Decision Support Algorithms for
Port of Entry Inspection
Fred S. Roberts
DIMACS Center, Rutgers University
In collaboration with Los Alamos National Laboratory
Preliminary Support: Office of Naval Research
1
Port of Entry Inspection Algorithms
•Goal: Find ways to intercept illicit
nuclear materials and weapons
destined for the U.S. via the
maritime transportation system
•Currently inspecting only small
% of containers arriving at ports
•Even inspecting 8% of containers in Port of
NY/NJ might bring international trade to a halt
(Larrabbee 2002)
2
Port of Entry Inspection Algorithms
•Aim: Develop decision support algorithms that
will help us to “optimally” intercept illicit
materials and weapons subject to limits on delays,
manpower, and equipment
•Find inspection schemes that minimize total
“cost” including “cost” of false positives and
false negatives
Mobile Vacis: truckmounted gamma ray
imaging system
3
Sequential Decision Making Problem
•Stream of containers arrives at a port
•The Decision Maker’s Problem:
•Which to inspect?
•Which inspections next based on previous results?
•Approach:
–“decision logics”
–combinatorial optimization methods
–Builds on ideas of Stroud
–and Saeger at LANL
–Need for new models
– and methods
4
Sequential Decision Making Problem
•Containers arriving to be classified into categories.
•Simple case: 0 = “ok”, 1 = “suspicious”
•Inspection scheme: specifies which inspections are
to be made based on previous observations
5
Sequential Decision Making Problem
•Containers have attributes, each in a number of
states
•Sample attributes:
–Does ship’s manifest set off an “alarm”?
–What is the neutron or Gamma emission
count? Is it above threshold?
–Does a radiograph image come up positive?
–Does an induced fission test come up positive?
Gamma
ray
detector
6
Sequential Decision Making Problem
•Simplest Case: Attributes are in state 0 or 1
•Then: Container is a binary string like 011001
•So: Classification is a decision function F that
assigns each binary string to a category.
011001
F(011001)
If attributes 2, 3, and 6 are present, assign container to
category F(011001).
7
Sequential Decision Making Problem
•If there are two categories, 0 and 1, decision
function F is a boolean function.
Example:
F(000) = F(111) = 1, F(abc) = 0 otherwise
This classifies a container as positive iff it has
none of the attributes or all of them.
1=
8
Sequential Decision Making Problem
•Given a container, test its attributes until know
enough to calculate the value of F.
•An inspection scheme tells us in which order to
test the attributes to minimize cost.
Hard Questions
•Even this simplified problem is hard
computationally.
9
Binary Decision Tree Approach
•Sensors measure presence/absence of attributes.
•Binary Decision Tree:
–Nodes are sensors or categories (0 or 1)
–Two arcs exit from each sensor node, labeled
left and right.
–Take the right arc when sensor says the
attribute is present, left arc otherwise
10
Binary Decision Tree Approach
•Reach category 1 from the
root only through the path
a0 to a1 to 1.
•Container is classified in
category 1 iff it has both
attributes a0 and a1.
•Corresponding boolean
function F(11) = 1, F(10) =
F(01) = F(00) = 0.
Figure 1
11
Binary Decision Tree Approach
•Reach category 1 from
the root by:
a0 L to a1 R a2 R 1 or
a0 R a2 R1
•Container classified in
category 1 iff it has
a1 and a2 and not a0 or
a0 and a2 and possibly a1.
•Corresponding boolean
function F(111) = F(101)
= F(011) = 1, F(abc) = 0
otherwise.
Figure 2
12
Binary Decision Tree Approach
•This binary decision
tree corresponds to the
same boolean function
F(111) = F(101) = F(011)
= 1, F(abc) = 0
otherwise.
However, it has one less
observation node ai. So,
it is more efficient if all
observations are equally
costly and equally likely.
Figure 3
13
Binary Decision Tree Approach
•Even if the boolean function F is fixed, the
problem of finding the “optimal” binary decision
tree for it is very hard (NP-complete).
•For small n = number of attributes, can try to
solve it by brute force enumeration.
Port of Long Beach
•Even for n = 4, not practical. (n = 4 at Port of
Long Beach-Los Angeles)
14
Binary Decision Tree Approach
Promising Approaches:
•Heuristic algorithms, approximations to optimal.
•Special assumptions about the boolean function F.
•Example: For “monotone” boolean functions,
integer programming formulations give promising
heuristics.
15
Cost Functions
•Above analysis: Only uses number of sensors
•Using a sensor has a cost:
–Unit cost of inspecting one item with it
–Fixed cost of purchasing and deploying it
–Delay cost from queuing up at the sensor
station
•Unit Cost Complication: How many nodes of
the decision tree are actually visited during
average container’s inspection? Depends on
“distribution” of containers.
16
Cost Functions: Delay Costs
•Stochastic process of containers arriving
•Distribution of delay times for inspections
•Use queuing theory to find average delay
times under different models
17
Cost Functions
•Cost of false positive: Cost of additional
tests.
–If it means opening the container, it’s
very expensive.
•Cost of false negative: Complex issue.
18
Cost Functions
•One Approach to False Positives/Negatives and
Sensor Errors: Modeling Sensor Operation
•Threshold Model:
•Sensors have different discriminating power
•Many use counts
•See if count exceeds
threshold
19
Cost Functions
Threshold Model:
•Sensor discriminating power K, threshold T
•Attribute present if counts exceed T
•Calculate fraction of objects in each category
whose readings exceed T
•Seek threshold values that minimize all costs:
inspection, false positive/negative
•Simulation approach
Mathematical
modeling
20
Complications
•Sensor errors –
probabilistic approach
•More than two values of an attribute
(present, absent, present with probability > 75%,
etc.)
•Inferring the boolean function from
observations (partially defined boolean
functions)
21
Complications
Machine learning approaches are promising:
–Bayesian binary regression
–Splitting strategies
–Pruning learned decision trees
22
Research Team
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Endre Boros, Rutgers, Operations Research
Elsayed Elsayed, Rutgers, Industrial and Systems Engineering
Paul Kantor, Rutgers, School of Information and Library Studies
Sallie Keller-McNulty, Los Alamos, Statistical Sciences Group
Alex Kogan, Rutgers, Business School
Paul Lioy, Rutgers/UMDNJ, Environmental and Occupational
Health and Sciences Institute
David Madigan, Rutgers, Statistics
Richard Mammone, Rutgers, Center for Advanced Information
Processing
S. Muthukrishnan, Rutgers, Computer Science
Feng Pan, Los Alamos, Energy and Infrastructure Analysis Group
Richard Picard, Los Alamos, Statistical Sciences Group
Fred Roberts, Rutgers, DIMACS Center
Kevin Saeger, Los Alamos, Homeland Security
Phillip Stroud, Los Alamos, Systems Engineering and Integration
23
Group
For Further Information
Fred Roberts
•Director of DIMACS
http://dimacs.rutgers.edu/
•Chair, Rutgers University Homeland Security
Research Initiative
http://dimacs.rutgers.edu/RUHSRI/
•Co-chair, New Jersey Universities Homeland
Security Research Consortium
http://dimacs.rutgers.edu/NJHSConsortium/
24