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© J. Christopher Beck 20051 Lecture 12: Constraint Programming 2
© J. Christopher Beck 2005 2 Outline Quick CP Review More propagation Edge Finding The Overall CP Loop
© J. Christopher Beck 2005 3 The Core of CP Modeling How to represent the problem Heuristic search How to branch How much effort to find a good branch Inference/propagation How much effort Backtracking
© J. Christopher Beck 2005 4 Generic CP Algorithm Assert Commitment Propagators Start Success Solution? Make Heuristic Decision Backtrack Technique Failure Nothing to retract? Dead-end?
© J. Christopher Beck 2005 5 Constraint-Based Analysis (CBA) 20 3580 15 9050 Operations on the same unary capacity resource What can you infer here?
© J. Christopher Beck 2005 6 CBA Rules For all pairs of activities, A i and A j : Case 1: If lft i – est j < dur i + dur j lft j – est i then A i must be before A j. Case 2: If dur i + dur j > lft j – est i and dur i + dur j > lft i – est j then dead-end. Case 3: If dur i + dur j lft j – est i and dur i + dur j lft i – est j then either OK. On the same unary-capacity resource
© J. Christopher Beck 2005 7 This Lecture Another propagator Edge Finding Exclusion “Big Picture CP” Solve the cut out example
© J. Christopher Beck 2005 8 Edge-Finding Exclusion 100 20 15 10 15 0 1080 S est(S) lft(S) 25
© J. Christopher Beck 2005 9 Edge-Finding Exclusion 100 20 15 10 15 0 10 75 Sest(S)lft(S) 25 70100
© J. Christopher Beck 2005 10 Exclusion Rules For all non-empty subsets, S, and activities A S: (lft(S) - est(S) < dur A + dur(S)) (lft(S) - est A < dur A + dur(S)) est A est(S) + dur(S) (lft(S) - est(S) < dur A + dur(S)) (lft A - est(S) < dur A + dur(S)) lft A lft(S) - dur(S) On the same, unary capacity resource
© J. Christopher Beck 2005 11 Edge Finding Exclusion Run CBA & Edge Finding Exclusion on the following activities A 3 4 12 A 1 6 17 A 2 5 0 1 11 1
© J. Christopher Beck 2005 12 Propagators Summary Analyze the current state in order to find new constraints that are implied Make commitments (e.g., remove values) that would otherwise have to be searched over Never make a mistake!
© J. Christopher Beck 2005 13 Heuristics/Branching Use the structure of the search state (e.g., flexibility) to guide the heuristic decisions (“commitment”) Could be mistaken – and so you might need to backtrack
© J. Christopher Beck 2005 14 Generic CP Algorithm Assert Commitment Propagators Start Success Solution? Make Heuristic Decision Backtrack Technique Failure Nothing to retract? Dead-end?
© J. Christopher Beck 2005 15 CP on Cut Out Problem Run CP on the cut out problem Use CBA, EF Exclusion Flexibility Heuristic Activities Jobs1234 1M1, 9M2, 8M3, 4M4, 4 2M1, 5M2, 6M4, 3M3, 6 3M3, 10M1, 4M2, 9M4, 2
© J. Christopher Beck Lecture 11: Constraint Programming 1.
© J. Christopher Beck Lecture 15: CP Search.
© J. Christopher Beck Lecture 13: Modeling in Constraint Programming.
8-1 Problem-Solving Examples (Preemptive Case). 8-2 Outline Preemptive job-shop scheduling problem (P-JSSP) –Problem definition –Basic search procedure.
© J. Christopher Beck Lecture 6: Job Shop Scheduling Introduction.
CP Summer School Modelling for Constraint Programming Barbara Smith 2. Implied Constraints, Optimization, Dominance Rules.
© J. Christopher Beck Lecture 6: Time/Cost Trade-off in Project Planning.
© J. Christopher Beck Lecture 5: Project Planning 2.
University of Toronto Mechanical & Industrial Engineering An Introduction to Constraint Programming Part II: Solving Scheduling Problems J. Christopher.
Constraint Programming for Supply Chain Management J. Christopher Beck Cork Constraint Computation Centre (4C) SCM Information Day, Nov.
© J. Christopher Beck Lecture 10: Integer Programming & Branch-and-Bound.
University of Toronto Mechanical & Industrial Engineering An Introduction to Constraint Programming J. Christopher Beck Dept. of Mechanical & Industrial.
Roman Barták (Charles University in Prague, Czech Republic) ACAT 2010.
Constraints and Search Toby Walsh Cork Constraint Computation Centre (4C) Logic & AR Summer School, 2002.
© J. Christopher Beck Lecture 17: Tabu Search.
Jobshop scheduling. We have a set of resources a set of jobs a job is a sequence of operations/activities sequence the activities on the resources.
Constraint Satisfaction Problems Constraint Satisfaction Problem (CSP) –Set of Variables: X 1, X 2, X 3, … X n –Set of Constraints: C 1, C 2, … C n –Each.
CP Summer School Modelling for Constraint Programming Barbara Smith 1.Definitions, Viewpoints, Constraints 2.Implied Constraints, Optimization,
Using Constructive Search in Resource Scheduling By Andrei Missine.
Finite Capacity Scheduling 6.834J, J. Overview of Presentation What is Finite Capacity Scheduling? Types of Scheduling Problems Background and History.
Distributed Scheduling. What is Distributed Scheduling? Scheduling: –A resource allocation problem –Often very complex set of constraints –Tied directly.
CPSC 322, Lecture 4Slide 1 Search: Intro Computer Science cpsc322, Lecture 4 (Textbook Chpt ) January, 12, 2009.
Put a different number in each circle (1 to 8) such that adjacent circles cannot take consecutive numbers.
© J. Christopher Beck Lecture 14: Assembly Line Scheduling 2.
Schreiber, Yevgeny. Value-Ordering Heuristics: Search Performance vs. Solution Diversity. In: D. Cohen (Ed.) CP 2010, LNCS 6308, pp Springer-
Chapter 5 Outline Formal definition of CSP CSP Examples Backtracking search for CSPs Problem structure and problem decomposition Local search for CSPs.
© J. Christopher Beck Lecture 7: Shifting Bottleneck.
Computer Science CPSC 322 Lecture 13 Arc Consistency (4.5, 4.6 ) Slide 1.
Arc Consistency CPSC 322 – CSP 3 Textbook § 4.5 February 2, 2011.
1 Constraint Satisfaction Problems A Quick Overview (based on AIMA book slides)
© J. Christopher Beck Lecture 25: Workforce Scheduling 3.
CS460 Fall 2013 Lecture 4 Constraint Satisfaction Problems.
Vehicle Routing & Job Shop Scheduling: Whats the Difference? ICAPS03, June 13, 2003 J. Christopher Beck, Patrick Prosser, & Evgeny Selensky Dept. of Computing.
CSC 423 ARTIFICIAL INTELLIGENCE Constraint Satisfaction Problems.
Truth Maintenance Systems. Outline What is a TMS? Basic TMS model Justification-based TMS.
Introduction to search Chapter 3. Why study search? §Search is a basis for all AI l search proposed as the basis of intelligence l inference l all learning.
M Tech Project – First Stage Improving Branch-And-Price Algorithms For Solving 1D Cutting Stock Problem Soumitra Pal [ ]
SAT Solving Presented by Avi Yadgar. The SAT Problem Given a Boolean formula, look for assignment A for such that. A is a solution for. A partial assignment.
Lecture 11 Last Time: Local Search, Constraint Satisfaction Problems Today: More on CSPs.
© J. Christopher Beck Lecture 10: (Full) Shifting Bottleneck.
CONSTRAINT-BASED SCHEDULING AND PLANNING Speaker: Olufikayo Adetunji CSCE 921 4/08/2013Olufikayo Adetunji 1 Authors: Philippe Baptiste, Philippe Laborie,
Algorithm Design Methods (I) Fall 2003 CSE, POSTECH.
Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License:
Arc Consistency and Domain Splitting in CSPs CPSC 322 – CSP 3 Textbook Poole and Mackworth: § 4.5 and 4.6 Lecturer: Alan Mackworth October 3, 2012.
CPSC 322, Lecture 12Slide 1 CSPs: Search and Arc Consistency Computer Science cpsc322, Lecture 12 (Textbook Chpt ) January, 29, 2010.
GRASP-an efficient SAT solver Pankaj Chauhan. 6/19/ : GRASP and Chaff2 What is SAT? Given a propositional formula in CNF, find an assignment.
© J. Christopher Beck Lecture 22: Local Search for Sports Scheduling.
Midterm Review Prateek Tandon, John Dickerson. Basic Uninformed Search (Summary) b = branching factor d = depth of shallowest goal state m = depth of.
Constraint Systems Laboratory 11/26/2015Zhang: MS Project Defense1 OPRAM: An Online System for Assigning Capstone Course Students to Sponsored Projects.
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