Providing a Multi-Objective Mathematical Model for Cardinality-Constrained Portfolio Optimization Using Genetic Algorithm

Document Type : Original Article

Authors

1 Ph.D Candidate, Department of Accounting, Sar.C., Islamic Azad University, Sari, Iran

2 Corresponding Author, Associate Prof, Department of Accounting, Se.C., Islamic Azad University, Semnan, Iran

3 Assistance Prof. Department of Accounting, Sar.C., Islamic Azad University, Sari, Iran

10.22091/jemsc.2026.15821.1373

Abstract

This study proposes a multi-objective mathematical model for optimal portfolio selection and asset allocation, integrating the classical Mean-Variance Markowitz framework with realistic market constraints. Specifically, the model incorporates cardinality constraints to limit the maximum number of held assets and bounding constraints to enforce upper and lower limits on asset weights. These constraints transform the standard quadratic optimization into an NP-hard combinatorial problem. To solve this efficiently, a non-dominated sorting-based Multi-Objective Genetic Algorithm is developed to generate the Pareto-optimal front. The proposed model is validated using empirical financial data from a case study of the top 10 companies on the Tehran Stock Exchange (TSE) during the highly volatile period of 2018–2019. The empirical results demonstrate that the hybrid genetic approach successfully identifies optimal capital allocation weights, generating a well-distributed Pareto frontier where portfolio risk is minimized by up to 14.5% for given target returns compared to equally-weighted benchmarks. Notably, Rampan (Mapna) consistently emerges as the dominant and most robust asset, carrying the highest allocation weights across the majority of the optimal investment scenarios due to its superior risk-adjusted return profile. These quantitative findings provide portfolio managers with a rigorous, data-driven decision-making tool for constrained asset allocation in highly volatile emerging markets.

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References

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