Major accomplishements

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How to Fuse Independent Sensors Fast? (Nuclear
Detection)
Endre Boros MSIS RUTCOR, Rutgers
University Endre.Boros_at_rutgers.edu
Joint work with Noam Goldberg, Paul B. Kantor and
Jonathan Word
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Statement of Problem

• The Problem
• There are several tests that can be applied
  (document checks, passive and active sensors of
  several kinds). Find the optimal detection
  policy based on these tests! Multiple branching
  policy mixing!

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Assumptions and Complexity

• Stochastically independent non-repeated sensors
• s sensors, k labels at each gtgt 2ks policies
• Futility of heuristic searches!

sensors labels policies
4 2 gtgt 216
4 5 gtgt 2625
8 2 gtgt 2256
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Move to a decision support model

• Minimize total damage over all available policies
  
• MinP C(P) pK(1- ?(P))
• ?(P), C(P) - detection rate, and operating
  cost of policy P
• p ( 0), K (very large) - a priori probability
  of a bomb, and expected cost of false negative
• MaxP ?(P) C(P) B
• mixing and domination of
  policies
• concave envelope of best
  policies

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Dynamic Programming Sensor Fusion

• Fusing sensor k on top of the given policies
  optimally is a multi-knapsack problem that can be
  solved by a modified greedy algorithm

Detection
Greedy Algorithm
Cost
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Dynamic Programming common concave envelope

• We then merge the given policies with the best
  combination of them with sensor k on top and
  generate the common concave envelope of all these
  policies

Detection
Greedy Algorithm
Cost
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Dynamic Programming Summary

• We build the concave envelope of best possible
  policies constructible from the given set of s
  sensors.
• We solve s2s sensor fusion problems (for up to s
  20)
• Each Sensor Fusion can be solved in
  O(PBPlog(P)) time, where B is the number of
  channels of the top sensor, and P is the number
  of pure strategies on the effective frontier.

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What about approximating the output in each step?
Stroud and Saeger sensors (4 sensors, 100 labels each) Stroud and Saeger sensors (4 sensors, 100 labels each) Stroud and Saeger sensors (4 sensors, 100 labels each)
Time (sec) Number of Policies Max. Relative Error
1440 52319 0.005
3.53 204 0.05
0.61 33 0.5
1.33 GHz Intel Atom processor 1.33 GHz Intel Atom processor 1.33 GHz Intel Atom processor
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Extremal frontier with 33 undominated policies
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Detection 81.527 Cost 0.1977826 units
11.867 (lt 13)
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Publications

• 1. Goldberg, N., Word, J., Boros, E. Kantor, P.
  (2008). Optimal Sequential Inspection Strategies.
  Annals of Operations Research Vol. 187, 2011.
• 2. Boros, E., Fedzhora, P.B., Kantor, P.B.,
  Saeger, K., Stroud, P. Large Scale LP Model for
  Finding Optimal Container Inspection Strategies.
  Naval Research Logistics Quarterly, Vol. 56 (5),
  404-420, 2009.
• 3. Kantor, P.B. Boros E. Deceptive Detection
  Methods for Optimal Security with Inadequate
  Budgets the Screening Power Index. Risk Analysis
  Vol. 30, 2010.