utilizing problem structure in local search the planning benchmarks as a case study l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Utilizing Problem Structure in Local Search: The Planning Benchmarks as a Case Study PowerPoint Presentation
Download Presentation
Utilizing Problem Structure in Local Search: The Planning Benchmarks as a Case Study

Loading in 2 Seconds...

play fullscreen
1 / 46

Utilizing Problem Structure in Local Search: The Planning Benchmarks as a Case Study - PowerPoint PPT Presentation


  • 173 Views
  • Uploaded on

Utilizing Problem Structure in Local Search: The Planning Benchmarks as a Case Study. Jőrg Hoffmann Alberts-Ludwigs-University Freiburg. Overview. The Planning Benchmarks A Local Search Approach Local Search Topology Conclusion. Overview. The Planning Benchmarks A Local Search Approach

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Utilizing Problem Structure in Local Search: The Planning Benchmarks as a Case Study' - jamal


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
utilizing problem structure in local search the planning benchmarks as a case study

Utilizing Problem Structure in Local Search: The Planning Benchmarks as a Case Study

Jőrg Hoffmann

Alberts-Ludwigs-University Freiburg

overview
Overview
  • The Planning Benchmarks
  • A Local Search Approach
  • Local Search Topology
  • Conclusion
overview3
Overview
  • The Planning Benchmarks
  • A Local Search Approach
    • FF Algorithms
    • AIPS´00 Competition
  • Local Search Topology
  • Conclusion
overview4
Overview
  • The Planning Benchmarks
  • A Local Search Approach
  • Local Search Topology
    • Gathering Insights: Looking at Small Instances
    • The Topology of h+
    • The Topology of Approximating h+
  • Conclusion
overview5
Overview
  • The Planning Benchmarks
  • A Local Search Approach
  • Local Search Topology
  • Conclusion
the planning benchmarks
„The“ Planning Benchmarks
  • Assembly, Blocksworld-arm, Blocksworld-no-arm, Briefcaseworld,Ferry, Fridge, Freecell, Grid, Gripper, Hanoi, Logistics, Miconic-ADL, Miconic-SIMPLE, Miconic-STRIPS, Movie, Mprime, Mystery, Schedule, Simple-Tsp, Tyreworld
the planning benchmarks7
„The“ Planning Benchmarks
  • Assembly, Blocksworld-arm, Blocksworld-no-arm, Briefcaseworld,Ferry, Fridge, Freecell, Grid, Gripper, Hanoi, Logistics, Miconic-ADL, Miconic-SIMPLE, Miconic-STRIPS, Movie, Mprime, Mystery, Schedule, Simple-Tsp, Tyreworld
the planning benchmarks8
„The“ Planning Benchmarks
  • Assembly, Blocksworld-arm, Blocksworld-no-arm, Briefcaseworld,Ferry, Fridge, Freecell, Grid, Gripper, Hanoi, Logistics, Miconic-ADL, Miconic-SIMPLE, Miconic-STRIPS, Movie, Mprime, Mystery, Schedule, Simple-Tsp, Tyreworld
the planning benchmarks9
„The“ Planning Benchmarks
  • Assembly, Blocksworld-arm, Blocksworld-no-arm, Briefcaseworld,Ferry, Fridge, Freecell, Grid, Gripper, Hanoi, Logistics, Miconic-ADL, Miconic-SIMPLE, Miconic-STRIPS, Movie, Mprime, Mystery, Schedule, Simple-Tsp, Tyreworld
overview10
Overview
  • The Planning Benchmarks
  • A Local Search Approach
    • FF Algorithms
    • AIPS´00 Competition
  • Local Search Topology
  • Conclusion
ff algorithms
FF Algorithms
  • FF can be seen as a refinement of HSP 1.0:
    • search forward in the state space
    • relax planning task by ignoring delete lists
  • Main Differences [Hoffmann & Nebel 2001]
    • heuristic (different approximation of h+)
    • search strategy (different hill-climbing variant)
    • pruning technique (new)
ff algorithms heuristic
FF Algorithms - Heuristic
  • Approach often used in heuristic search: relax problem, solve relaxation
  • In planning: ignore delete lists [Bonet et al.1997]
  • Optimal relaxed solution length h+ admissible but NP-hard to compute [Bylander 1994]
  • HSP 1.0: approximate h+ by weight value sums
  • FF: approximate h+ by running a relaxed version of GRAPHPLAN [Blum & Furst 1997]
ff algorithms search
FF Algorithms - Search
  • Local search as state evaluation is costly
  • HSP 1.0: (standard) hill-climbing
  • FF: enforced hill-climbing
    • start in initial state
    • in a state S, do breadth first search for S´ such that h(S´) < h(S)
  • Intuition: hill-climbing needs more „motion force“ towards the goal
ff algorithms pruning
FF Algorithms - Pruning
  • Observation: often, GRAPHPLAN´s relaxed solutions are close to what needs to be done, at least in first step
    • in Gripper, for example, actions that drop balls into room A are never selected
  • Restrict action choice in any state S to thoseselected by the first step of the relaxed plan for S
overview15
Overview
  • The Planning Benchmarks
  • A Local Search Approach
    • FF Algorithms
    • AIPS´00 Competition
  • Local Search Topology
  • Conclusion
aips 00 competition
AIPS´00 Competition
  • Planning systems competition alongside AIPS´00 [Bacchus 2001]
  • 15 participants, 12 in fully automated track
  • 5 domains, around 50 - 200 scaling instances each
  • we briefly look at the runtime curves in the fully automated track
aips 00 competition22
AIPS´00 Competition
  • As a result of the competition, FF
    • was nominated „Group A Distinguished Performance Planning System“ (together with TalPlanner from the hand-tailored track)
    • won the Schindler Award for Best Performance in the Miconic domain, ADL track
  • Note: we have only briefly seen one part of the competition
overview24
Overview
  • The Planning Benchmarks
  • A Local Search Approach
  • Local Search Topology
    • Gathering Insights: Looking at Small Instances
    • The Topology of h+
    • The Topology of Approximating h+
  • Conclusion
local search topology
Local Search Topology
  • The behaviour of local search depends crucially on the topology of the search space (studied in SAT, e.g. [Frank et al. 1997])
  • Identify, following [Frank et al. 1997], the topology of the benchmarks, under h+ and FF´s approximative h+
overview26
Overview
  • The Planning Benchmarks
  • A Local Search Approach
  • Local Search Topology
    • Gathering Insights: Looking at Small Instances
    • The Topology of h+
    • The Topology of Approximating h+
  • Conclusion
gathering insights
Gathering Insights
  • Start by looking at small instances: [Hoffmann 2001]
    • in the 20 domains, randomly generate suits of small examples
    • build the state spaces and compute h+ to all states (resp. FF‘s approximation of h+)
    • measure parameters of the resulting local search topology (definitions adapted from [Frank et al.1997])
topological phenomena
Topological Phenomena

Dead ends

Measured: how many are there? Recognized? (i.e. h+ = ∞)?

topological phenomena29
Topological Phenomena

Local Minima

Measured (amongst other things): how many are there?

topological phenomena30
Topological Phenomena

Benches

Measured (amongst other things): maximal exit distance

h topology in small instances
h+ Topology in Small Instances

In lowermost class, enforced hill-climbing is polynomial!

FF approximation similar: some, but few local minima

overview35
Overview
  • The Planning Benchmarks
  • A Local Search Approach
  • Local Search Topology
    • Gathering Insights: Looking at Small Instances
    • The Topology of h+
    • The Topology of Approximating h+
  • Conclusion
reasons for h topology
Reasons for h+ Topology
  • Invertible actions: actions a to which there exists an inverse action undoing exactly a‘s effects
  • Example Logistics
    • load obj truck --- unload obj truck
    • drive loc1 loc2 --- drive loc2 loc1
  • Implies non-existence of dead ends, and of local minima with: see next slide
reasons for h topology38
Reasons for h+ Topology
  • Actions that are respected by the relaxation: if astarts an optimal plan from S, then a also starts an optimal relaxed plan from S
  • Example Logistics
    • load obj truck: obj must be transported, and there is no other way of doing that
    • drive loc1 loc2: some obj must be loaded/unloaded at loc2, again no other choice for the relaxed plan
  • If all actions are invertible and respected by the relaxation, then there are no local minima under h+
overview39
Overview
  • The Planning Benchmarks
  • A Local Search Approach
  • Local Search Topology
    • Gathering Insights: Looking at Small Instances
    • The Topology of h+
    • The Topology of Approximating h+
  • Conclusion
the topology of approximating h
The Topology of Approximating h+
  • Dead ends behave provably the same
  • In domains where no local minima exist under h+:
    • check local minima percentage under approximative (FF) heuristic in large instances
  • In domains where maximal exit distance constant under h+:
    • checkmaximum over exit distances in large instances
investigating large instances
Investigating Large Instances
  • Take Samples from State Spaces: (following [Frank et al. 1997])
    • randomly generate suits of large instances
    • repeatedly, walk a random number of random steps into the state space, ending in a state S
    • check whether S lies on a local minimum, and what the exit distance is
    • visualize data against generator parameters
overview44
Overview
  • The Planning Benchmarks
  • A Local Search Approach
  • Local Search Topology
  • Conclusion
conclusion planning
Conclusion - Planning
  • Critically: time to move on to other benchmarks?
    • agree: time and resources
    • disagree: only NP-hard problems for benchmarking
  • Positively: we have a good suboptimal planner!
    • we know where it works well
    • we know why it works well
conclusion local search
Conclusion - Local Search

It is certainly an extreme example, but nevertheless:

Utilizing problem structure can be crucial

for doing successful local search

(though you‘d normally first identify the structure, then try to utilize it)

Thanks to: Bernhard Nebel; Jana Koehler;