On the optimal detection of an underwater intruder in a channel using unmanned underwater vehicles

Given a number of patrollers that are required to detect an intruder in a channel, the channel patrol problem consists of determining the periodic trajectories that the patrollers must trace out so as to maximized the probability of detection of the intruder. We formulate this problem as an optimal control problem. We assume that the patrollers' sensors are imperfect and that their motions are subject to turn‐rate constraints, and that the intruder travels straight down a channel with constant speed. Using discretization of time and space, we approximate the optimal control problem with a large‐scale nonlinear programming problem which we solve to obtain an approximately stationary solution and a corresponding optimized trajectory for each patroller. In numerical tests for one, two, and three underwater patrollers, an underwater intruder, different trajectory constraints, several intruder speeds and other specific parameter choices, we obtain new insight—not easily obtained using simply geometric calculations—into efficient patrol trajectory design under certain conditions for multiple patrollers in a narrow channel where interaction between the patrollers is unavoidable due to their limited turn rate.© 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Path optimization for the resource‐constrained searcher

We formulate and solve a discrete‐time path‐optimization problem where a single searcher, operating in a discretized three‐dimensional airspace, looks for a moving target in a finite set of cells. The searcher is constrained by maximum limits on the consumption of one or more resources such as time, fuel, and risk along any path. We develop a specialized branch‐and‐bound algorithm for this problem that uses several network reduction procedures as well as a new bounding technique based on Lagrangian relaxation and network expansion. The resulting algorithm outperforms a state‐of‐the‐art algorithm for solving time‐constrained problems and also is the first algorithm to solve multi‐constrained problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Neglected but affected: voices from the oil-producing regions of Ghana and Uganda

The ‘resource curse’ is the paradoxical theory frequently used to explain how a seemingly desirable asset, such as oil, can actually pervert an economy, erode governance, perpetuate conflict, and ruin local communities to the extent that it becomes a curse. New oil discoveries in western Ghana and western Uganda have raised concerns for the democratic prospects and future stability of these countries and their surrounding regions. Based on field interviews in these oil-producing regions, this report summarises how local communities have been affected thus far and their concerns for the future. The authors assess the extent to which each country is vulnerable to oil-induced instability, and identify groups or communities that would be most likely to perpetuate it. Lastly, it provides some assessment of the future trajectory of each country.     

Defense Burden and the Effect of Democracy: Evidence from a Spatial Panel Analysis

ABSTRACT

Do democracies spend less on national defense? This paper provides new evidence of the effect of democracy on defense burden based on a Spatial Durbin Model with panel data for 98 countries for the years 1992–2008. While democracy measured by means of an index variable covering the entire range from perfect democracy to perfect autocracy turns out to be insignificant, dummy variables indicating transition to higher levels of democracy reveal a statistically highly significant negative effect of democracy on a country’s defense burden. Allowing for country-specific effects reveals heterogeneity in the effect of democracy across countries. Apart from the effect of democracy, the estimation results indicate strong spatial dependence of military burdens across countries. Moreover, they provide statistical evidence for a peace dividend, for substitution effects in defense spending and for a negative effect on the military burden for countries when they exhibit a trade surplus instead of a trade deficit.     

Route optimization for multiple searchers

We consider a discrete time‐and‐space route‐optimization problem across a finite time horizon in which multiple searchers seek to detect one or more probabilistically moving targets. This article formulates a novel convex mixed‐integer nonlinear program for this problem that generalizes earlier models to situations with multiple targets, searcher deconfliction, and target‐ and location‐dependent search effectiveness. We present two solution approaches, one based on the cutting‐plane method and the other on linearization. These approaches result in the first practical exact algorithms for solving this important problem, which arises broadly in military, rescue, law enforcement, and border patrol operations. The cutting‐plane approach solves many realistically sized problem instances in a few minutes, while existing branch‐and‐bound algorithms fail. A specialized cut improves solution time by 50[percnt] in difficult problem instances. The approach based on linearization, which is applicable in important special cases, may further reduce solution time with one or two orders of magnitude. The solution time for the cutting‐plane approach tends to remain constant as the number of searchers grows. In part, then, we overcome the difficulty that earlier solution methods have with many searchers. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Optimal motion planning in rapid‐fire combat situations with attacker uncertainty

This article provides a modeling framework for quantifying cost and optimizing motion plans in combat situations with rapid weapon fire, multiple agents, and attacker uncertainty characterized by uncertain parameters. Recent developments in numerical optimal control enable the efficient computation of numerical solutions for optimization problems with multiple agents, nonlinear dynamics, and a broad class of objectives. This facilitates the application of more realistic, equipment‐based combat models, which track both more realistic models, which track both agent motion and dynamic equipment capabilities. We present such a framework, along with a described algorithm for finding numerical solutions, and a numerical example.     

Generalized orienteering problem with resource dependent rewards

We introduce a generalized orienteering problem (OP) where, as usual, a vehicle is routed from a prescribed start node, through a directed network, to a prescribed destination node, collecting rewards at each node visited, to maximize the total reward along the path. In our generalization, transit on arcs in the network and reward collection at nodes both consume a variable amount of the same limited resource. We exploit this resource trade‐off through a specialized branch‐and‐bound algorithm that relies on partial path relaxation problems that often yield tight bounds and lead to substantial pruning in the enumeration tree. We present the smuggler search problem (SSP) as an important real‐world application of our generalized OP. Numerical results show that our algorithm applied to the SSP outperforms standard mixed‐integer nonlinear programming solvers for moderate to large problem instances. We demonstrate model enhancements that allow practitioners to represent realistic search planning scenarios by accounting for multiple heterogeneous searchers and complex smuggler motion. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013