A Hybrid NAKA-FA-PSO Algorithm with Nakagami Distribution for Multi-Objective Portfolio Optimization

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.