An Optimal Branch-and-Bound Procedure for the Constrained Path, Moving Target Search Problem

Eagle, James N.; Yee, J.R.

doi:10.1287/opre.38.1.110

Cited by 111 publications

(57 citation statements)

References 6 publications

(2 reference statements)

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“…The glimpse function may typically take the form of (Dell et al, 1996, Eagle andYee, 1990), with being a measure of search effectiveness for a given cell Any function however can be used. This probability is assumed to be independent of past searches.…”

Section: Optimal Searcher Path Problem Formulationmentioning

confidence: 99%

“…When the searcher is permitted to span multiple cells at the same time, the FAB algorithm itself leads to a true and tight bound. Eagle and Yee (1990) also solved a relaxed problem made convex by no longer confining the searcher to be in one cell at a time. Eschewing sharpness for calculation speed, Martins (1993)'s MEAN method made linear relaxations through transforming the OSP into a longest path problem maximising the expected number of detections that preserves both searcher indivisibility and path constraints.…”

Section: Obtaining Bounds For the Ospmentioning

confidence: 99%

“…We use the search grids from Eagle and Yee (1990) to compare DMEAN's performance against known OSP bounds. An area is divided into a square of cells (see N n n = × Figure 1), where at each time step the searcher can only search its current cell or an adjacent (vertical or horizontal) neighbour.…”

Section: Uniform Osp Search Gridmentioning

confidence: 99%

“…A search plan respecting searcher travel constraints is sought to maximise the probability of detection within a specified time frame. Much work has been done in the past on this path constrained or optimal searcher path problem (OSP) (Stewart, 1979;Eagle and Yee, 1990;Dell et al 1996;Hohzaki, 1997;Washburn 1998), for the specific case where the environment is discretised into a grid of identically-sized cells and a searcher can immediately search one cell after another in successive time periods. In contrast, a platform searching a built environment cannot move from one region to another without expending some travel time for each transition.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Discounted MEAN bound for the optimal searcher path problem with non-uniform travel times

Lau¹,

Huang²,

Dissanayake³

2008

European Journal of Operational Research

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We consider an extension of the optimal searcher path problem (OSP), where a searcher moving through a discretised environment may now need to spend a nonuniform amount of time travelling from one region to another before being able to search it for the presence of a moving target. In constraining not only where but when the search of each cell can take place, the problem more appropriately models the search of environments which cannot be easily partitioned into equally-sized cells. An existing OSP bounding method in literature, the MEAN bound, is generalised to provide bounds for solving the new problem in a branch and bound framework. The main contribution of this paper is an enhancement, Discounted MEAN (DMEAN), which greatly tightens the bound for the new and existing problems alike with almost no additional computation. We test the new algorithm against existing OSP bounding methods and show it leads to faster solution times for moving target search problems.

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Section: Optimal Searcher Path Problem Formulationmentioning

confidence: 99%

Section: Obtaining Bounds For the Ospmentioning

confidence: 99%

Section: Uniform Osp Search Gridmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Discounted MEAN bound for the optimal searcher path problem with non-uniform travel times

Lau¹,

Huang²,

Dissanayake³

2008

European Journal of Operational Research

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show abstract

“…Related research focuses on search and rescue missions in which the number of searched objects is known at the beginning of the missions [1]- [3]. In other words, these works present problems in which the set of objects to be found is static.…”

Section: Introductionmentioning

confidence: 99%

Persistent patrol with limited-range on-board sensors

Huynh

Enright²

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-We propose and analyze the Persistent Patrol Problem (PPP). An unmanned aerial vehicle (UAV) moving with constant speed and unbounded acceleration patrols a bounded region of the plane where localized incidents occur according to a renewal process with known time intensity and spatial distribution. The UAV can detect incidents using onboard sensors with a limited visibility radius. We want to minimize the expected waiting time between the occurrence of an incident, and the time that it is detected. First, we provide a lower bound on the achievable expected detection time of any patrol policy in the limit as the visibility radius goes to zero. Second, we present the Biased Tile Sweep policy whose upper bound shows i) the lower bound's tightness, ii) the policy's asymptotic optimality, and iii) that the desired spatial distribution of the searching vehicle's position is proportional to the square root of the underlying spatial distribution of incidents it must find. Third, we present two online policies: i) a policy whose performance is provably within a constant factor of the optimal called TSP Sampling, ii) and the TSP Sampling with Receding Horizon heuristically yielding better performance than the former in practice. Fourth, we present a decision-theoretic approach to the PPP that attempts to solve for optimal policies offline. In addition, we use numerical experiments to compare performance of the four approaches and suggest suitable operational scenarios for each one.

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Using multiple searchers in constrained-path, moving-target search problems

Dell

Eagle

Martins

et al. 1996

Naval Research Logistics

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The search theory open literature has paid little, if any, attention to the multiple‐searcher, moving‐target search problem. We develop an optimal branch‐and‐bound procedure and six heuristics for solving constrained‐path problems with multiple searchers. Our optimal procedure outperforms existing approaches when used with only a single searcher. For more than one searcher, the time needed to guarantee an optimal solution is prohibitive. Our heuristics represent a wide variety of approaches: One solves partial problems optimally, two use paths based on maximizing the expected number of detections, two are genetic algorithm implementations, and one is local search with random restarts. A heuristic based on the expected number of detections obtains solutions within 2% of the best known for each one‐, two‐, and three‐searcher test problem considered. For one‐ and two‐searcher problems, the same heuristic's solution time is less than that of other heuristics. For three‐searcher problems, a genetic algorithm implementation obtains the best‐known solution in as little as 20% of other heuristic solution times. © 1996 John Wiley & Sons, Inc.

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An Optimal Branch-and-Bound Procedure for the Constrained Path, Moving Target Search Problem

Cited by 111 publications

References 6 publications

Discounted MEAN bound for the optimal searcher path problem with non-uniform travel times

Discounted MEAN bound for the optimal searcher path problem with non-uniform travel times

Persistent patrol with limited-range on-board sensors

Using multiple searchers in constrained-path, moving-target search problems

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