A memetic method for solving portfolio optimization problem under cardinality, quantity, and pre-assignment constraints

In industrial finance, portfolio selection has emerged as a critical challenge that has received considerable attention over the past few decades. The standard approach to this problem is the Markowitz mean–variance model, which seeks to balance two inherently conflicting objectives: maximizing returns and minimizing risk. This study investigates portfolio optimization under realistic constraints, including cardinality, quantity, and pre-allocation. To address these challenges, we propose a memetic algorithm specifically designed to solve constrained portfolio optimization problems. The performance of the algorithm was evaluated using benchmark datasets from major financial markets, including the Hang Seng, DAX 100, FTSE 100, S&P 100, NASDAQ, and Nikkei indices. A comparative analysis with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Particle Swarm Optimization (PSO) demonstrated that the memetic algorithm consistently outperformed both NSGA-II and PSO in terms of execution time and the quality of efficient solutions. Across all tested markets, the memetic algorithm achieved superior risk/return ratios and faster computation times, confirming its effectiveness in solving complex portfolio optimization problems with real-world constraints.