Shortcomings of Traditional Backtrack Search on Large, Tight CSPs:

1
Shortcomings of Traditional Backtrack Search on
Large, Tight CSPs A Real-world Example
Venkata Praveen Guddeti and Berthe Y. Choueiry
Constraint Systems Laboratory Department of
Computer Science and Engineering, University of
Nebraska-Lincoln vguddetichoueiry_at_cse.unl.edu
Methodology
Abstract

• We compared the ordering heuristics according to
  five criteria
• Unassigned courses the number of courses that
  are not assigned a GTA.
• CC the number of constraint checks.
• NNV the number of nodes visited.
• Number of backtracks the number of backtracks
  done.

Problems of systematic BT search
Unassigned variables The table below shows the
number of unassigned variables and the CPU run
time taken for the solution.
Systematic Search
Many ordering heuristics have also been
implemented to improve the performance of search
and the embedded forward checking (FC) mechanism
implemented for the GTA problem 1. We
experimented with various data sets of the GTA
assignment problem to analyze and compare the
performance of the various ordering heuristics
implemented. We report our observations and
summarize our analysis of the shortcomings of
traditional backtrack search methods on large
over-constrained CSPs. We show that the
performance of value and variable ordering
heuristics depend on the problem instance. And
the BT mechanism gets thrashed in a small
portion of the search space unable to undo early
choice, regardless of the ordering heuristic
used.
Systematic Search Forward checking algorithm
augmented with various ordering heuristics.
Problems of random BT search
The search tree of the GTA problem is so large
that even random BT search is not enough to avoid
the thrashing during search. Although the
solutions vary with each run, the shallowest BT
level does not improve.

• Value Ordering Heuristics 3 value ordering
  heuristics
• First in last out (FIL) The first available
  value is selected.
• Highest preference value (PREFERENCE) The value
  having the highest preference is selected.
• Least occurring value (OCCURRENCE) The value
  occurring the least number of times in the future
  variables is selected.

Current investigations

• We are testing various restart strategies based
  on
• Fixed restarts and
• Dynamic restarts 2.
• Limited BT search Keeping a count of the amount
  of backtracking done so far and abandoning the
  search if more than the cutoff value 3.
• Credit based search Each search path is assigned
  some credit. This credit may or may not be
  uniform. If credit is over than perform
  deterministic search and/or small amount of local
  search 3.

• Random Ordering Heuristics 2 heuristics using
  randomness
• All Random The value and variable selection were
  done randomly.
• Hybrid heuristic Random heuristics in
  combination with the above mentioned ordering
  heuristics.

References
Experiments

1. R. Glaubius and B. Y. Choueiry, Constraint
   Modeling and Reformulation in the Context of
   Academic Task Assignment. In Working Notes of
   the Workshop Modeling and Solving Problems with
   Constraints, ECAI 2002.
2. H. Kautz, E. Horvitz, Y. Ruan, C. Gomes, B.
   Selman Dynamic Restart Policies. In
   Proceedings of the Eighteenth National Conference
   on Artificial Intelligence, Edmonton, Alberta,
   July 2002. AAAI Press.
3. H. Simonis, Invited Talk at the Constraint
   Systems Laboratory, UNL, November 2000.

The combination of the 4 variable ordering
heuristics and the 3 value ordering heuristic
yielded 12 ordering heuristics. Three real-world
data sets of spring 2001, fall2001 and fall2002
were used for the experiments. Thus, 48
experiments were carried out. Each experiment was
run for 10 minutes. Results were noted for both
the best solution found and for full 10 minute
run.