1. Solvable problem 0 10 20 30 40 50 60 70 80 90 100 0510152025 Deviation from best known solution [%] Percentage of test runs ERA RDGR RGR LS Over-constrained problem 0 10 20 30 40 50 60 70 80 90 100 01020304050 Deviation from best known solution [%] Percentage of test runs RDGR RGR LS ERA Graduate Teaching Assistants Assignment Problem (GTAAP) It is a resource allocation problem where GTAs must be assigned to courses depending on their qualifications, availability, and preferences. It is modeled as a constrained optimization problem with the goal of maximizing the number of covered courses (primary criterion) while maximizing the preferences of the GTAs (secondary criterion) [2]. It offers an appealing platform for the development & evaluation of new problem-solving strategies and new techniques for interaction with users. Search strategies tested Heuristic backtrack search (BT): DFS with forward checking. We tested various variable/value ordering heuristics. Local search (LS): LS is a hill-climbing search with the min-conflict heuristic for value selection. It uses propagation on global constraints and operates in a greedy manner. We use random-walk and random restarts to recover from local optima. Multi-agent-based search (ERA): ERA is a multi-agent-based search for solving Constraint Satisfaction Problems (CSP) [3]. Randomization and geometric restarts (RGR): It randomizes variable/value selection in backtrack search and restarts with a geometrically increasing cutoff value [4]. Randomization and dynamic geometric restarts (RDGR): Our proposed restart strategy, improves upon RGR by making the restart strategy adapt to the progress of the search [1]. A New Dynamic Restart Strategy for Randomized Backtrack Search Venkata Praveen Guddeti and Berthe Y. Choueiry Constraint Systems Laboratory Computer Science & Engineering University of Nebraska-Lincoln vguddeti, choueiry@cse.unl.edu 1.We propose RDGR ( Randomization and Dynamic Geometric Restarts ) an improved restart strategy for randomized backtrack search. 2.We compare its performance to that of a number of deterministic and stochastic search techniques in the context of solving a tight, real-world, resource allocation problem. 3.We show that distinguishing between solvable and over-constrained problem instances yields new insights on the relative performance of the search techniques tested. 4.We propose to use this characterization as a basis for building new strategies of cooperative, hybrid search. Contributions 1.Study the behavior of thrashing. 2.Study the effect of running time on RGR & RDGR (given their stochastic nature and the inherent incompleteness of search on large spaces). 3.Study of the influence of the choice of the ratio r used in RGR & RDGR. 4.Compare the relative performance of BT, LS, ERA, RGR, and RDGR. Data sets: 6 GTAAP data-sets & 4 sets of randomly generated problems. Evaluation criteria: Solution quality distribution, 95% confidence interval. [1] P. Guddeti and B. Y. Choueiry, “An Empirical Study of a New Restart Strategy for Randomized Backtrack Search.” Workshop on CSP Techniques with Immediate Application, CP 2004. [2] R. Glaubius and B. Y. Choueiry, “Constraint Modeling and Reformulation in the Context of Academic Task Assignment.” Workshop on Modeling and Solving Problems with Constraints, ECAI 2002. [3] J. Liu, H. Jing, Y. Tang; “Multi-agent oriented constraint satisfaction.” Artificial Intelligence, 2002. [4] T. Walsh; “Search in a small world”. In Proceedings of the Sixteenth IJCAI 1999. Context This research is supported by NSF CAREER Award #0133568. Experiments were conducted utilizing the Research Computing Facility of the University of Nebraska-Lincoln. Experiments Future research directions References Effect of thrashing Thrashing in large search spaces Performance of BT for various CPU run-times. SQD on GTAAP data-sets: over-constrained (data set 1) and solvable (data set 5) problems (500 runs, 10 minutes each). Different run-times for over-constrained (data set 1) and solvable (data set 5) problems (500 runs) Validate our findings on 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 RDGR. Conclusions RDGR and RGR with different ratios r (500 runs, 5 minutes each) RDGR improves over RGR for all values of running time. Best values of r: RGR: r = 1.1 for both GTAAP and random problems. RDGR: r = 1.1 for GTAAP and r = 2 for random problems. Algorithm dominance: Under-constrained problems: ERA > RDGR > RGR > BT > LS Over-constrained problems: RDGR > RGR > BT > LS > ERA Phase transition (random problems): RDGR > RGR > BT > ERA > LS June 17, 2015 Theoretically complete. Thrashes badly because of high branching factor. Randomized backtrack search Random variable/value selection to visit wider areas of the search space. Restart strategies to avoid heavy-tailed behavior of BT search: Restart search when number of nodes visited exceeds a cutoff value. Cutoff value updated at every restart as a function of a parameter r. Systematic backtrack search Unsolvable 0 10 20 30 40 50 60 70 80 90 100 02468101214 Deviation from best known solution [%] Percentage of test runs RDGR RGR BT ERA LS 14 Deviation from best known solution [%] Percentage of test runs Solvable 0 10 20 30 40 50 60 70 80 90 100 024681012 RDGR RGR BT ERA LS SQD on random CSPs: unsolvable and solvable random problems at the phase transition. (100 instances, 3 minutes each). 24 hr: 51 (26%) 1 min: 55 (20%) Max depth: 57 Depth of tree: 69 by BT after... Shallowest level reached Comparing LS, ERA, RGR, & RDGR Influence of r : RGR & RDGR Effect of running time: RGR & RDGR Solvable problem 0 10 20 30 40 50 60 70 80 90 100 02468101214 Deviation from best known solution [%] Percentage of test runs RDGR-20min RGR-20min RDGR-10min RGR-10min RDGR-5min RGR-5min