GraphPlan Jim Blythe.

Slides:



Advertisements
Similar presentations
Language for planning problems
Advertisements

Planning Module THREE: Planning, Production Systems,Expert Systems, Uncertainty Dr M M Awais.
Graphplan. Automated Planning: Introduction and Overview 2 The Dock-Worker Robots (DWR) Domain informal description: – harbour with several locations.
Causal-link Planning II José Luis Ambite. 2 CS 541 Causal Link Planning II Planning as Search State SpacePlan Space AlgorithmProgression, Regression POP.
Constraint Based Reasoning over Mutex Relations in Graphplan Algorithm Pavel Surynek Charles University, Prague Czech Republic.
Planning Module THREE: Planning, Production Systems,Expert Systems, Uncertainty Dr M M Awais.
CLASSICAL PLANNING What is planning ?  Planning is an AI approach to control  It is deliberation about actions  Key ideas  We have a model of the.
1 Graphplan José Luis Ambite * [* based in part on slides by Jim Blythe and Dan Weld]
Plan Generation & Causal-Link Planning 1 José Luis Ambite.
Graph-based Planning Brian C. Williams Sept. 25 th & 30 th, J/6.834J.
Planning Graphs * Based on slides by Alan Fern, Berthe Choueiry and Sungwook Yoon.
Graphplan Joe Souto CSE 497: AI Planning Sources: Ch. 6 “Fast Planning through Planning Graph Analysis”, A. Blum & M. Furst.
For Monday Finish chapter 12 Homework: –Chapter 13, exercises 8 and 15.
Planning CSE 473 Chapters 10.3 and 11. © D. Weld, D. Fox 2 Planning Given a logical description of the initial situation, a logical description of the.
Fast Planning through Planning Graph Analysis By Jan Weber Jörg Mennicke.
Planning: Part 3 Planning Graphs COMP151 April 4, 2007.
Extending Graphplan to handle Resources Presenter: Pham Van Cuong Department of Computer Science New Mexico State University.
Planning II CSE 473. © Daniel S. Weld 2 Logistics Tournament! PS3 – later today Non programming exercises Programming component: (mini project) SPAM detection.
1 Planning Chapters 11 and 12 Thanks: Professor Dan Weld, University of Washington.
Classical Planning via State-space search COMP3431 Malcolm Ryan.
Planning II CSE 573. © Daniel S. Weld 2 Logistics Reading for Wed Ch 18 thru 18.3 Office Hours No Office Hour Today.
An Introduction to Artificial Intelligence CE Chapter 11 – Planning Ramin Halavati In which we see how an agent can take.
Classical Planning Chapter 10.
GraphPlan Alan Fern * * Based in part on slides by Daniel Weld and José Luis Ambite.
For Wednesday Read chapter 12, sections 3-5 Program 2 progress due.
Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License:
Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License:
Jonathon Doran. The Planning Domain A domain describes the objects, facts, and actions in the universe. We may have a box and a table in our universe.
Homework 1 ( Written Portion )  Max : 75  Min : 38  Avg : 57.6  Median : 58 (77%)
Midterm Review Prateek Tandon, John Dickerson. Basic Uninformed Search (Summary) b = branching factor d = depth of shallowest goal state m = depth of.
For Monday Read chapter 12, sections 1-2 Homework: –Chapter 10, exercise 3.
CPS 270: Artificial Intelligence Planning Instructor: Vincent Conitzer.
1 Chapter 16 Planning Methods. 2 Chapter 16 Contents (1) l STRIPS l STRIPS Implementation l Partial Order Planning l The Principle of Least Commitment.
Introduction to Planning Dr. Shazzad Hosain Department of EECS North South Universtiy
AI Lecture 17 Planning Noémie Elhadad (substituting for Prof. McKeown)
Graphplan/ SATPlan Chapter Some material adapted from slides by Jean-Claude Latombe / Lise Getoor.
Classical Planning Chapter 10 Mausam / Andrey Kolobov (Based on slides of Dan Weld, Marie desJardins)
Graphplan.
© Daniel S. Weld 1 Logistics Travel Wed class led by Mausam Week’s reading R&N ch17 Project meetings.
Graphplan: Fast Planning through Planning Graph Analysis Avrim Blum Merrick Furst Carnegie Mellon University.
Automated Planning and Decision Making Prof. Ronen Brafman Automated Planning and Decision Making Graphplan Based on slides by: Ambite, Blyth and.
Graphplan CSE 574 April 4, 2003 Dan Weld. Schedule BASICS Intro Graphplan SATplan State-space Refinement SPEEDUP EBL & DDB Heuristic Gen TEMPORAL Partial-O.
1 GraphPlan, Satplan and Markov Decision Processes Sungwook Yoon* * Based in part on slides by Alan Fern.
Heuristic Search Planners. 2 USC INFORMATION SCIENCES INSTITUTE Planning as heuristic search Use standard search techniques, e.g. A*, best-first, hill-climbing.
Deadlocks References –text: Tanenbaum ch.3. Deadly Embrace Deadlock definition –A set of process is dead locked if each process in the set is waiting.
1 Chapter 6 Planning-Graph Techniques. 2 Motivation A big source of inefficiency in search algorithms is the branching factor  the number of children.
An Introduction to Artificial Intelligence CE 40417
Planning as Satisfiability
Planning as Search State Space Plan Space Algorihtm Progression
Classical Planning via State-space search
Computability and Complexity
Planning AIMA: 10.1, 10.2, Follow slides and use textbook as reference
Deadlocks References text: Tanenbaum ch.3.
Class #17 – Thursday, October 27
Planning José Luis Ambite.
Complexity 6-1 The Class P Complexity Andrei Bulatov.
Graph-based Planning Slides based on material from: Prof. Maria Fox
Graphplan/ SATPlan Chapter
Planning CSE 473 AIMA, 10.3 and 11.
Planning CSE 573 A handful of GENERAL SEARCH TECHNIQUES lie at the heart of practically all work in AI We will encounter the SAME PRINCIPLES again and.
Planning Problems On(C, A)‏ On(A, Table)‏ On(B, Table)‏ Clear(C)‏
Deadlocks References text: Tanenbaum ch.3.
Class #19 – Monday, November 3
Chapter 6 Planning-Graph Techniques
Graphplan/ SATPlan Chapter
Graphplan/ SATPlan Chapter
An Introduction to Planning Graph
Graph-based Planning Slides based on material from: Prof. Maria Fox
Deadlocks References text: Tanenbaum ch.3.
[* based in part on slides by Jim Blythe and Dan Weld]
Presentation transcript:

GraphPlan Jim Blythe

Basic idea Construct a graph that encodes constraints on possible plans Use this “planning graph” to constrain search for a valid plan Planning graph can be built for each problem in relatively short time

Problem handled by GraphPlan STRIPS operators: conjunctive preconditions, no conditional or universal effects, no negations Finds “shortest” plans (by some definition) Sound, complete and will terminate with failure if there is no plan. Wait, isn’t planning undecidable?

Planning graph Nodes divided into “levels”, arcs go from one level to the next For each time period, a state level and an action level Arcs represent preconditions, adds and deletes

What actions and what literals? Add an action in level Ai if all its preconditions are present in level Pi Add a precondition in level Pi if it is the effect of some action in level Ai-1 (including no-ops) Level P1 has all the literals from the initial state

Example planning graph at A L load A L at A L load A L at A L at B L load B L at B L load B L at B L at R L at R L at R L move L P move L P fuel R fuel R at A P fuel R unload A P in A R in A R at B P unload B P move P L in B R in B R at R P at R P Props Time 1 Actions Time 1 Props Time 2 Actions Time 2 Props Time 3 Actions Time 3 Goals

Valid plans A valid plan is a planning graph where: Actions at the same level don’t interfere (delete each other’s preconditions or add effects) Each action’s preconditions are made true by the plan Goals are satisfied

Exclusion relations (mutexes) Two actions (or literals) are mutually exclusive at some stage if no valid plan could contain both. Can quickly find and mark some mutexes: Interference: If two actions interfere Competing needs: If some precond of one action is mutex with a precond of the other action Two propositions are mutex if all ways of creating them both are mutex

GraphPlan algorithm (without termination) Grow the planning graph (PG) until all goals are reachable and not mutex. (If PG levels off first, fail) Search the PG for a valid plan If non found, add a level to the PG and try again

Extending the planning graph Action level: For each possible instantiation of each operator (including no-ops), add if all of its preconditions are in the previous level and no two are mutex. Proposition level: Add all effects of actions in previous level (including no-ops). Mark pairs of propositions mutex if all ways to create one are mutex of all ways to create the other

Creating the planning graph is usually fast Theorem 1: The size of the t-level PG and the time to create it are polynomial in t, n (= number of objects), m (= number of operators) and p (= propositions in the initial state)

Searching for a plan Backward chain on the planning graph Complete all goals at one level before going back: At each level, pick a subset of actions to achieve the goals that are not mutex. Their preconditions become the goals at the earlier level. Build subset by picking each goal and choosing an action to add. Use one already selected if possible. Do forward checking on remaining goals.

Termination for unsolvable problems Planning graphs ‘level off’. This is because it’s a finite space, the set of literals never decreases and mutexes don’t reappear. Notiving memoized sets of unsolvable goals can provide necessary and sufficient conditions for termination. U(I,t) = unsolvable goals at level i after stage t. If U(n, t-1) = U(n, t) then we know we’re in a loop and can terminate safely.