Nonlinear Programming: A Unified Approach

In the present study, the overall economic impact of hull fouling on a mid-sized naval surface ship (Arleigh Burke-class destroyer DDG-51) has been analyzed. A range of costs associated with hull fouling was examined, including expenditures for fuel, hull coatings, hull coating application and removal, and hull cleaning. The results indicate that the primary cost associated with fouling is due to increased fuel consumption attributable to increased frictional drag. The costs related to hull cleaning and painting are much lower than the fuel costs. The overall cost associated with hull fouling for the Navy's present coating, cleaning, and fouling level is estimated to be $56M per year for the entire DDG-51 class or $1B over 15 years. The results of this study provide guidance as to the amount of money that can be reasonably spent for research, development, acquisition, and implementation of new technologies or management strategies to combat hull fouling.

Economic impact of biofouling on a naval surface ship

Numerical Methods for Scientists and Engineers

We study the problem of interdicting the arcs in a network in order to maximize the shortest s–t path length. “Interdiction” is an attack on an arc that destroys the arc or increases its effective length; there is a limited interdiction budget. We formulate this bilevel, max–min problem as a mixed-integer program (MIP), which can be solved directly, but we develop more efficient decomposition algorithms. One algorithm enhances Benders decomposition by adding generalized integer cutting planes, called “supervalid inequalities” (SVIs), to the master problem. A second algorithm exploits a unique set-covering master problem. Computational results demonstrate orders-of-magnitude improvements of the decomposition algorithms over direct solution of the MIP and show that SVIs also help solve the original MIP faster. Published 2002 Wiley Periodicals, Inc.

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Shortest‐path network interdiction

This paper surveys recent results in pursuit-evasion and autonomous search relevant to applications in mobile robotics. We provide a taxonomy of search problems that highlights the differences resulting from varying assumptions on the searchers, targets, and the environment. We then list a number of fundamental results in the areas of pursuit-evasion and probabilistic search, and we discuss field implementations on mobile robotic systems. In addition, we highlight current open problems in the area and explore avenues for future work.

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Search and pursuit-evasion in mobile robotics

A single evader attempts to traverse a path between two nodes in a network while a single interdictor attempts to detect the evader by setting up an inspection point along one of the network arcs. For each arc there is a known probability of detection if the evader traverses the arc that the interdictor is inspecting. The evader must determine a probabilistic "path-selection" strategy which minimizes the probability of detection while the interdictor must determine a probabilistic "arc-inspection" strategy which maximizes the probability of detection. The interdictor represents, in a simplified form, U.S. and allied forces attempting to interdict drugs and precursor chemicals as they are moved through river, road, and air routes in Latin America and the Caribbean. We show that the basic scenario is a two-person zero-sum game that might require the enumeration of an exponential number of paths, but then show that optimal strategies can be found using network flow techniques of polynomial complexity. To enhance realism, we also solve problems with unknown origins and destinations, multiple interdictors or evaders, and other generalizations.

Two-Person Zero-Sum Games for Network Interdiction

We propose and study an iterative Forward And Backward FAB algorithm applicable to the problem of computing optimal search plans when the target's motion is modeled by a discrete space and time Markov chain. This paper generalizes the class of objective functions to which the method applies.

Search for a Moving Target: The FAB Algorithm

Combat Modeling is a systematic learning resource and reference text for the quantitative analysis of combat. After a brief overview, authors Washburn and Kress present individual chapters on shooting without feedback; shooting with feedback; target defense; attrition models; game theory and wargames; search; unmanned aerial vehicles; and terror and insurgency. Three appendices provide a review of basic probability concepts, probability distributions, and Markov models; an introduction to optimization models; and a discussion of Monte-Carlo simulations. This is a book that can be used as a military manual, reference book, and textbook for military courses on this vital subject. The authors also provide a link for downloading Microsoft Excel workbooks theyve developed and that are used throughout the book that include VBA (Visual Basic for Applications) code for certain functions or commands. Drawing on their many years of experience at the Naval Postgraduate School in Monterey, California, Washburn and Kress have created a reference that will provide the tools and techniques for analysts involved in the underpinnings of combat decisions.

Combat Modeling

The problem of searching for randomly moving targets such as children and submarines is known to be fundamentally difficult, but finding efficient methods for generating optimal or near optimal solutions is nonetheless an important practical problem. This paper investigates the efficiency of Branch and Bound methods, with emphasis on the tradeoff between the accuracy of the bound employed and the time required to compute it. A variety of bounds are investigated, some of which are new. In most cases the best bounds turn out to be imprecise, but very easy to compute. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 243–257, 1998

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Branch and bound methods for a search problem

We consider the problem of searching for a target that moves in discrete time and space according to some Markovian process. At each time, a searcher attempts to detect the target. If the searcher's action at each time is such as to maximize his chances of immediate detection, we call his strategy “myopic.” We provide a computationally useful necessary condition for optimality, and use it to provide an example wherein the myopic strategy is not optimal.

Alan R. Washburn

Papers

Two-Person Zero-Sum Games for Network Interdiction

Search for a Moving Target: The FAB Algorithm

Combat Modeling

Branch and bound methods for a search problem

On a search for a moving target