Index Policies for Shooting Problems

Glazebrook, K. D.; Kirkbride, C.; Mitchell, H. M.; Gaver, Donald P.; Jacobs, Patricia A.

doi:10.1287/opre.1070.0444

Cited by 14 publications

(11 citation statements)

References 23 publications

(20 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We refer the reader to Gittins et al (2011) for a recent account. Whittle index policies for restless bandits have seen near-optimal performance in many other applications (Archibald et al 2009;Glazebrook et al 2007Glazebrook et al , 2009). Below, we outline how to compute a heuristic policy.…”

Section: Heuristic Policies On Complete Graphsmentioning

confidence: 99%

“…The index-based heuristics have been successful in earlier works (Archibald et al 2009;Glazebrook et al 2007Glazebrook et al , 2009, where a resource (patroller) is dynamically moved among projects (nodes) to optimize system performance. These earlier works focused on the case when the decision maker knows the probability rule that governs the underlying stochastic process-analogous to random attackers.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Graph Patrol Problem with Random Attack Times

Lin

Atkinson

Chung

et al. 2013

Operations Research

View full text Add to dashboard Cite

This paper presents a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. To design a patrol policy, the patroller needs to take into account not only the graph structure, but also the different attack time distributions, as well as different costs incurred due to successful attacks, at different nodes. We consider both random attackers and strategic attackers. A random attacker chooses which node to attack according to a probability distribution known to the patroller. A strategic attacker plays a two-person zero-sum game with the patroller. For each case, we give an exact linear program to compute the optimal solution. Because the linear programs quickly become computationally intractable as the problem size grows, we develop index-based heuristics. In the random-attacker case, our heuristic is optimal when there are two nodes, and in a suitably chosen asymptotic regime. In the strategic-attacker case, our heuristic is optimal when there are two nodes if the attack times are deterministic taking integer values. In our numerical experiments, our heuristic typically achieves within 1% of optimality with computation time orders of magnitude less than what is required to compute the optimal policy.

show abstract

Section: Heuristic Policies On Complete Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Graph Patrol Problem with Random Attack Times

Lin

Atkinson

Chung

et al. 2013

Operations Research

View full text Add to dashboard Cite

show abstract

“…Other interesting formulations and applications are discussed in Glazebrook et al [23], Glazebrook et al [24], Su et al [46], Agmon et al [2], Lai et al [34], Liu et al [36] and Aalto et al [1], Katehakis et al [30], Weber [51], Weber and Weiss [52] and Chang and Lai [10].…”

Section: Introductionmentioning

confidence: 99%

Multi-Armed Bandits Under General Depreciation and Commitment

Cowan

Katehakis

2014

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

Generally, the multi-armed has been studied under the setting that at each time step over an infinite horizon a controller chooses to activate a single process or bandit out of a finite collection of independent processes (statistical experiments, populations, etc.) for a single period, receiving a reward that is a function of the activated process, and in doing so advancing the chosen process. Classically, rewards are discounted by a constant factor β ∈ (0, 1) per round.In this paper, we present a solution to the problem, with potentially non-Markovian, uncountable state space reward processes, under a framework in which, first, the discount factors may be non-uniform and vary over time, and second, the periods of activation of each bandit may be not be fixed or uniform, subject instead to a possibly stochastic duration of activation before a change to a different bandit is allowed. The solution is based on generalized restart-in-state indices, and it utilizes a view of the problem not as "decisions over state space" but rather "decisions over time".

show abstract

“…Manor and Kress (1997) investigate the optimality of greedy shooting in the presence of incomplete damage information. Glazebrook, Kirkbride, Mitchell, Gaver, and Jacobs (2007) and Glazebrook and Washburn (2004) investigate policies for shooting problems to maximize the expected number of targets killed.…”

Section: Literature Reviewmentioning

confidence: 99%

Bi‐objective missile rescheduling for a naval task group with dynamic disruptions

Silav

Karasakal

2019

Naval Research Logistics

View full text Add to dashboard Cite

This paper considers the rescheduling of surface‐to‐air missiles (SAMs) for a naval task group (TG), where a set of SAMs have already been scheduled to intercept a set of anti‐ship missiles (ASMs). In missile defense, the initial engagement schedule is developed according to the initial state of the defensive and attacking units. However, unforeseen events may arise during the engagement, creating a dynamic environment to be handled, and making the initial schedule infeasible or inefficient. In this study, the initial engagement schedule of a TG is assumed to be disrupted by the occurrence of a destroyed ASM, the breakdown of a SAM system, or an incoming new target ASM. To produce an updated schedule, a new biobjective mathematical model is formulated that maximizes the no‐leaker probability value for the TG and minimizes the total deviation from the initial schedule. With the problem shown to be NP‐hard, some special cases are presented that can be solved in polynomial time. We solve small size problems by the augmented ϵ‐constraint method and propose heuristic procedures to generate a set of nondominated solutions for larger problems. The results are presented for different size problems and the total effectiveness of the model is evaluated.

show abstract

Index Policies for Shooting Problems

Cited by 14 publications

References 23 publications

A Graph Patrol Problem with Random Attack Times

A Graph Patrol Problem with Random Attack Times

Multi-Armed Bandits Under General Depreciation and Commitment

Bi‐objective missile rescheduling for a naval task group with dynamic disruptions

Contact Info

Product

Resources

About