problem space analysis for plan library generation and algorithm selection in real-time systems...
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Problem Space Analysis for Plan Library Generation and Algorithm Selection in
Real-time Systems
Robert H. Holder, III
Dissertation Proposal Defense
August 26, 2009Committee:Dr. Tim Finin, ChairDr. Marie desJardinsDr. Tim OatesDr. R. Scott Cost
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``...it was not obvious what you had to do next so you had to think two, six, ten moves ahead. Scenario planning is about having twelve plans, so if one does not work you go to the next. The fun is figuring out a backup for whatever could go wrong.'‘
-Seth Godin, entrepreneur, describing his strategy for success in games and entrepreneurship. From The Red Rubber Ball At Work by Kevin Carroll
-Scott Adams, “Dilbert” comic, June 1, 2008
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Outline
Motivation Related Work Approach
Problem-Solution (PS) Map Solution-Problem-Utility (SPU) Map Solution Similarity (SS) Map
Map Utilization Plan Library Generation Algorithm Selection and Configuration Informed Problem Decomposition
Map Generation Domain-Based Hints Sampling Interpolation
Research Directions Summary
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Outline
Motivation Related Work Approach
Problem-Solution (PS) Map Solution-Problem-Utility (SPU) Map Solution Similarity (SS) Map
Map Utilization Plan Library Generation Algorithm Selection and Configuration Informed Problem Decomposition
Map Generation Domain-Based Hints Sampling Interpolation
Research Directions Summary
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Motivation
Real-time Planning Problems Shipboard Computing Resource Allocation Mobile Sensor Scheduling Unmanned Vehicle Routing Wireless Sensor Network (WSN) Reconfiguration
Motivation For planning problems in a real-time environment,
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Plan Library: Problem space analysis can inform the efficient creation of a plan library.
Problem Space Analysis: A sampling of problem instances and their solutions can lend insight into the underlying structure of the domain.
A plan library is a means of rapidly adapting to a new environment.
Hypothesis:
Motivation
7Additional benefits of problem space analysis
Contributions
Framework to model and reason about the topological structure of the solutions of related plans
Techniques to predict and leverage the effect of problem instance characteristics and attributes on the topological structure of the solution space
Novel algorithms that exploit solution space structure to generate plan libraries, select & configure algorithms, and decompose large problems
Evaluation of these algorithms by comparison to competing techniques for a set of sample problems
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Dynamic Vehicle Routing Problem
Three vehicles to visit twelve destinations
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Dynamic Vehicle Routing Problem
Static solution for known destinations
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Dynamic Vehicle Routing Problem
Consideration for potential additional destination
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Dynamic Vehicle Routing Problem
X
X
X
Contingency solution for additional destination
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Dynamic Vehicle Routing Problem
Implementation of contingency solution
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Dynamic Vehicle Routing Problem
How to plan contingencies for arbitrary possibilities?
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Outline
Motivation Related Work Approach
Problem-Solution (PS) Map Solution-Problem-Utility (SPU) Map Solution Similarity (SS) Map
Map Utilization Plan Library Generation Algorithm Selection and Configuration Informed Problem Decomposition
Map Generation Domain-Based Hints Sampling Interpolation
Research Directions Summary
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Related Work –Technique Comparison
Plan Library generation case-based reasoning (created after runtime) reactive planning (subset of input, localized) conditional & contingency planning (localized) decision-theoretic (relies on probabilities)
Real-time Planning plan repair (runtime, works for small changes) anytime & contract algorithms (runtime)
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Related Work – Case-Based Reasoning
Smyth & McKenna (2001)
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Related Work – Domain Space Analysis
State Space Analysis Bulka (2009) – Backbone planning Kondaris (2008) – Automated skill learning Hoffman (2001) – State space “benches” and “exits”
Solution Space Analysis Miner (2009) – Solution gradient lines Rosen, et. al. (2005) – Medical plan comparison Gopal & Starkschall (2002) – Medical plan topology
Plan-Space Planning Trinquart (2003) – Plan space reachability Hoffman & Nebel (2001) – Uses plan space structure to estimate
distance to goal state
Related Work – Gopal & Starkschall (2002)
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Outline
Motivation Related Work Approach
Problem-Solution (PS) Map Solution-Problem-Utility (SPU) Map Solution Similarity (SS) Map
Map Utilization Plan Library Generation Algorithm Selection and Configuration Informed Problem Decomposition
Map Generation Domain-Based Hints Sampling Interpolation
Research Directions Summary
Approach Overview
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Traveling Salesperson Problem
Four fixed cities Central starting point Unknown fifth city
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Approach: Problem-Solution Map
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Each point represents a potential location of the fifth city. The color of the point represents the optimal solution for the resulting 5-city TSP.
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Approach:Problem-Solution Map
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0-1-4-2-3-5
0-1-3-2-5-4
0-1-3-5-2-4
0-1-5-4-2-3
0-1-5-3-2-4
0-3-2-4-1-5
0-1-3-2-4-5
0-5-1-3-2-4
Each point represents a potential location of the fifth city. The color of the point represents the optimal solution for the resulting 5-city TSP.
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Approach
Problem-Solution Map (PS Map) contiguous regions – only need to store one
solution per region complexity – higher interaction of regions
indicates a more complex space
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Approach: Solution-Problem-Utility Map
Optimal library requires 8/120 = 6.7% of possible solutions. Is this too many?
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Approach: Solution-Problem-Utility Map
Tolerating solution degradation and extending the scope of neighboring solutions can reduce library size
Approach: Solution-Problem- Utility Map
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Discrete and continuous SPU Maps showing global competency of one solution
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Approach
Solution Problem Utility Map (SPU Map) reduce solution regions (and thus library size) by
tolerating utility degradation gradient of solution degradation
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0-1-4-2-3-5
0-1-3-2-5-4
0-1-3-5-2-4
0-1-5-4-2-3
0-1-5-3-2-4
0-3-2-4-1-5
0-1-3-2-4-5
0-5-1-3-2-4
Approach:Solution-Similarity Map
high similarity low similarity
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Approach Solution Similarity Map (SS Map)
reduce library size by relying on run-time adaptation creating parameterized solutions
suggests regions where regular world assumption does not hold
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Outline
Motivation Related Work Approach
Problem-Solution (PS) Map Solution-Problem-Utility (SPU) Map Solution Similarity (SS) Map
Map Utilization Plan Library Generation Algorithm Selection and Configuration Informed Problem Decomposition
Map Generation Domain-Based Hints Sampling Interpolation
Research Directions Summary
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Algorithm Selection & Configuration
Initial solution – use fast, aggressive heuristics
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Algorithm Selection & Configuration
Initial solution – use more precise heuristics, emphasize exploration over exploitation, use less aggressive hill-climbingAdaptation – if solutions are similar, use hill-climbing, else use genetic algorithm
less contiguous
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Informed Problem Decomposition To decompose a DVRP or DTSP, a system can fix one of the
unknown city locations. Choosing cities such that the subproblem yields a more contiguous
map will be advantageous for planning.
more contiguous
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Outline
Motivation Related Work Approach
Problem-Solution (PS) Map Solution-Problem-Utility (SPU) Map Solution Similarity (SS) Map
Map Utilization Plan Library Generation Algorithm Selection and Configuration Informed Problem Decomposition
Map Generation Sampling Interpolation Domain-Based Hints
Research Directions Summary
5-city TSP (1 unknown city) small problem with two degrees of freedom 12k problem instances naive solver fast runtime
5-city TSP (2 unknown cities) larger problem with four degrees of freedom 311k problem instances naive solver ~20 minutes runtime
Map Generation
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Map Generation
Complete map generation is not feasible (would make algorithm selection irrelevant) how can we approximate the map efficiently?
Map approximation sampling interpolation domain-based hints
example: fixed city locations lie on regional borders
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Map Generation
Initial view of solution space topology
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Map Generation
Ideal view of solution space topology
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Map Generation
Preliminary experiment with random sampling and nearest neighbor classification
Map Generation
Ideal PS Map Approximated PS Map
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Preliminary experiment with random sampling and nearest neighbor classification
Map Generation
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Preliminary experiment with random sampling and nearest neighbor classification demonstrates
75% accuracy from a 0.5% sample rate.
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Sampling & Classification
Sampling uniform/random/NOLHS/Rapidly expanding Random Trees (RRT) strategic sampling (active learning) schemes biased by domain hints
Classification Nearest neighbor
k nearest neighbors vs. radius of nearest neighbors weighting neighbors by distance
Support Vector Machine (linear, non-linear) Bayesian Network Neural Network
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Domain-Based Hints
All the fixed points lie on regional boundaries
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Domain-Based Hints
All the fixed points lie on regional boundaries
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SPU and SS Map Generation
SPU Map calculate utility of solution for
sample of problem instances regression to find limits of
solution competence does optimal region shape
inform tolerated region shape? SS Map
for each solution, find similarity to each neighbor
look for similarities to non-neighbors?
algorithm selection - can we characterize how quickly solution is changing?
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Regression
Regression depends on a function form, i.e. a “kernel” Can we determine the appropriate kernel based on
problem characteristics? Piecemeal regression may allow local customization of
regression Support Vector Regression Machines (Drucker, 1996)
Approach Overview
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Outline
Motivation Related Work Approach
Problem-Solution (PS) Map Solution-Problem-Utility (SPU) Map Solution Similarity (SS) Map
Map Utilization Plan Library Generation Algorithm Selection and Configuration Informed Problem Decomposition
Map Generation Domain-Based Hints Sampling Interpolation
Research Directions Summary
Domains
Dynamic Traveling Salesman Problem Dynamic Vehicle Routing Problem Wireless Sensor Network (Re)Configuration
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Research Plan Goals
Investigate inferring a problem space analysis and solution topology from a sample set of problem instance and solution pairs
Apply problem space analysis and other domain characteristics to the creation of an efficient plan library
Apply problem space analysis to the selection of algorithms suited for a particular region of the problem space
Apply problem space analysis to strategic decomposition of large planning problems
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Research Plan
Fall 2009 Generate ideal set of PS and SPU Maps for various TSP, VRP, and WSN problems Test PS Map generation using various sampling and classification schemes Test SPU Map generation using various sampling and regression schemes
Spring 2010 Confirm usefulness of domain-based hints Apply bias to sampling and classification schemes
Summer 2010 Library generation algorithm Evaluation
Fall 2010 Algorithm selection technique Problem decomposition algorithm Evaluation
Spring 2011 Final experiments and evaluation Writing and defense
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Evaluation
System performance Comparison to other DTSP, DVRP algorithms Comparison to known optimal solutions (TSP/VRP) Comparison to baseline communication throughput and network life
metrics (WSN) Characterize performance as function of library size Offline computation time vs. online performance
Map approximation Raw accuracy Function of proximity to optimal solution region Expected utility degradation due to inaccuracies Characterize performance as function of sampling and interpolation
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Contributions
Framework to model and reason about the topological structure of the solutions of related plans
Techniques to predict and leverage the effect of problem instance characteristics and attributes on the topological structure of the solution space
Novel algorithms that exploit solution space structure to generate plan libraries, select & configure algorithms, and decompose large problems
Evaluation of these algorithms on a sample problems by comparison to competing techniques
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Summary
Use of problem space analysis to facilitate real-time planning plan library creation algorithm selection problem decomposition
Use of sampling and interpolation techniques to create problem space maps traditional techniques domain-based hints informed kernel selection
References
Bulka (2009) “Efficient Planning Using Plan Libraries to Capture the Structure of the State Space”
Gopal & Starkschall (2002) “Plan space: representation of treatment plans in multidimensional space”
Hoffman (2001) “Local Search Topology in Planning Benchmarks: An Empirical Analysis”
Hoffman & Nebel (2001) “The FF Planning System: Fast Plan Generation Through Heuristic Search”
Onder & Pollack (1996) “Contingency Selection in Plan Generation” Kondaris (2008) “Autonomous Robot Skill Acquisition” Miner (2009) “Rule Abstraction: Understanding Emergent Behavior in Swarm
Systems” Smyth & McKenny (2001) “Competence Models and the Maintenance Problem” Rosen, et. al. (2005) “Interactively exploring optimized treatment plans” Trinquart (2003) “Analyzing Reachability within Plan Space”
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Thank you
Questions…
Suggestions…
Comments…
Backup
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Related Work –Contingency Planning
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Onder & Pollock (1996)
Related Work – Miner (2009)
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