Adaptive Problem-Solving for Large-Scale Scheduling Problems: A Case Study by Jonathan Gratch and Steve Chien Published in JAIR, 1996

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Adaptive Problem-Solving for Large-Scale
Scheduling Problems A Case Studyby Jonathan
Gratch and Steve ChienPublished in JAIR, 1996

• EARG presentation Oct 3, 2008by Frank Hutter

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Overview

• Problem domain
• Cool scheduling for the deep space network
• Scheduling algorithm
• Branch Bound with a Lagrangian relaxation at
  each search node
• Adaptive Problem Solving
• Automatic Parameter Tuning by Local Search
• Already contains many good ideas, 12 years ago!

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Domain Scheduling for the Deep Space Network

• Collection of ground-based radio antennas
• Maintain communication with research satellites
  and deep space probes
• NASAs Jet Propulsion Laboratory (JPL) automate
  scheduling of 26-meter subnet
• Three 26-meter antennas
• Goldstone, CA, USA
• Canberra, Australia
• Madrid, Spain

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Scheduling problemWhen should which antenna
talk to which satellite?

• Project requirements
• Number of communication events per period
• Duration of communication events
• Allowable gap between communication events
• E.g. Nimbus-7 (meteorogical satellite) needs at
  least four 15-minute slots per day, not more
  than 5 hours apart
• Antenna constraints
• Only one communication at once
• Antenna can only communicate with satellites in
  view
• Routine maintenance ? antenna offline

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Problem formulation

• 0-1 integer linear programming formulation
• Time periods 0-1 integer variables (in/out)
• Typical problem 700 variables, 1300 constraints
• Scheduling has to be fast
• So human user can try what if scenarios
• For these reasons, the focus of development is
  upon heuristic techniques that do not necessarily
  uncover the optimal schedule, but rather produce
  adequate schedules quickly.
• Alas, they still dont use local search -)

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Scheduling algorithm

• Branch and Bound (Split-and-prune)
• At each node
• arc consistency (check all constraints containing
  time period just committed)
• Lagrangian relaxation each antenna by itself
• Can be solved in linear time (dynamic programming
  for each antenna to get non-exclusive sequence
  of time periods with maximum cumulative weight)

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Lagrangian relaxation

• Relax project constraints, penalize violation by
  weight uj weight search for best vector u

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The LR-26 scheduler
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Search Algorithm Parameters

• Constraint ordering
• Choose a constraint that maximally constrains
  the rest of the search space
• 9 heuristics, same 9 as secondary tie-breakers
• Value ordering maximize the number of options
  available for future assignments
• 5 heuristics implemented
• Weight search (for weight vector u)
• 4 methods implemented
• Refinement methods
• 2 options Standard BB vs. (Ax fails, then try
  By instead of A1-x --- does this have a name??)

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Problem distribution

• Not many problem instances available
• Syntactic manipulation of set of real problems
• Yields 6,600 problem instances
• Only use subset of these 6,600 instances
• Some generated instances seemed much harder than
  original instances
• Discard intractable instances (original or
  generated)
• Intractable instances taking longer than 5
  minutes

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Determination of Resource Bound

• Only 12 of problems unsolved in 5 minutes were
  solved in an hour
• Reference to statistical analysis for that factor
• ? should read that in EARG (Etzioni Etzioni,
  1994)

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Adaptive Problem Solving Approaches

• Syntactic approach
• Transform into more efficient form, using only
  syntactic structure
• Recognize structural properties that influence
  effectiveness of different heuristic methods
• Big lookup table, specifying heuristic to use
• Somewhat similar to SATzilla ? Lin should look
  into it
• (I think includes newer research on symmetry
  breaking, etc)
• Generative approach
• Generate new heuristics based on partial runs of
  solver ? focus on inefficiencies in previous runs
• Often learning is within an instance and does
  not generalize to distributions of problems
• Statistical approach
• Explicitly reason about performance of different
  heuristics across distribution of problems
• Often statistical generate-and-test approaches
• Widely applicable (domains, utility functions)
• Computationally expensive local optima (?
  ParamILS)

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Adaptive Problem Solving Composer

• Statistical approach
• Generate-and-test hillclimbing
• When evaluating a move
• Perform runs with neighbour
• Collect differences in performance
• Perform test to see if mean(differences) lt 0 or
  gt0
• Test assumes Normal distribution of differences
• Terminate in first local optimum
• Evaluation
• On large set of test instances (1000)

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Meta-Control Knowledge in Composer Layered Search

• Order parameters by their importance
• First only allow move in the first level, then
  allow move in the second level, etc
• Not sure whether they iterate
• Levels
• Level 0 weight search method
• Level 1 Refinement method
• Level 2 Secondary refinement, value ordering
• Level 3 Primary constraint ordering
• (this comes last since they strongly believed
  their manual one was best it was indeed chosen)

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Composer pseudo code
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Empirical evaluation

• Setting of Composer parameters
• ? 0.05, n0 15 (empirically determined)
• Training set 300 problem instances
• Test set 1000 problem instances
• They say independent, but I dont think
  disjoint
• Stochasticity from drawing instances at random
• Estimate expected performance as average over
  multiple experimental trials
• But dont tell us how many trials they did ?
• Measure performance every 20 samples

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Experimental results subset
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Experimental result full set
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Kernel density estimate of strategies subset
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Kernel density estimate of strategies full set
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My view of their approach

• Some very good ideas, already 12 years ago
• Proper use of training/test set
• Statistical test for move is interesting
• Problems I see
• If a move neither decreases nor increases
  expected utility, the statistical test can force
  an infinite number of evaluations
• Even if this just decides between two poor
  configurations
• Stuck in local minima
• Never re-using instances? Once theyre out of
  instances, they stop (also still a little unclear)