Decomposition Techniques for a LooselyCoupled Resource Allocation Problem

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Decomposition Techniques for a Loosely-Coupled
Resource Allocation Problem

• Pierrick Plamondon, Brahim Chaib-draa, and
• Abder Rezak Benaskeur

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Motivation

• We are motivated by a real-time resource
  allocation problem
• We decompose the problem in strongly connected
  components, using an acyclic graph
• A standard method supposes that all the problem
  is strongly connected
• Using our algorithms, the planning time is
  greatly reduced

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Overview

• Problem
• Definitions and model of the problem
• Decomposition techniques
• Conclusion

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NEREUS Project

• Planning agent Frigate
• Tasks To counter each threat (Platforms and
  Missiles)
• Resources Weapons, sensors and movements of the
  frigate
• Action To use resources

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Problem

• This problem needs a response (plan) before a
  very short hard deadline
• The number of states is the combination of each
  task individual state spaces, and individual
  resources
• The number of actions is the combination of
  possible assignments of each resource to tasks

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Overview

• Problem
• Definitions and model of the problem
• Decomposition techniques
• Conclusion

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Problem model

• The states of a task are strongly connected, and
  the tasks are weakly connected

Task 2
Task 1
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Dynamic programming

• The value of a state is
• With local and global resource constraints
  and

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Overview

• Problem
• Definitions and model of the problem
• Decomposition techniques
• Conclusion

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Acyclic decomposition

• We form an acyclic graph containing cyclic
  components
• Where a component is a group of task to accomplish

Here, a task may create one other task in maximum
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Acyclic decomposition

• may be any
• algorithm to solve an MDP

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Acyclic decomposition

• This algorithm produces an optimal solution
• The acyclic decomposition diminishes greatly the
  planning time, but not sufficiently
• The online decomposition is inspired from the
  acyclic decomposition

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On-line decomposition

• The tasks are solved a priori
• The action is computed on-line

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Results
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Results

• Difference from the optimal for the on-line
  decomposition algorithm

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Overview

• Problem
• Definitions and model of the problem
• Decomposition techniques
• Conclusion

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Conclusion

• We presented two algorithms which diminishes
  greatly the planning time for our problem type
• The acyclic decomposition algorithm is optimal
• The on-line decomposition algorithm is
  approximate but very fast
• The planning time would be further reduced when
  coupled with a method that consider the actions
• For example, if we plan for each resource while
  using our acyclic method, the planning time would
  be further reduced

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Questions

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