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An Empirical Study of a New Restart Strategy for Randomized Backtrack Search

This study presents an improved restart strategy (RDGR) for randomized backtrack search, evaluating it against other techniques and identifying dominance regimes. The context is the Graduate Teaching Assistants Assignment Problem (GTAAP) within constraint-based models, aiming to find consistent and satisfactory assignments. Empirical evaluations show RDGR consistently outperforming RGR, especially in under-constrained scenarios. Future research directions include more real-world evaluations and designing progress-aware restart strategies.

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An Empirical Study of a New Restart Strategy for Randomized Backtrack Search

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  1. An Empirical Study of a New Restart Strategy for Randomized Backtrack Search Venkata P. Guddeti and Berthe Y. Choueiry Constraint Systems Laboratory University of Nebraska-Lincoln CSPIA 04

  2. Outline • Summary of contributions • Context: Graduate Teaching Assistants Assignment Problem (GTAAP) • Randomized BT search with restarts • Empirical evaluations • Conclusions & future research directions CSPIA 04

  3. Summary of contributions • An improved restart strategy for randomized backtrack search (RDGR) • Evaluation & characterization • Comparison with BT, LS, ERA, RGR • Problem types: GTAAP & random CSPs • Criterion: solution quality distribution • Conclusions • Identified regimes where a given technique dominates • Building blocks for cooperative, hybrid search CSPIA 04

  4. Context: GTAAP Hiring & managing GTAs as instructors + graders • Given • A set of courses • A set of GTAs • A set of constraints that specify allowable assignments • Find a consistent & satisfactory assignment • Consistent: assignment breaks no (hard) constraints • Satisfactory: assignment maximizes • number of courses covered • happiness of the GTAs CSPIA 04

  5. Constraint-based model • Variables (typically70 courses) • Grading, conducting lectures, labs & recitations • Values (30 GTAs) • Hired GTAs (+ preference for each value in domain) • Constraints • Unary, binary, global (e.g., capacity) • Objective • longest consistent solution (primary criterion) • maximize geometric mean of preferences (secondary criterion) CSPIA 04

  6. Backtrack search (BT) • In theory, complete. In practice... forget it • Huge branching factor causes thrashing  backtrack never reaches early variables • Tested 12 ordering heuristics • No significant difference • Use randomization & • restarts [Gomes et al. 98] CSPIA 04

  7. Randomized BT with restarts • On stagnation of backtrack search • Interrupt search, then restart • Explore wider areas of search space: randomized variable-value ordering • Restart strategies • Fixed-cutoff, universal strategy [Luby et al. 93] • RRR: randomization & rapid restarts [Gomes et al. 98] • Fixed optimal cutoff value • Priori knowledge of cost distribution required • RGR:randomization & geometric restarts[Walsh 99] CSPIA 04

  8. RGR • Static restart strategy • As cutoff value increases, RGR degenerates into BT • Ensures completeness (utopian in our setting) • But… restart is obstructed • … and thrashing reappears  diminishing the probability of finding a solution CSPIA 04

  9. RDGR • Randomization & Dynamic Geometric Restarts • Cutoff value • Depends on the progress of search • Never decreases • Increases at a much slower rate than RGR • Feature: restart is ‘less’ obstructed CSPIA 04

  10. Experiments: 3 sets • Effect of run time on RGR & RDGR • Choiceofr in RGR & RDGR • Relative performance of RDGR versus • Backtrack search (BT) [Glaubius 01] • Local Search (LS) [Zou 03] • Multi-Agent Search (ERA) [Liu et al. 02, Zou 03] • RGR All implementations use same platform and executed to the best of our abilities (internal competition) CSPIA 04

  11. Evaluation criteria • Solution Quality Distribution (SQD) • cumulative distributions of solution quality • measured as percentage deviation from best known solution • Descriptive statistics • Mean, median, mode, std dev, max, min • 95% confidence interval using Mann-Whitney test CSPIA 04

  12. Data sets • 6 real-world data sets (GTAAP) • 3 solvable, 3 over-constrained • Experiment repeated 500 times • 4 sets of randomly generated problems • Model B, 100 instances, each instance runs for 3 minutes Solvable <25,15,0.5,0.36> Unsolvable <25,15,0.5,0.36> <40,20,0.5,0.2> <40,20,0.5,0.5> CSPIA 04

  13. 1. Effect of varying run time • RDGR consistently outperforms RGR • Running time does not affect the relative dominance CSPIA 04

  14. 2. Choice ofrin RGR r = 1.1 for RGR for GTAAP & random CSPs CSPIA 04

  15. 2. Choice of rin RDGR r = 1.1 for GTAAP r = 2 for random CSPs CSPIA 04

  16. 3. Performance: SQDs • Under-constrained: ERA > RDGR > RGR > BT > LS • Over-constrained: RDGR > RGR > BT > LS > ERA CSPIA 04

  17. 3. SQDs at phase transition • Solvable: ERA still wins for smallest deviations • Unsolvable: RDGR > RGR > BT > ERA > LS CSPIA 04

  18. 3. Performance: RDGR vs. RGR • RDGR allows more restarts than RGR • RDGR is more stable than RGR CSPIA 04

  19. Summary: algorithm dominance On GTAAP and randomly generated CSPs • Solvable instances ERA > RDGR > RGR > BT > LS • Over-constrained instances RDGR > RGR > BT > LS > ERA CSPIA 04

  20. Future research • More evaluations on real-world problems • Design ‘progress-aware’ restart strategies • Where cutoff value is changed during search • Design new search strategies • Hybrids: a solution from a given technique is fed to another • Cooperative: strategies applied where most appropriate within a given problem instance CSPIA 04

  21. CSPIA 04

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