The Mean-Variance Cardinality Constrained Portfolio Selection using an Enhanced Genetic Algorithm with a Novel Crossover Operator

Portfolio selection has been recognized as one of the most significant and challenging problems in financial engineering since Markowitz’s pioneering work on the mean-variance model. This problem centers on the optimal allocation of wealth across a set of assets to maximize returns while minimizing investment risk. While the basic Markowitz mean-variance framework is theoretically elegant and foundational, it has faced criticism from investment practitioners due to its reliance on unrealistic assumptions that limit its practical applicability. Specifically, the traditional model assumes perfect market conditions and neglects real-world constraints, such as the need to limit the number of assets in a portfolio (cardinality), which can significantly reduce its practical applicability. To address these limitations, this paper extends the mean-variance portfolio selection model by incorporating cardinality and floor-ceiling (quantity) constraints. The cardinality constraint ensures that the portfolio includes a specified number of assets, while the floor-ceiling constraint regulates the allocation to each asset, restricting it within predefined bounds. These added constraints transform the classical quadratic optimization problem into a mixed-integer quadratic problem, which necessitates the use of approximation algorithms such as metaheuristic algorithms for efficient and feasible solutions. Although numerous metaheuristic algorithms have been employed to tackle this problem, genetic algorithms have gained prominence due to their balance between solution quality and computational efficiency. However, the standard genetic algorithm is not without its shortcomings, particularly when handling the complexity of constrained portfolio optimization. To overcome these limitations, we propose a novel crossover operator designed to enhance the performance of the genetic algorithm.