Portfolio optimization involves the optimal assignment of limited capital to different available financial assets to achieve a reasonable trade-off between profit and risk objectives. In this paper, we studied the extended Markowitz's mean-variance portfolio optimization model. We considered the cardinality, quantity, pre-assignment and round lot constraints in the extended model. These four real-world constraints limit the number of assets in a portfolio, restrict the minimum and maximum proportions of assets held in the portfolio, require some specific assets to be included in the portfolio and require to invest the assets in units of a certain size respectively. An efficient learning-guided hybrid multi-objective evolutionary algorithm is proposed to solve the constrained portfolio optimization problem in the extended mean-variance framework. A learning-guided solution generation strategy is incorporated into the multi-objective optimization process to promote the efficient convergence by guiding the evolutionary search towards the promising regions of the search space. The proposed algorithm is compared against four existing state-of-the-art multi-objective evolutionary algorithms, namely Non-dominated Sorting Genetic Algorithm (NSGA-II), Strength Pareto Evolutionary Algorithm (SPEA-2), Pareto Envelope-based Selection Algorithm (PESA-II) and Pareto Archived Evolution Strategy (PAES). Computational results are reported for publicly available OR-library datasets from seven market indices involving up to 1318 assets. Experimental results on the constrained portfolio optimization problem demonstrate that the proposed algorithm significantly outperforms the four well-known multi-objective evolutionary algorithms with respect to the quality of obtained efficient frontier in the conducted experiments. 
A learning-guided multi-objective evolutionary algorithm for constrained portfolio optimization