Meta-heurísticas GRASP e BRKGA aplicadas ao problema da diversidade máxima
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Bibliographic record
Abstract
In this work we study the Maximum Diversity Problem (MDP), which consists of selecting among a set of elements, a subset as diverse as possible. The problem is classified as NP-hard. We present the quadratic and mixed integer linear formulations, applications and numerical example. We solve small problems exactly and we note that for larger problems it is necessary to use heuristics or metaheuristics on its resolution. Therefore, we chose Greedy Randomized Adaptive Search Procedure (GRASP) and Biased Random-Key Genetic Algorithm (BRKGA) metaheuristics to be applied to the MDP. In GRASP, we adopted a solution construction by selecting the element according to its corresponding contribution to the objective function value. After the construction of each solution, we apply a local search and then we activate the path relinking technique. In the local search procedure, we used a exhaustive search, making the best exchange between an element which belongs to solution and another element that does not belong. Once the solutions were generated, we apply path relinking in the expectation that between each pair of solutions, there is a solution with better objective function value. In BRKGA, we implemented a fitness function and a solution decoder adapted to the Maximum Diversity Problem. The fitness function adopted is the sum of diversities between selected elements e the decoding of solutions is based on sorting random-keys. The objective of this work is to analyze and compare the results obtained by GRASP and BRKGA metaheuristics, having as reference the best results in the literature. The problems analyzed in the computational tests were extracted from the MDPLIB library. We observed that the two metaheuristics showed good results on MDP's resolution, moreover for small and medium sized problems BRKGA obtained better performance than GRASP, while for large problems, GRASP outperforms BRKGA.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.006 | 0.002 |
| Open science | 0.009 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 0.005 |
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 it