Subcontractors and Collaborators

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


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.


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


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


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


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


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.


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)


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)


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



• 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.



• 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



• Anytime performance of DSA and DBA on scan scheduling

• Solution quality • Communication cost

DBA

DBA



• Distributed scan scheduling using DSA and DBA

• Results from DSA • Results from DBA

• Scalability – next sets of experiments to be done


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.


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


• 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


Technology Transition/Transfer

• To be worked on


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

Documents

Subcontractors and Collaborators