More on BT Search
This presentation is the property of its rightful owner.
Sponsored Links
1 / 17

Foundations of Constraint Processing CSCE421/821, Fall 2004: PowerPoint PPT Presentation


  • 47 Views
  • Uploaded on
  • Presentation posted in: General

More on BT Search. Foundations of Constraint Processing CSCE421/821, Fall 2004: www.cse.unl.edu/~choueiry/F04-421-821/ Berthe Y. Choueiry (Shu-we-ri) Avery Hall, Room 123B [email protected] Tel: +1(402)472-5444. Outline. Lookahead Variations of backtrack search

Download Presentation

Foundations of Constraint Processing CSCE421/821, Fall 2004:

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Foundations of constraint processing csce421 821 fall 2004

More on BT Search

Foundations of Constraint Processing

CSCE421/821, Fall 2004:

www.cse.unl.edu/~choueiry/F04-421-821/

Berthe Y. Choueiry (Shu-we-ri)

Avery Hall, Room 123B

[email protected]

Tel: +1(402)472-5444

More on BT search


Outline

Outline

  • Lookahead

  • Variations of backtrack search

  • Backtrack search for optimization

More on BT search


Lookahead

Lookahead

  • Rationale

    • As decisions are made (conditioning) eliminate inconsistent choices in future sub-problem

    • Domain annihilation of a future variable avoids expansion of useless portions of the tree

  • Techniques

    • Partial: forward-checking (FC), directional arc-consistency (DAC)

    • Full: Maintaining arc-consistency (MAC)

  • MAC: more pruning at the cost of more consistency checks

  • Empirical results:

More on BT search


Outline1

Outline

  • Lookahead

  • Variations of backtrack search

  • Backtrack search for optimization

More on BT search


Variations on bt search

Variations on BT search

  • Bounded number of backtracks search

  • Bounded backtrack-depth search

  • Limited discrepancy search

    • 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)

More on BT search


Credit based search

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

More on BT search


Randomized bt search

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

More on BT search


Restart strategies

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]

More on BT search


Rgr walsh 99

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

More on BT search


Rdgr guddeti 04

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

More on BT search


Outline2

Outline

  • Lookahead

  • Variations of backtrack search

  • Backtrack search for optimization

More on BT search


Bt search for optimization

BT search for optimization

Courtesy of Markus Fromherz

  • Branch & bound

    • Application to over-constrained CSPs

  • Binary search

  • Iterative deepening

  • Etc.

More on BT search


Branch bound

Branch & Bound

  • Branch & bound

    • Find a first solution, compute its quality, call it the incumbent

    • Search for other solutions, comparing them with the incumbent

    • As soon a better solution is found, make it the incumbent

    • Continue until you run out of time, patience, or solutions

More on BT search


B b over constrained csps

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

More on BT search


Binary search

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]=[u,l’]

    • If there is, set the bounds [u, u+l’/2] and search for a solution

    • If there is not, set the bounds to [l’, l+l’/2] and search for a solution…

  • Restart search with progressively narrower lower and upper bounds on the solution

More on BT search


Iterative deepening

Iterative deepening

  • Restart search with an increasing upper limit on the solution quality until a solution is found

More on BT search


Rest of the course

Rest of the course?

  • Local search

  • Binary vs. non-binary

  • Phase Transition

  • All-diff constraint (Shasha?)

  • Backtrack-free, backtrack-bounded search

  • Temporal CSPs

  • Interchangeability

  • Dynamic CSPs

More on BT search


  • Login