A Hybrid NAKA-FA-PSO Algorithm with Nakagami Distribution for Multi-Objective Portfolio Optimization
Bibliographic record
Abstract
Objective: This study aims to optimize portfolio allocation under cardinality constraints by maximizing expected return and minimizing risk, while addressing the NP-complete nature of the problem. Research Design & Methods: A hybrid multi-objective optimization approach is proposed by combining Particle Swarm Optimization and Firefly Algorithm (PSO-FA) with Nakagami distribution to preserve solution diversity and achieve optimal results. The algorithms were applied to the OR-library dataset and executed 30 times for analysis and evaluation. Findings: The experimental results demonstrate that the proposed algorithm outperforms existing methods in terms of accuracy, diversity, and stability. On the P5 test sample, the reported metrics were 2.76E-07 IGD, 7.43E-08 GD, and 2.94E-03 HV, with consistent improvements also observed in other test samples. Implications & Recommendations: The findings suggest that the PSO-FA with Nakagami distribution can serve as an effective alternative for solving cardinality-constrained portfolio optimization problems, particularly in tackling NP-complete challenges in finance. Future research may extend its application to larger datasets and dynamic market conditions. Contribution & Value Added: This study contributes by introducing a novel hybrid optimization framework (PSO-FA and Nakagami distribution) that enhances solution quality in portfolio optimization. The value added lies in its ability to balance return, risk, and solution diversity, offering new insights beyond existing approaches in the literature.
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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 | 0.001 | 0.003 |
| 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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".