1. SDQ for data set 5 (500 runs, 5 mins each) PDF for relative solution size for data set 5 (500 runs, 5 mins each) 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 How interactive selection works: 1. Manager chooses perspective to work from 2. An updated and sorted list of possible and consistent choices is provided 3. Manager selects a choice and makes an assignment 4. 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. ERA performance on solvable problem 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 Project Summary 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. System Architecture 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. The architecture of our system Problem Modeling and Constraint Reformulation 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. Unary ITA certification – GTA must be ITA qualified to teach the constrained course Enrollment – GTA cannot be enrolled in the constrained course. Overlapping – GTA cannot be assigned to a course that requires an instructor if he/she is enrolled in a course at the same time Zero Preference – GTA cannot have a preference of 0 for the course. Binary Mutex – Courses cannot be assigned the same GTA. Non- binary Equality – all courses should be assigned the same GTA Capacity – no GTA should be assigned to a workload that exceeds his/her capacity Confinement – assignments to two specific sets of courses should be mutually exclusive Reformulation of non-binary constraints: A constraint is network decomposable [2] when it can be represented by an equivalent network of binary constraints. Interactive Decision Making Interactive Selection allows the manager to interactively make decisions by examining the problem from two perspectives: Backtrack search The main issues in backtrack search are the following 1.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 2.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 3.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) Stochastic Local Search 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. Data set # of vars BT running for … 5 mins6 hours Max depth ShallowestMax depth Shallowest Level% % I69575323575126 II65635515635416 III54524418544124 IV59494818504523 V54625415624726 VI3128135828390 BT search thrashing. Reformulation of the non-binary confinement constraint into a binary confinement constraint. Reformulation of the non-binary equality constraint into a binary equality constraint. Multi-Agent Search 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. 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. 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. [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. 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. 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. 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. Characteristics of the GTA data set. A list of courses with a sorted list of selectable GTAs. A list of GTAs with a sorted list of selectable courses. We have developed an interactive, web-based system for hiring and managing Graduate Teaching Assistants (GTAs) at the Department of Computer Science. 24 hr: 51 (26%) 1 min: 55 (20%) Max depth: 57 Shallowest level reached by BT after … Number of variables: 69 BT search thrashing in a large search space. Randomized Backtrack Search with Restarts References Comparison of Techniques ERAGeneral: Stochastic and incomplete. Tight but solvable problems: Immune to local optima and solves tight CSPs. Over-constrained problems: Deadlock causes instability and yields shorter solutions. LSGeneral: Stochastic, incomplete, and quickly stabilizes. Tight but solvable problems: Liable to local optima and fails to solve tight CSPs even with random-walk and restart strategies. Over-constrained problems: Finds longer solutions than ERA. RDGRGeneral: Stochastic, incomplete, immune to thrashing, produces longer solutions than BT, immune to deadlock, reliable on unknown instances, and immune to local optima, but less than ERA. RGRGeneral: Stochastic, approximately complete, less immune to thrashing than RDGR, and yields shorter solutions than RDGR in general. BTGeneral: Systematic, complete (theoretically, rarely in practice), liable to thrashing, yields shorter solutions than RDGR and RGR, stable behavior, and more stable solutions than stochastic methods in general. Summary and Future Work In the future, we plan to: 1.Validate our findings on randomly generated problems and other real-world case-studies. 2.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. Data Set I (69 variables, over-constrained) CPU run time30 secs 5 mins30 mins 1 hour6 hours24 hours Shallowest BT level545352 51 Longest solution57 Geometric mean of preference2.152.17 2.212.27 # of backtracks183547951261536532787327476713070031 # of nodes visited352689788486462989136605963824146133 Performance of BT for various CPU run-times.