The TEVASPOT Toolkit

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The TEVA-SPOT Toolkit

• William E Hart1, Jonathan W Berry1,
• Regan Murray2, Cynthia A Phillips1,
• Lee Ann Riesen1, Jean-Paul Watson1
• 1Discrete Algorithms and Mathematics Department,
  Sandia National Laboratories, Albuquerque, NM
• 2NHSRC, Environmental Protection Agency,
  Cincinnati, OH

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CWS Design

• Goal design an online contaminant warning system
  to protect against contamination events
• Challenge placement of sensors for the CWS
  within a budget
• Sensor placement issues
• How do sensors work?
• What is the design basis threat?
• How does a utility respond to detection events?
• What performance measures are used to evaluate
  the CWS?
• What are the potential sensor locations?

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SPOT Sensor Placement Optimization Toolkit

• TEVA-SPOT A GUI interface for vulnerability
  assessment and sensor placement
• Development led by EPA and ANL
• TEVA-SPOT Tookit The sensor placement library
  used by TEVA-SPOT
• Development led by EPA and SNL
• Academic collaborators UC, CU Denver, IBM, PNNL,
  UNM
• but Ill just call this SPOT for convenience.

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Motivations for SPOT

• Flexible solvers that can optimize many different
  objectives
• Scalable solvers for large-scale problems
• 10,000s junctions and pipes
• Limited-memory problem representations
• Flexible specification of problem formulation
• Flexible specification of performance constraints
• Fast, flexible solvers
• Methods for rigorously evaluating solver
  performance

Application Driver The EPA needs a robust sensor
placement capability for ongoing water security
analyses (TEVA Program).
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A Canonical Problem Formulation

• Minimize expected impact of contamination events
• Over a selected set of times and locations
• Cost constraint
• Limit number of sensors
• Limit cost of installation
• Note
• This is the formulation considered by most of the
  literature
• This assumes the adversary has no knowledge of
  how event time/location relates to impact of the
  event

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An Integer Programming Formulation

• Variables
• a event likelihood
• w event impact
• b event witness indicator
• s sensor placement indicator
• IP model
• Objective is to minimize the expected impact of
  all events
• Very general formulation
• Can capture different objectives/networks
• Can be solved with COTS software

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(A) Performance Objectives

• This formulation can capture a wide range of
  performance objectives
• Extent of contamination
• Population exposed
• Population Sickened
• Response time
• Mass of contaminant in the network
• Volume of contaminant in the network
• Number of sensors
• Total cost (weighted by sensor lcoation)

Key Idea These performance objectives are
derived from external contaminant transport
calculations and impact assessments, which can be
arbitrarily complex.
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(B) Scalability

• IP Size
• n junctions (10,000s)
• m contamination times (100s)
• Up to nm contamination locations
• Up to n2m contamination impact values
• Observations
• A 64-bit workstation is required to solve
  applications with 1000s of junctions and many
  contamination times
• Need ability to solve applications with 10,000s
  of junctions

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(B) Scalability Techniques

• Witness Aggregation
• Combine witness indicator variables (e.g. if they
  are equal or nearly equal)
• Can compute a bound on the aggregated problem
• Scenario Aggregation
• Combine scenarios that could contaminant sites in
  the same order
• This allows the optimal sensor placements for
  multiple types of contaminants
• Representative Sensor Locations
• Select representative or candidate sensor
  locations
• The problem representation only needs to reflect
  those locations

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(C) Alternative Problem Formulations

• Minimize Worst-Case Performance
• Mathematically equivalent to the p-mean problem
• Difficult to solve with IP or heuristic solvers
• Robustness Formulations
• Can handle data uncertainties with min-max
  formulations
• Are solvable as IPs in some cases, but they are
  harder
• Can handle uncertainty in contamination
  location/time explicitly
• Risk measures Value at Risk, Tail-conditioned
  expectation
• Solving these formulations is still difficult
• Can reduce worst-case impacts while maintaining
  good expected-case performance

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(D) Performance Constraints

• Observations
• Different performance objectives need to be
  considered in practice
• Cannot generally minimize all objectives
• Idea iteratively optimize different objectives
• SPOT can use side-constraints to constraint
  secondary objectives
• Solver performance is poor with more than one
  constraint
• Solvers can cache nearly feasible solutions to
  illustrate the trade-off between the new
  objective and the constraint

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(E) Fast, Flexible Solvers

• SPOT Solver Options
• PICO integer programming solver
• CPLEX integer programming solver (commercial)
• GRASP heuristic
• Lagrangian heuristic
• GRASP
• Optimizes with multiple local searches
• Can rapidly solve problems with 10,000s of
  junctions (minutes)
• Heuristic solutions are often optimal
• Lagrangian
• Optimizes with iterative penalties on constraint
  violations
• Uses very little memory
• Provides a bound on the value of the final
  solution

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(F) Confidence Bounds

• Goal find near-optimal solutions AND quantify
  how close to optimum they are
• IP Solvers find a globally optimal solution (but
  only for modest-scale problems)
• Heuristic
• Often finds globally optimal solutions
• Can bound the global optimum with a LP-relaxtion
  of the IP
• Lagrangian
• Finds near-optimal solutions
• Provides a bound on the value of the global
  optimum

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How SPOT Works
TEVA-SPOT performs optimization to find a sensor
placement. The sensor placement minimizes the
potential impact of the ensemble of contamination
events defined in Impact files. One or more
sensor placements are generated.
TEVA-Sim executes an ensemble of EPANET
simulations. This ensemble is defined by
characteristics of the contamination events that
are relevant for sensor placement (e.g. when and
where contamination events might occur.) TSO
files are formatted in a generic manner to
encompass a wide range of water quality
statistics about contamination events.
TEVA-CAT computes consequences from water quality
simulations. Consequence analysis varies based
on the type of impact being measured. Some
analyses use water quality statistics, while
others simply use the extent of
contamination. Impact files are formatted in a
generic manner they summarize how the impact of
events can be minimized by placing sensors that
can observe them.
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Future Directions

• Ongoing applications to large-scale water
  utilities
• Especially within the USEPAs TEVA Program
• Academic collaborations to integrate other sensor
  placement techniques
• E.g. include multi-objective optimization
  capabilities
• Planning public release of TEVA-SPOT Toolkit in
  2008
• Some consequence assessment capabilities may be
  limited to water utilities with a business need
• An upcoming TEVA webpage will include a link to
  TEVA-SPOT when it is released!

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Questions?