SDQ for data set 5 (500 runs, 5 mins each)

1. References • Backtrack search • Stochastic Local Search • Project Summary • Randomized Backtrack Search with Restarts • Multi-Agent Search • Interactive Decision Making • Summary and Future Work • System Architecture • The architecture of our system • Problem Modeling and Constraint Reformulation ERA performance on solvable problem Statistics of solution size (500 runs, 5 mins each) SDQ for data set 1 (500 runs, 5 mins each) PDF for relative solution size for data set 1 (500 runs, 5 mins each) ERA performance on unsolvable problems Statistics of solution size (500 runs, 5 mins each) SDQ for data set 5 (500 runs, 5 mins each) PDF for relative solution size for data set 5 (500 runs, 5 mins each) • Reformulation of the non-binary confinement constraint into a binary confinement constraint. • Reformulation of the non-binary equality constraint into a binary equality constraint. An Interactive, Constraint-Based System for Task Allocation in an Academic Environment Ryan Lim, Venkata Praveen Guddeti, Venkateshwar Rao Thota, Hui Zou, and Berthe Y. Choueiry http://cse.unl.edu/~gta Constraint Systems Laboratory • Computer Science & Engineering • University or Nebraska • {rlim|vguddeti|vthota|hzou|choueiry}@cse.unl.edu • The system has the following main components: • A GTA web-interface accessible to GTAs for application • A manager web-interface for data management and decision making • View/edit GTA records • Setup classes • Specify constraints • Perform interactive selections or automated search • A relational database to store collected data. • Facilities for interactive decision making and exploration of solutions and bottlenecks. • A variety of search algorithms for automated problem solving. We have developed an interactive, web-based system for hiring and managing Graduate Teaching Assistants (GTAs) at the Department of Computer Science. • This is a hill-climbing search using the min-conflict heuristic for value selection. • Consistent assignments are not undone (greedy). • Constraint propagation is used to handle non-binary constraints. • Random Walk used to avoid local optima, random restarts used to recover from them. • This system has yielded research contributions in the following areas: • Formulation of the GTA assignment problem as a Constraint Satisfaction Problem (CSP) [2]. • Design a new convention for consistency checking to deal with over-constrained problems. • Reformulation of some global constraints into binary ones, and evaluation of the computational benefits of the reformulation. • Design, implementation, and deployment of a prototype for data acquisition and for interactive problem solving. • Design, evaluation, and new characterization of both heuristic and stochastic search techniques for automatically solving the problem. • Heuristic backtrack [5] • Stochastic local search [9] • Multi-agent ERA search [8] • Randomized backtrack [5] This project has opened up the following research directions: • A portfolio mechanism for on-line hybridization of search techniques • Development of constraint-based techniques for data-warehousing and compact representation of solution. • The practical benefits of the research conducted so far: • A number of research results published and presented in international scientific meetings. • Training of undergraduate and graduate students in Constraint Processing techniques, and production of a number of dissertations. • Practical benefit for the department: decreased time and effort for finding a solution, reduced the number of assignment conflicts and modifications, improved matching of GTAs to classes. • Multi-agent based search using the ERA (environment, reactive rules, agents) algorithm. • Agents are variables that seek to occupy good positions in the environment (values). • Environment records the number of constraint violations of each position. • Agent moves according to reactive rules and can force another agent out of a position • The algorithm acts as an ‘extremely’ decentralized local search. • Able to solve instances that remained unsolved by other techniques we tested. • Deadlock in over-constrained problems undermines stability & results in short solutions However, useful to identify, isolate, and represent conflicts in a compact manner. Interactive Selection allows the manager to interactively make decisions by examining the problem from two perspectives: Each circle corresponds to a position (i.e., a GTA). Each square represents an agent (i.e, a task). Blank squares indicate that the position is a zero position for the agent. The filled squares indicate that although the position is the best one for the agent, it results in some broken constraints, and the actual assignment of the position to the agent cannot be made. A list of courses with a sorted list of selectable GTAs. • Randomization to visit wider area of the space, restarts to overcome thrashing. • Randomization & Geometric restarts (RGR) [Walsh 99]: fixed restart schedule. • Randomization & Dynamic Geometric restarts (RDGR): dynamic restart schedule. • Problem definition: Given a set GTAs, a set of courses, and a set of constraints that specify the allowable assignments of GTAs to courses, the goal is to an assignment that is: • Consistent: the assignment breaks no constraint • Satisfactory: maximizes the number of courses covered and the happiness of the assigned GTAs. Variables: Courses are modeled as variables in our CSP. There are 3 types of courses (lecture, labs, recitation). Lectures may require a grader GTA while labs and recitations require an instructor GTA. A list of GTAs with a sorted list of selectable courses. Domains: GTAs make up the domains of the variables. GTAs may serve as an instructor if he/she is ITA certified. Each GTA may specify a preference value on the scale of 0 to 5 for each course offered. Constraints: We have 3 types of constraints – unary, binary, and non-binary constraints. How interactive selection works: Manager chooses perspective to work from An updated and sorted list of possible and consistent choices is provided Manager selects a choice and makes an assignment Constraint propagation is performed and removes choices that are no longer available (alternatively, restore choices that were ruled out). This ensures that the manager is always only presented with consistent options. • The main issues in backtrack search are the following • The problem is always tight (difficult to solve) and often over constrained (not enough GTAs hired) • We modified the basic backtrack mechanism to handle over-constrained problems • The performance of search depends on the sequence in which decisions are made (i.e. variable and value ordering) • We developed various ordering heuristics, and evaluated them with static and dynamic decision strategies • The branching factor of the search tree is particularly large • We identified the reasons for thrashing and characterized the thrashing behavior, which we solve with randomization (see Randomized Backtrack Search) Reformulation of non-binary constraints: A constraint is network decomposable [2] when it can be represented by an equivalent network of binary constraints. • In the future, we plan to: • Validate our findings on randomly generated problems and other real-world case-studies. • Design new search hybrids where a solution from a given technique such as ERA is fed as a seed to another one such as heuristic backtrack search. [1] R. Glaubius. A Constraint Processing Approach to Assigning Graduate Teaching Assistants to Courses. Undergraduate Honors Thesis. Department of Computer Science and Engineering, University of Nebraska-Lincoln, 2001. [2] R. Glaubius and B.Y. Choueiry. Constraint Modeling and Reformulation in the Context of Academic Task Assignment. In Working Notes of the Workshop on Modelling and Solving Problems with Constraints, ECAI 2002, Lyon, France, 2002. [3] R. Glaubius and B.Y. Choueiry. Constraint Modeling and Reformulation in the Context of Academic Task Assignment. Poster presentation at the Fifth International Symposium on Abstraction, Reformulation and Approximation (SARA 2002), 2002. [4] R. Glaubius and B.Y. Choueiry. Constraint Modeling in the Context of Academic Task Assignment. In Pascal Van Hentenryck, editor, Proceedings of 8th International Conference on Principle and Practice of Constraint Programming (CP02), volume 2470 of Lecture Notes in Computer Science, page 789, Ithaca, NY, 2002. Springer Verlag. [5] V. Guddeti, H. Zou, and B.Y. Choueiry. An Empirical Study of Heuristic and Randomized Search Techniques in a Real-World Setting, 2004. Under review. [6] R. Lim, V. Guddeti, and B.Y. Choueiry. An Interactive System for Hiring and Managing Graduate Teaching Assistants, 2004. Under review. [7] H. Zou. Iterative Improvement Techniques for Solving Tight Constraint Satisfaction Problems. Masters thesis, Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, NE, December 2003. [8] H. Zou and B.Y. Choueiry. Characterizing the Behavior of a Multi-Agent Search by Using it to Solve a Tight, Real-World Resource Allocation Problem. In Workshop on Applications of Constraint Programming, pages 81—101, Kinsale, County Cork, Ireland, 2003. [9] H. Zou and B.Y. Choueiry. Multi-agent Based Search versus Local Search and Backtrack Search for Solving Tight CSPs: A Practical Case Study. In Working Notes of the Workshop on Stochastic Search Algorithms (IJCAI 03), pages 17—24, Acapulco, Mexico, 2003. Shallowest level reached by BT after … Number of variables: 69 24 hr: 51 (26%) 1 min: 55 (20%) Max depth: 57 • Characteristics of the GTA data set. • BT search thrashing in a large search space. • BT search thrashing. • Performance of BT for various CPU run-times. Support: NSF grant #EPS-0091900, Department of Computer Science & Engineering, and Constraint Systems Laboratory. Experiments were carried out on PrairieFire, courtesy of the Research Computing Facility of Computer Science & Engineering.