1. Extensions to BT Search Foundations of Constraint Processing
CSCE 421/821, Spring 2018
Berthe Y. Choueiry (Shu-we-ri)
Avery Hall, Room 360
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2. Outline Variations of backtrack search
Backtrack search for optimization
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3. Variations on BT search
Bounded number of backtracks search
Bounded backtrack-depth search
Limited discrepancy search (LDS)
Heuristic may be blind at shallowest level of search-tree
Disobey heuristic a given number of times
Credit-based backtrack search
Randomized backtrack search (+ restart)
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4. Credit-Based Search Start with a given credit (usually n3)
Assign ½ credit to current assignment, ½ to the remaining ones
Keep going, in a depth-first manner until credit is used up, (chronoligically) backtrack from there
ECLiPSe uses it in conjunction with backtrack-bounded search
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5. Randomized BT search In systematic backtrack search
Ordering of variables/values determines which parts of the solution space are explored
Randomization allows us to explore wider portion of search tree
Thrashing causes stagnation of BT search
Interrupt search, then restart
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6. Restart strategies Fixed-cutoff & universal strategy [Luby et al., 93]
Randomization & Rapid restarts (RRR) [Gomes et al., 98]
Fixed optimal cutoff value
Priori knowledge of cost distribution required
Randomization & geometric restarts (RGR) [Walsh 99]
Randomization & dynamic geometric restarts (RDGR)
[Guddeti 04]
Bayesian approach [Kautz et al., 02]
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7. RGR [Walsh 99] Static restart strategy
As the cutoff value increases, RGR degenerates into randomized BT
Ensures completeness (utopian in our setting)
But… restart is obstructed
… and thrashing reappears  diminishing the probability of finding a solution
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8. RDGR [Guddeti 04] Randomization & Dynamic Geometric Restarts
Cutoff value
Depends on the progress of search
Never decreases, may stagnate
Increases at a much slower rate than RGR
Feature: restart is ‘less’ obstructed
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9. Outline Variations of backtrack search
Backtrack search for optimization
Courtesy of Markus Fromherz
Branch and bound
Binary search
Iterative deepening
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10. Branch & Bound
Find a first solution, compute its quality, call it the incumbent
Systematically explore alternative solutions
While building an alternative solution, ‘estimate’ its quality and compare the estimated quality with that of the incumbent
If a partial solution has no chance of becoming better than the incumbent
Then prune it
Else, keep building it
As soon as a better solution is found, make it the incumbent
Continue until you run out of time, patience, or solutions
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11. B&B: over-constrained-CSPs
Max-CSP
Goal: minimize the number of broken constraints (while instantiating all variables)
Maximize solution length
Goal: maximize number of variables instantiated (while satisfying all constraints)
We compare the incumbent and the partial solution along current path according to
the number of broken constraints or
the number of instantiated variables
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12. Binary search
Given l, u lower and upper bounds of the quality of the solution
Check whether there is a solution in [l, u-l/2]=[l,u’]
If there is, set the bounds [l,u’]= [l,u-l/2] and apply the mechanism again
If there is not, set the bounds to [u’, u] and apply the mechanism again
Restart search with progressively narrower lower and upper bounds on the solution
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13. Iterative deepening
Restart search with an increasing lower limit on the solution quality until a solution of an acceptable quality is found
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