Criteria and approximate methods for path-constrained moving-target search problems

Thomas, Lyn C.; Eagle, James N.

doi:10.1002/1520-6750(199502)42:1<27::aid-nav3220420105>3.0.co;2-h

Cited by 21 publications

(12 citation statements)

References 13 publications

(1 reference statement)

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“…Alternative formulations exist in literature for the OSP (Thomas and Eagle 1995;Washburn, 1995), but the above, similar to that used in Dell et al (1996), is chosen here to make clear the intended generalisation in Section 6.…”

Section: Optimal Searcher Path Problem Formulationmentioning

confidence: 99%

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%

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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“…+ p^'i/'^ = 1, determine a system of differential equations for finding optimal p{s) and V'(s) Substitution of the last formulas into the first equation of (17) eliminates variable s from the system (17) and reduces it to the nonlinear first-order differential equation (11) determining p as a function of if; with boundary conditions (12). Since variable s was eliminated from (17), the second equation of (17) is satisfied identically, and, thus, a constraint on trajectory length should be included in the form of (13).…”

Section: Ljmentioning

confidence: 99%

“…It addresses several types of problems with various objectives, constraints on resources and control limitations, for instance, ■ Minimizing risk of aircraft detection by radars, sensors or surface air missiles (SAM) [5,19,22] ■ Minimizing risk of submarine detection by sensors [21] ■ Minimizing cumulative radiation damage in passing through a contaminated area ■ Finding optimal trajectories for multiple aircraft avoiding collisions [15] ■ Maximizing the probability of target detecting by a searcher [1,3,9,12,13,16,17,20] …”

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confidence: 99%

Robust Decision Making: Addressing Uncertainties in Distributions

Uryasev¹,

Pardalos²

2004

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including ■ gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Servic 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be awars that notwiths penalty for failing to comply with a collection of information if it does not display a currently valid 0MB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.AFRL-SR-AR-TR-04- PERFORMING ORGANIZATION NAME{S) AND ADDRESS(ES)University of Florida 310 Weil Hall Gainesville, FL 32611-6550 SPONSORING/MONITORING AGENCY NAME{S) AND ADDRESS(ES)Air SummaryThe project was concentrated on development of new methodologies for decision making in uncertain environment and relevant applications. The first part of the project was focused on analytical and discrete optimization approaches for routing an aircraft in threat environment. The model considered aircraft trajectory in three-dimensional space. Several threats were studied, including risk of aircraft detection by radars, sensors, and the risk of being killed by surface to air missiles. The problem of finding aircraft optirhal risk trajectory subject to a constraint on the trajectory length was solved by analytical and discrete optimization approaches.The second part of the project resulted in general approach to risk management for the case with uncertainties in distributions. The risk of loss, damage, or failure was measured by the Conditional Value-at-Risk (CVaR) measure. As a function of decision variables, CVaR is convex, and therefore can be efficiendy controlled/optimized using convex or linear programming. The methodology was tested on two Weapon-Target Assignment (WTA) problems. The total cost of a mission was minimized, while satisfying the operational constraints and ensuring destruction of targets with high probability. The risk of a failure of the mission is controlled by CVaR constraints. The case studies showed that there were significant qualitative and quantitative differences in solutions of deterministic and stochastic WTA problems.The third part of the project studied the Multiple Traveling Salesmen Problem (Multiple-TSP) in several variations. The research was focused on MIN-MAX 2-TSP, which cannot be solved by standard methods. The relation between this class of problems and a subclass of the self-dual monotonic Boolean functions was established. This resulted in new efficient optimization algorithms.

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“…Mangel [10] [11] looked at the problem where a target was assumed to move in the plane and the searcher in space. Optimal search path problems have been addressed by Washburn [12] [13], Eagle and his co-workers [14]- [17]. The conflict between simplicity and optimality in searching for a 2-D stationary target was dealt with by Washburn [18].…”

Section: Introductionmentioning

confidence: 99%

Computational Studies on Detecting a Diffusing Target in a Square Region by a Stationary or Moving Searcher

Wang

Zhou

2015

AJOR

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In this paper, we compute the non-detection probability of a randomly moving target by a stationary or moving searcher in a square search region. We find that when the searcher is stationary, the decay rate of the non-detection probability achieves the maximum value when the searcher is fixed at the center of the square search region; when both the searcher and the target diffuse with significant diffusion coefficients, the decay rate of the non-detection probability only depends on the sum of the diffusion coefficients of the target and searcher. When the searcher moves along prescribed deterministic tracks, our study shows that the fastest decay of the non-detection probability is achieved when the searcher scans horizontally and vertically.

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Criteria and approximate methods for path-constrained moving-target search problems

Cited by 21 publications

References 13 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

Robust Decision Making: Addressing Uncertainties in Distributions

Computational Studies on Detecting a Diffusing Target in a Square Region by a Stationary or Moving Searcher

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