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Constraint Processing - Embedded Intelligent Robotics - Lecture Slides, Slides of Robotics

Course title is Embedded Intelligent Robotics. This course is for Electrical engineering students. Though good thing is everyone can learn about robotics in this course. This lecture includes: Constraint Processing, Backtracking, Informal Definition of Csp, Map Coloring, Constraint Network, Unaryconstraint, Crossword Puzzle, Generate and Test, Systematic Search

Typology: Slides

2013/2014

Uploaded on 01/29/2014

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Constraint Processing / Constraint Satisfaction Problem
(CSP) paradigm
Algorithms for CSPs
Backtracking (systematic search)
Constraint propagation (k-consistency)
Variable ordering heuristics
Backjumping and dependency-directed backtracking
Viewing scheduling as a CSP
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1

  • Constraint Processing / Constraint Satisfaction Problem (CSP) paradigm
  • Algorithms for CSPs
    • Backtracking (systematic search)
    • Constraint propagation (k-consistency)
    • Variable ordering heuristics
    • Backjumping and dependency-directed backtracking
  • Viewing scheduling as a CSP

2

Constraint

Processing

4

Informal Definition of CSP

  • CSP = Constraint Satisfaction Problem
  • Given (1) a finite set of variables (2) each with a domain of possible values (often finite) (3) a set of constraints that limit the values the variables can take on
  • A solution is an assignment of a value to each variable such that the constraints are all satisfied.
  • Tasks might be:
    • to decide if a solution exists,
    • to find a solution,
    • to find all solutions, or
    • to find the “best solution” according to some metric.

5 Informal Example: Map Coloring

  • Color the following map using three colors (red, green, blue) such that no two adjacent regions have the same color. E D A C B

7 Example: SATisfiability

  • Given a set of propositions containing variables, find an assignment of the variables to {false,true} that satisfies them.
  • Example, the clauses:
    • A or B or ~C, ~A or D
    • (equivalent to C - > A or B, D - > A)
  • Are satisfied by A = false B = true C = false D = false

8 Real-world problems

  • Scheduling
  • Temporal reasoning
  • Building design
  • Planning
  • Optimization/satisfaction
  • Vision
    • Graph layout
    • Network management
    • Natural language processing
    • Molecular biology / genomics
    • VLSI design Useful in the projects

10 Formal definition of a CN (cont.)

  • Instantiations
    • An instantiation of a subset of variables S is an

assignment of a legal domain value to each

variable in in S

  • An instantiation is legal iff it does not violate any

(relevant) constraints.

  • A solution is an instantiation of all of the variables in the network.

11 Typical Tasks for CSP

  • Solutions:
    • Does a solution exist?
    • Find one solution
    • Find all solutions
    • Given a partial instantiation, do any of the above
  • Transform the CN into an equivalent CN that is easier to solve.

13 Example: Crossword Puzzle 1 2 3 4 5

14

Running Example: XWORD Puzzle

  • Variables and their domains
    • X1 is 1 across D1 is 5-letter words
    • X2 is 2 down D2 is 4-letter words
    • X3 is 3 down D3 is 3-letter words
    • X4 is 4 across D4 is 4-letter words
    • X5 is 5 across D5 is 2-letter words
  • Constraints (implicit/intensional)
    • C12 is “the 3rd letter of X1 must equal the 1st letter of X2”
    • C13 is “the 5th letter of X1 must equal the 1st letter of X3”.
    • C24 is …
    • C25 is …
    • C34 is ...

16 Solving Constraint Problems

  • Systematic search
    • Generate and test
    • Backtracking
  • Constraint propagation (consistency)
  • Variable ordering heuristics
  • Backjumping and dependency-directed backtracking

17 Generate and test: XWORD

  • Try each possible combination until you find one that works:
    • Hoses – hike – run – hike – no
    • Hoses – hike – run – hike – be
    • Hoses – hike – run – hike – us
  • Doesn’t check constraints until all variables have been instantiated
  • Very inefficient way to explore the space of possibilities

19 Backtracking: XWORD (^1 2 ) 4 5

X1=hoses X1=laser X2=aron X2=same X2=hike X2=hike …

X3=run (^) X3=sun X3=let X4=hike … X4=same h o s e s u n a m e

20 Problems with backtracking

  • Thrashing: keep repeating the same failed variable assignments - Consistency checking can help - Intelligent backtracking schemes can also help
  • Inefficiency: can explore areas of the search space that aren’t likely to succeed - Variable ordering can help