Oblivious and non-oblivious local search for combinatorial optimization
Bibliographic record
Abstract
Standard local search algorithms for combinatorial optimization problems repeatedly apply small changes to a current solution to improve the problem's given objective function. In contrast, non-oblivious local search algorithms are guided by an auxiliary potential function, which is distinct from the problem's objective. In this thesis, we compare the standard and non-oblivious approaches for a variety of problems, and derive new, improved non-oblivious local search algorithms for several problems in the area of constrained linear and monotone submodular maximization. First, we give a new, randomized approximation algorithm for maximizing a monotone submodular function subject to a matroid constraint. Our algorithm's approximation ratio matches both the known hardness of approximation bounds for the problem and the performance of the recent greedy'' algorithm. Unlike the continuous greedy algorithm, our algorithm is straightforward and combinatorial. In the case that the monotone submodular function is a coverage function, we can obtain a further simplified, deterministic algorithm with improved running time. Moving beyond the case of single matroid constraints, we then consider general classes of set systems that capture problems that can be approximated well. While previous such classes have focused primarily on greedy algorithms, we give a new class that captures problems amenable to optimization by local search algorithms. We show that several combinatorial optimization problems can be placed in this class, and give a non-oblivious local search algorithm that delivers improved approximations for a variety of specific problems. In contrast, we show that standard local search algorithms give no improvement over known approximation results for these problems, even when allowed to search larger neighborhoods than their non-oblivious counterparts. Finally, we expand on these results by considering standard local search algorithms for constraint satisfaction problems. We develop conditions under which the approximation ratio of standard local search remains limited even for super-polynomial or exponential local neighborhoods. In the special case of MaxCut, we further show that a variety of techniques including random or greedy initialization, large neighborhoods, and best-improvement pivot rules cannot improve the approximation performance of standard local search.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".