A New Explicit Penalty Method for Evolutionary Multimodal Optimization
Why this work is in the frame
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Bibliographic record
Abstract
When employing evolutionary algorithms (EAs) to solve multimodal optimization problems (MMOPs), effectively utilizing diversity information is crucial to prevent the population from converging to a single peak. This requires balancing diversity and objective value—a challenge that inherently constitutes a penalty problem. Although some implicit penalty methods have been proposed to address this issue, most lack flexibility in penalty formulation. In this study, we present a novel explicit penalty method (EPM) designed to effectively leverage diversity information for multimodal optimization. First, the diversity of a solution is quantified by its distance to the nearest neighbor with a better objective value. Then, an explicit penalty function is formulated by integrating diversity and objective value. This function facilitates the capture of multiple peaks and balances the search among them. If a reasonable number of peaks are identified, a local search is applied to each for refinement; otherwise, a global search is conducted across the decision space. Through this adaptive process, EPM locates multiple optima both efficiently and accurately. Extensive experiments demonstrate that EPM outperforms several multimodal optimization methods, including 11 popular approaches, eight recent state-of-the-art algorithms, and an IEEE CEC competition winner. Moreover, even when integrated with classic differential evolution (DE), EPM exhibits highly competitive performance.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it