ANTs PI meeting, May 29-31, 2002Washington University / DCMP 1
Flexible Methods for Multi-agent Distributed Resource Allocation by Exploiting Phase Transitions
- Distributed Constraint Minimization Problems (DCMP)
PM: Vijay Raghavan PI: Weixiong Zhang
PI phone: (314)935-8788PI email: [email protected]
Institutions: Washington University in St. LouisContract #: F30602-00-2-0531
AO #: K278Award start date: 5/1/2000Award end date: 4/31/2003
Agents: Daniel Daskiewich and Robert ParagiAgent Organization: US Airforce Lome Lab
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 2
Subcontractors and Collaborators• Subcontractor
– Washington University in St. Louis• The project was transferred with the PI
• Collaborators– ISI/Camera, Vanderbilt (logistic scheduling)
• Achieved: Analyzed the complexity of Marbles scheduling problems. Developed modeling and encoding techniques, and studied various search algorithms for the problem
• Next step: Complexity of combined scheduling problems• Goals: Understanding the complexity and features of the
training scheduling problems. New search methods– Kestrel (challenge problem)
• Achieved: Studied low-cost distributed algorithms for scheduling problems. Some phase transition results on distributed algorithms in sensor networks.
• Nest step: Complexity of distributed resource allocation• Goal: Understanding the complexity of distributed resource
allocation. New methods based on analysis.
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 3
Problem Description, Objectives
• Understanding and characterizing distributed resource allocation problems in ANTs domains.
– Modeling methods (e.g., soft constraint satisfaction/optimization)
– Phase transitions and backbones (sources of complexity)
– Scalability (impact of problem structures)
• Developing general and efficient algorithms for resource allocations
– Effective problem-solving methods for problems in ANTs domains
• Systematic search, approximation methods, distributed algorithms
• Phase-aware problem solving for good enough/sooner enough solutions• What we try to do for the program
– Understanding computational challenges in ANTs
– Providing methods for avoiding computational thrashing
– Improving real-time performance
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 4
Flexible Methods for Multi-Agent Distributed Flexible Methods for Multi-Agent Distributed Resource Allocations by Exploiting Phase Transitions Resource Allocations by Exploiting Phase Transitions
(DCMP)(DCMP)
IMPACT SCHEDULE
NEW IDEAS
• Understanding and theoretical characterization of the dynamics and computational complexity of distributed resource allocation problems
• Providing guidelines for designing and developing high performance multi-agent systems and agent negotiation strategies
• Demonstration of innovative, phase-aware distributed problem-solving methods for finding satisfactory solutions within limited resource bounds
• Modeling distributed resource allocation problem (DRAP) as distributed soft constraint minimization problem (DCMP)
• Using soft/hard constraints with different penalties• Finding solutions with minimal overall penalties
• Characterizing features of DCMP and DRAP• Phase transitions and backbones, algorithmic complexity
• Efficient constraint solving approaches• Modeling and encoding methods• Systematic and approximate search algorithms
• Transformations methods exploiting phase transitions• Estimating complexity through experimentation• Adjust constraints at running time for anytime solutions
PHASE-AWARE PROBLEM SOLVING
Unsolvablewithin bounds
Env
iron
men
t Global state estimator
Transformationand constraint
relaxation
Problem solver
Progressmonitor
Difficultphase
Lessconstrained
Probablysolvable
progress
Year 1
Year 2
Year 3
Modeling
Complexity and algorithms
Distributed constraint solvers
Phase-aware methods
Integrated solutions
Models, phase transitions and algorithms
Demo on challenge problems
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 5
Project Status
• Marbles pilot scheduling problems– Worst-case complexity
– Various modeling and encoding schemes
– Many search algorithms
– Experiments on Marbles problems
• EW challenge problem– Low-overhead distributed algorithms
– Some phase transition results
– Distributed scan scheduling
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 6
Status on Marbles: Previous Results
• The problem is NP-hard– Reduced from set packing (NP-complete)
• Two general approaches– Model checking – a set of satisfaction models– Optimization – attacking the problem directly
• Four types of models and ten resulting models– Constraint optimization (COP), MAX-SAT– Constraint satisfaction (CSP), SAT
• Encoding schemes (k-encoding)• Experimental results (end of last quarter)
– Optimization models and algorithms are more efficient than satisfaction models and model-checking methods
– Encoding with using small variable domains does not help
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 7
Status on Marbles: Results of this Period
• More local search algorithms considered– Developed a COP solver for COP models
– Analyzed NB-Wsat for CSP models, WalkSat for SAT models and Wsat(OIP) for MAX-SAT models
– A large number of experiments• Instances from ISI and randomly generated (e.g., 100 tasks and
200 resources)
• Conclusions– Optimization models and algorithms are more efficient than
satisfaction models and algorithms
– Problem features interplay with search algorithms• E.g., number of resource requirements has significant impact on
the efficiency of a search algorithm.
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 8
Status on CP
• Technical issues considered– Scalability
• how do problem structures affect complexity?
– Anytime (real-time) performance
– Scan scheduling for detecting new targets quickly with small amount of energy
– Tracking (just started)
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 9
Status on CP: Distributed Algorithms
• Distributed constraint optimization as a way of resource allocation
• Low-overhead distributed algorithms– Scalability (information from local neighborhood)– Simply strategies– High performance (solution quality)– Fast convergence (real-time feature)
• Distributed algorithms considered– Distributed breakout algorithm (DBA)
• Previously developed for distributed CSP
– Distributed stochastic algorithm (DSA) – a set of algorithms (conservative fixed probability algorithm (CFP) considered by Kestrel is one variation)
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 10
Status on CP: Summary of Results (1)
• Distributed breakout algorithm (DBA)– Completeness on acyclic constraint graphs (self-
stabilization)• Finding a solution or determining there exists no solution
in O(n^2) steps, where n is the number of nodes
• The results can be extended to optimization
– Incompleteness on cyclic constraint graphs• Constructed a ring structure on which DBA won’t
terminate
– Developed stochastic strategies to increase DBA’s performance on graphs
– Experimental results on graph coloring and scan scheduling in ANTs domain
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 11
Status on CP: Summary of Results (2)
• Distributed stochastic algorithm (DSA or CFP)– It is an efficient algorithm in general
– It has a phase transition behavior (solution quality and communication cost) if not controlled properly
• Extensive experimental study– Distributed graph coloring
– Distributed scan scheduling in ANTs CP.
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 12
Status on CP: Summary of Results (3)
• DSA’s phase-transition behavior on scan scheduling– Shortest schedule T to cover all the sectors of each sensor– Minimal energy use – minimizing overlapping of multiple sensors scanning shared area – optimization
• Solution quality • Communication cost
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 13
Status on CP: Summary of Results (4)
• Anytime performance of DSA and DBA on scan scheduling
• Solution quality • Communication cost
DBA
DBA
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 14
Status on CP: Summary of Results (5)
• Distributed scan scheduling using DSA and DBA
• Results from DSA • Results from DBA
• Scalability – next sets of experiments to be done
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 15
Status on CP: Publications• Publications on distributed algorithms for problems in ANTs
– W. Zhang and L. Wittenburg, Distributed breakout revisited, AAAI-2002, to appear.
– W. Zhang, et al., Distributed problem solving in sensor networks, 1st Intern. Joint Conf. on Autonomous Agents and Multi-agent systems (AAMAS-2002), to appear.
– W. Zhang, G. Wang and L. Wittenberg, distributed stochastic search for constraint satisfaction and optimization: Parallel, phase transitions and performance, AAAI-2002 Workshop on Probabilistic Strategies in Search, to appear.
– W. Zhang and Z. Xing, Distributed breakout vs. distributed stochastic: A comparative evaluation on scan scheduling, AAMAS-2002 Workshop on Distributed Constraint Reasoning, to appear.
• Publications on complexity and phase transitions– S. Climer and W. Zhang, Searching for backbones and fat: A limit-
crossing approach with applications, AAAI-2002, to appear. – A. K. Sen, A. Bagchi and W. Zhang, An average-case analysis of
graph search, AAAI-2002, to appear.
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 16
Project Plans
• Scheduling in Logistics domain– Analyzing the complexity and features of Marbles 2 and the
integrated problems combining pilot and maintenance scheduling
• Challenge problem– Extending the current work to distributed tracking
– Complexity of distributed resource allocation• Possible phase transition in terms of the speed of moving targets;
• Possible phase transition due to limited resources and the number of moving targets.
• Phase-aware (or phase-inspired) problem solving– General optimization problems
– ANTs problems
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 17
• Finished tasks– Marbles: modeling methods, encoding schemes, complexity, and search algorithms– CP: distributed algorithms and phase-transition behavior, distributed scan scheduling– General phase-aware methods (for TSP and number partitioning)
• Ongoing tasks– Scheduling in logistic domain: integrated scheduling– Distributed scan scheduling and tracking– Phase-aware methods for ANTs problems
• Tasks to start– Integrated solutions for all ANTs problems
Project Schedule and Milestones
Year 1
Year 2
Year 3
Models and modeling techniques
Complexity and algorithms
Phase transitions, constraint solver
Phase-aware methods
Integrated solutions
Milestone1: Models, phase transitions and algorithms
Demo on challenge problems
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 18
Technology Transition/Transfer
• To be worked on
ANTs PI meeting, May 29-31, 2002Washington University / DCMP 19
Program Issues
• Complexity and phase-transition analysis– How can the complexity and phase-transition results be
directly shown in the systems?
– How close is a simulation to a real problem setup?
• How do we handle sensor interference?– What to do when no reading?
• The complexity workshops for Marbles scheduling problems that we had before were very useful. Should we continue to have them in the future?– Looking forward to the Vanderbilt workshop
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