Machine learning-based framework to cover optimal Pareto-front in many-objective optimization
Bibliographic record
Abstract
Abstract One of the crucial challenges of solving many-objective optimization problems is uniformly well covering of the Pareto-front (PF). However, many the state-of-the-art optimization algorithms are capable of approximating the shape of many-objective PF by generating a limited number of non-dominated solutions. The exponential increase of the population size is an inefficient strategy that increases the computational complexity of the algorithm dramatically—especially when solving many-objective problems. In this paper, we introduce a machine learning-based framework to cover sparse PF surface which is initially generated by many-objective optimization algorithms; either by classical or meta-heuristic methods. The proposed method, called many-objective reverse mapping (MORM), is based on constructing a learning model on the initial PF set as the training data to reversely map the objective values to corresponding decision variables. Using the trained model, a set of candidate solutions can be generated by a variety of inexpensive generative techniques such as Opposition-based Learning and Latin Hypercube Sampling in both objective and decision spaces. Iteratively generated non-dominated candidate solutions cover the initial PF efficiently with no further need to utilize any optimization algorithm. We validate the proposed framework using a set of well-known many-objective optimization benchmarks and two well-known real-world problems. The coverage of PF is illustrated and numerically compared with the state-of-the-art many-objective algorithms. The statistical tests conducted on comparison measures such as HV, IGD, and the contribution ratio on the built PF reveal that the proposed collaborative framework surpasses the competitors on most of the problems. In addition, MORM covers the PF effectively compared to other methods even with the aid of large population size.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| 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 | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".