Alan R. Washburn

Search for a Moving Target: The FAB Algorithm

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

Branch and Bound Methods for a Search Problem

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.

Search-Evasion Game in a Fixed Region

A game where a Searcher attempts to trap an Evader who knows the location of all past traps is formulated and solved, using average time to capture as the payoff. The Evader can move around freely, except that he is constrained to remain within a certain region.

The Effects of Discounting Profits in the Presence of Learning in the Optimization of Production Rates

Abstract When production involves learning, so that the rate of cash flow depends on cumulative production as well as on the rate of production, then the maximization of total program profit can be a Calculus of Variations problem. This paper explores some characteristics of optimal production schedules in such circumstances, and presents an application to a problem in aircraft production.

Dynamic search games

In these games the searcher has a sequence of looks in which to detect the target, while the target chooses a new cell after each look in the knowledge of what cells have been searched so far. Since time is of the essence and the searchers speed is bounded, the target has a tendency to choose cells far away from the most recent look. A theory for such games is developed and used to approximate a game involving a dipping sonar.

The LP/POMDP Marriage: Optimization with Imperfect Information

Anewtechniqueforsolvinglarge-scaleallocationproblemswithpartiallyobservable states and constrained action and observation resources is introduced. The technique uses a master linear program (LP) to determine allocations among a set of control policies, and uses partially observable Markov decision processes (POMDPs) to determine improving policies using dual prices from the master LP. An application is made to a military problem where aircraft attack targets in a sequence of stages, with information acquired in one stage being used to plan attacks in the next. c 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 607{619, 2000

Shoot-Look-Shoot: A Review and Extension

We consider the optimal use of information in shooting at a collection of targets, generally with the object of maximizing the average number (or value) of targets killed. The shooting problem is viewed as a Markov decision process, and the modal solution technique is stochastic dynamic programming. Information obtained about target status may or may not be perfect, and there may or may not be constraints on the number of shots. Previous results are reviewed, and some new results are obtained.

Estimating NHL Scoring Rates

We propose a model to estimate the rates at which NHL teams score and yield goals. In the model, goals occur as if from a Poisson process whose rate depends on the two teams playing, the home-ice advantage, and the manpower (power-play, short-handed) situation. Data on all the games from the 2008-2009 season was downloaded and processed into a form suitable for the analysis. The model seems to perform adequately in prediction and should be useful for handicapping and for informing the decision as to when to pull the goalie.

Steaming on Convex Hulls

This is a sea story about using a simple classroom example to save a great deal of money, as well as to convince beginning Postgraduate Naval School operations research students---experienced, skeptical military officers---that mathematical analysis can yield immediate results. The application is planning a ships transit from one point to another in a fixed amount of time, given that the ship can operate with one or more of its propulsion plants idled to save fuel. Simple analysis yields nonintuitive results that US Navy shipboard energy-conservation guides overlook. One of the authors (Kline) solved this homework problem as a student and subsequently applied this example when he took command of USS AQUILA, a patrol hydrofoil missile ship. AQUILA achieved results so striking in comparison to her sister ships that the squadron material officer inspected her engineering plant to ensure that no safety settings were being overridden to achieve this record. Klines spreadsheet decision-support tool was provided to other hydrofoil commanders. A more general version has been conveyed to the US Navy. Considering that our navy spends about a billion dollars per year on fuel for surface-combatant ships alone, this development promises substantial, long-term returns. “But thou, contracted to thine own bright eyes, Feedst thy lightst flame with self-substantial fuel.” Shakespeare, Sonnet I

Deterministic graphical games

Abstract This paper gives a simple algorithm for solving a class of graphical games where infinite play is possible.