Systematic Initialization Approaches for Portfolio Optimization Problems

Abstract

Selecting the number of assents to obtain the maximized expected return under the possible lowest risk is the main concern of portfolio optimization problems. Optimization algorithms -multi/manyobjective-are evaluated to find the desired/possible level of investment. Converging to the best possible asset set and -if possible-distribution of the many possible solution sets for an efficient frontier is expected as the result of the multi/many-objective optimization algorithms. Obtaining an accurate and well-distributed set of solutions is the main motivation. Hence, in this paper, two initialization approaches are proposed for multi/many-objective optimization algorithms to obtain a better convergence and distribution solution set for the portfolio optimization problem. The initial population set is composed of the assets with the largest income and binary combinations of the assets where their sum returns the maximum income. These proposed approaches are integrated with eight different optimization algorithms and the performance of the algorithms is compared with respect to the convergence and diversity metrics.

A Self-Learning Based Preference Model for Portfolio Optimization

“…Among them, some models are derived by creating additional or variational objectives based on the MV model, e.g., skewness [4], volatility in the portfolios [5], mean absolute deviation [6], minimax [7], and value at risk [8,9]; some by incorporating additional constraints into the MV model, e.g., boundaries [10], cardinality [11], and transaction costs [12], or by relaxing existing constraints, such as weight from non-negativity to negativity [13]; and some by being extended before their suitability in a dynamic market, such as a prediction-based portfolio optimization model that can predict each stock's Mathematics 2021, 9, 2621 2 of 17 future return [14]. Since these portfolio optimization models are almost multi-objective and are very difficult to solve efficiently using mathematical programming and exact methods [15,16], further attention has been paid to the metaheuristic algorithms that have displayed high performance levels in solving multi-objective optimization problems in other fields. These algorithms include the niched Pareto genetic algorithm II (NPGA-II) [17], the strength Pareto evolutionary algorithm 2 (SPEA2) [18], the multi-objective evolutionary algorithm based on decomposition (MOEA/D) [19], particle swarm optimization (PSO) [20], an artificial bee colony (ABC) [21], a biased-randomized iterated local search algorithm [22], and so on.…”