Heuristic techniques for variable and value ordering in CSPs
Bibliographic record
Abstract
A Constraint Satisfaction Problem (CSP) is a powerful framework for representing and solving constraint problems. When solving a CSP using a backtrack search method, one important factor that reduces the size of the search space drastically is the order in which variables and values are examined. Many heuristics for static and dynamic variable ordering have been proposed and the most popular and powerful are those that gather information about the failures during the constraint propagation phase, in the form of constraint weights. These later heuristics are called conflict driven heuristics. In this paper, we propose two of these heuristics respectively based on Hill Climbing (HC) and Ant Colony Optimization (ACO) for weighing constraints. In addition, we propose two new value ordering techniques, respectively based on HC and ACO, that rank the values based on their ability to satisfy the constraints attached to their corresponding variables. Several experiments were conducted on various types of problems including random, quasi random and patterned problems. The results show that the proposed variable ordering heuristics, are successful especially in the case of hard random problems. Also, when using the proposed value and variable ordering together, we can improve the performance particularly in the case of random problems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".