rendezvous in time at most 3.5 for any of the 3!2³ = 48 possible initial configurations corresponding to positions and directions of each agent. A connection is established between the above rendezvous problem and a search problem of L. Thomas in which two parents search separately to find their lost child and then meet again. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 244–255, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10005     

航天器交会中的多圈Lambert问题研究

针对大椭圆轨道追踪器固定时间直接碰撞交会问题,介绍了一种快速确定多圈Lambert问题最优解的新方法。研究了多圈Lambert转移解,分析了转移时间与转移轨道参数的关系;研究了无时间约束最优直接碰撞交会及其必要条件。仿真表明:最优解快速确定方法有效、可行,并可提高计算效率。     

Algorithms for the multi‐item multi‐vehicles dynamic lot sizing problem

We consider a two‐stage supply chain, in which multi‐items are shipped from a manufacturing facility or a central warehouse to a downstream retailer that faces deterministic external demand for each of the items over a finite planning horizon. The items are shipped through identical capacitated vehicles, each incurring a fixed cost per trip. In addition, there exist item‐dependent variable shipping costs and inventory holding costs at the retailer for items stored at the end of the period; these costs are constant over time. The sum of all costs must be minimized while satisfying the external demand without backlogging. In this paper we develop a search algorithm to solve the problem optimally. Our search algorithm, although exponential in the worst case, is very efficient empirically due to new properties of the optimal solution that we found, which allow us to restrict the number of solutions examined. Second, we perform a computational study that compares the empirical running time of our search methods to other available exact solution methods to the problem. Finally, we characterize the conditions under which each of the solution methods is likely to be faster than the others and suggest efficient heuristic solutions that we recommend using when the problem is large in all dimensions. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

Rendez‐vous search on a rectangular lattice

In a rendez‐vous search two or more teams called seekers try to minimize the time needed to find each other. In this paper, we consider s seekers in a rectangular lattice of locations where each knows the configuration of the lattice, the distribution of the seekers at time 0, and its own location, but not the location of any other. We measure time discretely, in turns. A meeting takes place when the two seekers reach the same point or adjacent points. The main result is that for any dimension of lattice, any initial distribution of seekers there are optimal strategies for the seekers that converge (in a way we shall make clear) to a center. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

集群搜索对策理论在搜索-规避对抗中的应用

使用对策论的观点和方法 ,结合搜索论的知识 ,建立了一类搜索 -规避对抗对策模型 .对模型的结论做了系统分析 ,考虑了对策双方的最优策略及使用 .     

一类对固定目标的集群搜寻对策问题及求解

利用集群搜索对策的理论与方法 ,建立了集群对固定目标的一类搜索对策模型 ,给出了集群的ε -最优搜寻策略 ,并考虑了其在搜索过程中的应用     

A search game taking account of attributes of searching resources

This article deals with a two‐person zero‐sum game called a search allocation game (SAG), in which a searcher and a target participate as players. The searcher distributes his searching resources in a search space to detect the target. The effect of resources lasts a certain period of time and extends to some areas at a distance from the resources' dropped points. On the other hand, the target moves around in the search space to evade the searcher. In the history of search games, there has been little research covering the durability and reachability of searching resources. This article proposes two linear programming formulations to solve the SAG with durable and reachable resources, and at the same time provide an optimal strategy of distributing searching resources for the searcher and an optimal moving strategy for the target. Using examples, we will analyze the influences of two attributes of resources on optimal strategies. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 2008     

Total optimality of incrementally optimal allocations

This paper considers the problem of finding optimal solutions to a class of separable constrained extremal problems involving nonlinear functionals. The results are proved for rather general situations, but they may be easily stated for the case of search for a stationary object whose a priori location distribution is given by a density function on R, a subset of Euclidean n-space. The functional to be optimized in this case is the probability of detection and the constraint is on the amount of effort to be used Suppose that a search of the above type is conducted in such a manner as to produce the maximum increase in probability of detection for each increment of effort added to the search. Then under very weak assumptions, it is proven that this search will produce an optimal allocation of the total effort involved. Under some additional assumptions, it is shown that any amount of search effort may be allocated in an optimal fashion.     

基于NSGA-II和多属性决策的防空火力分配

为了解决防空火力分配问题,首先运用NSGA-II算法求出Pareto最优解集,然后运用多属性决策方法对Pareto最优解集中的解进行综合评估,并从中找出一个最优解。用区间数定性描述各属性,建立了防空火力分配的三目标优化模型。描述了NSGA-II算法和多属性决策方法的运算步骤。在仿真算例中,得到了一个最佳防空火力分配方案,说明该方法对于防空火力分配问题有良好的应用价值。     

航天器近距离交会斜滑制导算法

提出了满足测量视场、最小脉冲间隔、最大脉冲受限等约束的燃料最省的航天器近距离交会多脉冲斜滑制导算法.建立了近距离交会(接近和撤离)多脉冲斜滑制导算法的统一数学模型;提出了理想交会轨道距离和速率的指数函数变化关系,使得算法能够实现任意时间的近距离交会,同时满足接近操作减速和撤离过程加速的任务要求;设计了对数函数映射法进行脉冲寻优.最后通过接近段和撤离段的操作仿真算例进行验证,仿真结果表明,相比最优化方法,对数函数映射法以较小的计算量实现了较好的寻优效果;算法能够以较省的燃料消耗实现轨道面内任意方向、任意时间内满足约束的近距离交会.     

面向多最优解组合优化问题的决策求解算法

针对具有固定物品总和、多最优解特征的组合优化问题,以固定总和实数子集问题和购买鸡翅问题为例,给出了这类多最优解组合优化问题的形式化表示。在分析枚举等经典算法基础上,提出了基于整数状态表示和实数状态表示的0-1决策递归搜索多最优解动态规划算法。针对该算法在最优解数量较大时,时间复杂度趋向O(mⁿ)的问题,提出了基于相同决策路径合并和基于0-x决策的两种改进算法。实验中两种改进算法的计算时间基本符合与O(nb+nm)的正比关系,表明对于这类多最优解组合优化问题具有良好的求解性能。     

The search for an intelligent evader: Strategies for searcher and evader in the two-region problem

This paper considers the search for an evader concealed in one of two regions, each of which is characterized by its detection probability. The single-sided problem, in which the searcher is told the probability of the evader being located in a particular region, has been examined previously. We shall be concerned with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move: his optimal strategy consists of that probability distribution which maximizes the expected time to detection, while the searcher's optimal strategy is the sequence of searches which limits the evader to this expected time. It transpires for this problem that optimal strategies for both searcher and evader may generally be obtained to a surprisingly good degree of approximation by using the optimal strategies for the closely related (but far more easily solved) problem in which the evader is completely free to move between searches.     

A note on explicit solution in linear fractional programming

In this note we analyze the fractional interval programming problem (FIP) and find, explicitly, all its optimal solutions. Though our results are essentially the same as those in Charnes and Cooper [4], the proofs and analysis we provide here are considerably simpler.     

搜索路径给定时的搜索对策问题及其应用

搜索路径给定时的最优搜索方案问题,也可以理解为是关于搜索者和目标的二人对策问题,主要讨论了当搜索路径给定时的单个搜索者和单个目标的搜索对策问题。首先根据问题的特点,利用动态规划和迭代的方法,确定关于目标逃逸路径混合策略的最优分区,证明该分区是多面体凸集;针对目标不同逃逸路径的分区,求出搜索者的最大期望收益,再将问题转化为二人有限零和对策,计算出搜索者的支付矩阵,确定最优搜索策略。最后结合海军护航行动,对我舰载直升机搜索小型海盗船进行分析和计算,说明搜索路径给定时的最优搜索对策对于双方的资源分配和提高搜索效率具有一定的应用价值。     

小行星探测多脉冲交会轨道多目标优化

现有的小行星探测交会轨道研究多集中于二脉冲最优燃料研究,本文则研究了小行星探测多脉冲交会轨道多目标优化问题.基于Lambert交会算法建立了包含地球逃逸轨道和日心转移轨道的多脉冲交会轨道优化模型,以燃料消耗最小和转移时间最短为两个优化目标函数.采用一类典型的多目标进化算法——NSGA -Ⅱ用于Pareto最优解的确定....     

Solving partially observable agent‐intruder games with an application to border security problems

In this paper, we introduce partially observable agent‐intruder games (POAIGs). These games model dynamic search games on graphs between security forces (an agent) and an intruder given possible (border) entry points and high value assets that require protection. The agent faces situations with dynamically changing, partially observable information about the state of the intruder and vice versa. The agent may place sensors at selected locations, while the intruder may recruit partners to observe the agent's movement. We formulate the problem as a two‐person zero‐sum game, and develop efficient algorithms to compute each player's optimal strategy. The solution to the game will help the agent choose sensor locations and design patrol routes that can handle imperfect information. First, we prove the existence of ?‐optimal strategies for POAIGs with an infinite time horizon. Second, we introduce a Bayesian approximation algorithm to identify these ?‐optimal strategies using belief functions that incorporate the imperfect information that becomes available during the game. For the solutions of large POAIGs with a finite time horizon, we use a solution method common to extensive form games, namely, the sequence form representation. To illustrate the POAIGs, we present several examples and numerical results.     

Interval estimation of a global optimum for large combinatorial problems

Consider an “intractable” optimization problem for which no efficient solution technique exists. Given a systematic procedure for generating independent heuristic solutions, we seek to obtain interval estimates for the globally optimal solution using statistical inference. In previous work, accurate point estimates have been derived. Determining interval estimates, however, is a considerably more difficult task. In this paper, we develop straightforward procedures which compute confidence intervals efficiently in order to evaluate heuristic solutions and assess deviations from optimality. The strategy presented is applicable to a host of combinatorial optimization problems. The assumptions of our model, along with computational experience, are discussed.