A self-tuning multi-objective optimization framework for geometric programming with gate sizing applications
Bibliographic record
Abstract
Most engineering problems involve optimizing different and competing objectives. To solve multi-objective problems, normally a weighted sum of the objectives is optimized. However, how the weights are assigned can greatly affect the outcome. Therefore, many designers have to resort to producing the Pareto surface - a time-consuming procedure. In this paper, we propose a framework for solving multi-objective geometric programming problems where weights in the objective are optimally calculated during the optimization problem without having to produce the Pareto surface. It is shown that the proposed self-tuning multi-objective framework can be applied to geometric programming gate sizing problems. Then, the efficacy of the proposed framework is proven using the clock network buffer sizing problem as an application. The problem is first formulated as a geometric programming (GP) problem with the objectives of reducing power, skew, and slew. The problem is solved using ISPD09 circuits. The power, skew and slew of the optimized networks are calculated using ngspice. The results show on average 52% reduction in power and 28% reduction in skew compared to the original networks. The self-tuning multi-objective solution is shown superior to any single objective solution with no impact on runtime.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".