A Memetic Method for Solving Portfolio Optimization  Problem Under Cardinality, Quantity and Pre-Assignment Constraints

Abstract

In the realm of industrial finance, portfolio selection stands as a critical problem that has garnered significant attention over recent decades. The conventional model employed for this purpose is known as the Markowitz mean-variance (MV) model, which encompasses two conflicting criteria: returns and risks. This model aims to attain a balance between the desire for high returns and the need to minimize potential risks. In this study, we address a portfolio optimization problem that incorporates realistic constraints, such as cardinality, quantity, and pre-assignment. To tackle this challenge, we introduce a memetic algorithm specifically designed to solve constrained portfolio optimization problems. This method effectively combines the global search capabilities of genetic algorithms with the fine-tuning provided by local search technique of the Hill Climbing. The test dataset used for evaluating the performance of our proposed memetic algorithm is derived from well-known financial benchmarks, including the ``Hang Seng in Hong Kong'', ``DAX 100 in Germany'', ``FTSE 100 in the United Kingdom'', ``S\&P 100 in the United States'', and ``Nikkei in Japan''. The memetic algorithm's performance is compared to the results obtained by exact optimization methods and other metaheuristic approaches to determine its relative efficiency and effectiveness.The experimental results confirmed an out performance of the devised memetic algorithm over the counterparts. It shows the effectiveness of suggested approach in solving the constrained portfolio optimization problem and promises its applicability towards the complex financial optimization problems with real constraints.

Keywords: Portfolio optimization, Constrained portfolio, Memetic algorithms, Multiobjective Optimization