Maintaining Arc Consistency (MAC) MAC is the same as Back-tracking, but with calls to AC-3 interleaved... function Backtracking-Search(csp) returns.

Slides:



Advertisements
Similar presentations
Non-Binary Constraint Satisfaction Toby Walsh Cork Constraint Computation Center.
Advertisements

Backward Checking Search BT, BM, BJ, CBJ. An example problem Colour each of the 5 nodes, such that if they are adjacent, they take different colours 12.
Constraint Satisfaction Problems Russell and Norvig: Chapter
Local Search Jim Little UBC CS 322 – CSP October 3, 2014 Textbook §4.8
Constraint Satisfaction Problems Russell and Norvig: Parts of Chapter 5 Slides adapted from: robotics.stanford.edu/~latombe/cs121/2004/home.htm Prof: Dekang.
Maintaining Arc Consistency We have a constraint graph G of variables X 1,...X n, and constraint relations {X i  X j}, and each Xi has a value set V (X.
This lecture topic (two lectures) Chapter 6.1 – 6.4, except
1 Constraint Satisfaction Problems A Quick Overview (based on AIMA book slides)
1 Constraint Satisfaction Problems. 2 Intro Example: 8-Queens Generate-and-test: 8 8 combinations.
This lecture topic (two lectures) Chapter 6.1 – 6.4, except 6.3.3
1 Finite Constraint Domains. 2 u Constraint satisfaction problems (CSP) u A backtracking solver u Node and arc consistency u Bounds consistency u Generalized.
Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License:
ICS-271:Notes 5: 1 Lecture 5: Constraint Satisfaction Problems ICS 271 Fall 2008.
Artificial Intelligence Constraint satisfaction problems Fall 2008 professor: Luigi Ceccaroni.
CSP Yaron Kassner Winter Reminder Arc Consistency: the domains of pairs of variables are consistent. k-consistency: the domains of every k variables.
Constraint Satisfaction problems (CSP)
IBM Labs in Haifa Generation Core: IBM's Systematic Constraint Solver.
Review: Constraint Satisfaction Problems How is a CSP defined? How do we solve CSPs?
Constraint Satisfaction CSE 473 University of Washington.
Artificial Intelligence Constraint satisfaction Chapter 5, AIMA.
Foundations of Constraint Processing, Fall 2005 November 16, 2005nFCi1 Foundations of Constraint Processing CSCE421/821, Fall 2005:
Constraint Satisfaction Problems
Constraint Satisfaction
Constraint Satisfaction Problems Russell and Norvig: Chapter 3, Section 3.7 Chapter 4, Pages Slides adapted from: robotics.stanford.edu/~latombe/cs121/2003/home.htm.
CAP 492 Course Dr. Souham Meshoul 1 CONSTRAINT SATISFACTION PROBLEMS Chapter 5.
Chapter 5 Outline Formal definition of CSP CSP Examples
Crossword Puzzle Solver Michael Keefe. Solver structure.
Constraint Satisfaction Problems
Constraint Satisfaction Problems (CSPs) Chapter 6.1 – 6.4, except
Artificial Intelligence CS482, CS682, MW 1 – 2:15, SEM 201, MS 227 Prerequisites: 302, 365 Instructor: Sushil Louis,
CSPs Tamara Berg CS Artificial Intelligence Many slides throughout the course adapted from Svetlana Lazebnik, Dan Klein, Stuart Russell, Andrew.
CS 484 – Artificial Intelligence1 Announcements Homework 2 due today Lab 1 due Thursday, 9/20 Homework 3 has been posted Autumn – Current Event Tuesday.
N Model problem ä specify in terms of constraints on acceptable solutions ä define variables (denotations) and domains ä define constraints in some language.
Constraint Satisfaction Read Chapter 5. Model Finite set of variables: X1,…Xn Variable Xi has values in domain Di. Constraints C1…Cm. A constraint specifies.
Constraint Satisfaction Problems (CSPs) This lecture topic (two lectures) Chapter 6.1 – 6.4, except Next lecture topic (two lectures) Chapter 7.1.
Constraint Satisfaction CPSC 386 Artificial Intelligence Ellen Walker Hiram College.
Constraint Satisfaction Problems (CSPs) This lecture topic (two lectures) Chapter 6.1 – 6.4, except Next lecture topic (two lectures) Chapter 7.1.
CSCI 5582 Fall 2006 CSCI 5582 Artificial Intelligence Fall 2006 Jim Martin.
Chapter 5 Constraint Satisfaction Problems
Review Test1. Robotics & Future Technology Future of Intelligent Systems / Ray Kurzweil futurist Ray Kurzweil / A Long Bet A Long Bet / Robot Soccer.
Constraint Satisfaction Problems 부산대학교 전자전기컴퓨터공학과 인공지능연구실 김민호
An Introduction to Artificial Intelligence Lecture 5: Constraint Satisfaction Problems Ramin Halavati In which we see how treating.
Constraint Satisfaction Problems Chapter 6. Outline CSP? Backtracking for CSP Local search for CSPs Problem structure and decomposition.
Monster (“Mega”) Sudoku
Constraint Propagation Artificial Intelligence CMSC January 22, 2002.
CS 171: Intro to AI Discussion Week 2 Jan 15 th 2016.
Constraint Satisfaction Problems Chapter 6.1 – 6.4 Derived from slides by S. Russell and P. Norvig, A. Moore, and R. Khoury.
IBM Labs in Haifa © 2005 IBM Corporation Assumption-based Pruning in Conditional CSP Felix Geller and Michael Veksler.
Constraint Satisfaction Problems/Programming ZUI 2012/2013.
1 Constraint Satisfaction Problems (CSP). Announcements Second Test Wednesday, April 27.
Cbj. What’s a csp? a set of variables each with a domain of values a collection of constraints (I’m going to assume binary for the present) assign each.
ARTIFICIAL INTELLIGENCE (CS 461D) Dr. Abeer Mahmoud Computer science Department Princess Nora University Faculty of Computer & Information Systems.
Monster (“Mega”) Sudoku
Computer Science cpsc322, Lecture 13
Solve Linear Systems by Graphing
Constraint Satisfaction Problem
Lecture 7 Constraint Satisfaction Problems
Computer Science cpsc322, Lecture 14
CS B551: Elements of Artificial Intelligence
Computer Science cpsc322, Lecture 13
Chapter 3: Finite Constraint Domains
CSP Search Techniques Backtracking Forward checking
Heuristic Ordering for Asynchronous Backtracking
Constraint Satisfaction Problems
Constraints and Search
Chapter 5: General search strategies: Look-ahead
Constraint Satisfaction Problems. A Quick Overview
Constraint Satisfaction
Constraint Graph Binary CSPs
Constraint Satisfaction Problems (CSP)
Presentation transcript:

Maintaining Arc Consistency (MAC) MAC is the same as Back-tracking, but with calls to AC-3 interleaved... function Backtracking-Search(csp) returns solution/failure return Recursive-Backtracking({ }, csp, domains) function Recursive-Backtracking(assignment,csp,domains) returns domains/failure if assignment is complete then return assignment var  Select-Unassigned-Variable(Variables[csp], assignment, csp) for each value in Order-Domain-Values(var, assignment, csp) do if value is consistent with assignment given Constraints[csp] then add {var = value} to assignment reduced_domains  AC-3(assignment,csp) // check for failure too result Recursive-Backtracking(assignment, csp, reduced_domains) if result  failure then return result remove {var = value} from assignment return failure

function Min-Conflicts(csp,max_steps) returns soln/failure current  complete, random initial var assignment for i=1 to max_steps do if current is a solution (satisfies all constraints) then return current var  randomly chosen conflicted variable val  value that minimizes Conflicts(var,val,current,csp) current  current  {var=val} return failure (or best assignment found)