Subcontractors and Collaborators

1. Flexible Methods for Multi-agent Distributed Resource Allocation by Exploiting Phase Transitions- Distributed Constraint Minimization Problems (DCMP) PM: Vijay Raghavan PI: Weixiong ZhangPI phone: (314)935-8788PI email: zhang@cs.wustl.eduInstitutions: Washington University in St. LouisContract #:F30602-00-2-0531AO #: K278Award start date: 5/1/2000Award end date: 4/31/2003Agents: Daniel Daskiewich and Robert ParagiAgent Organization: US Airforce Lome Lab Washington 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. Washington 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 Washington University / DCMP

4. Less constrained Transformation and constraint relaxation Global state estimator Difficult phase Environment Probably solvable Unsolvable within bounds Progress monitor Problem solver progress Flexible Methods for Multi-Agent Distributed Resource Allocations by Exploiting Phase Transitions (DCMP) PHASE-AWARE PROBLEM SOLVING NEW IDEAS • 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 SCHEDULE IMPACT Integrated solutions • 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 Phase-aware methods Distributed constraint solvers Complexity and algorithms Demo on challenge problems Modeling Models, phase transitions and algorithms Year 1 Year 2 Year 3 Washington 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 Washington 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 Washington 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. Washington 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) Washington 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 (conservativefixed probability algorithm (CFP) considered by Kestrel is one variation) Washington 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 Washington 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. Washington 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 Washington University / DCMP

13. DBA DBA Status on CP: Summary of Results (4) • Anytime performance of DSA and DBA on scan scheduling • Solution quality • Communication cost Washington 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 Washington 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. Washington 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 Washington University / DCMP

17. Project Schedule and Milestones • 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 Integrated solutions Phase-aware methods Phase transitions,constraint solver Demo on challenge problems Complexityand algorithms Models and modeling techniques Milestone1: Models, phase transitions and algorithms Year 1 Year 2 Year 3 Washington University / DCMP

18. Technology Transition/Transfer • To be worked on Washington 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 Washington University / DCMP