Constraint Handling Methods for Portfolio Optimization Using Particle Swarm Optimization

Given a portfolio of securities, portfolio optimization aims to optimize the proportion of capital allocated to each security such that either the risk of the portfolio is minimized for a given level of expected return, expected return is maximized for a given risk budget, or the risk-adjusted expected return of the portfolio is maximized. Extensions to the portfolio optimization problem can result in it becoming more difficult to solve which has prompted the use of computational intelligence optimization methods over classical optimization methods. The portfolio optimization problem is subject to two primary constraints namely, that all of the capital available to the portfolio should be allocated between the constituent securities and that the portfolio remain long only and unleveraged. Two popular methods for finding feasible solutions when using classical optimization methods are the penalty function and augmented Lagrangian methods. This paper presents two new constraint handling methods namely, a portfolio repair method and a preserving feasibility method based on the barebones particle swarm optimization (PSO) algorithm. The purpose is to investigate which constraint handling techniques are better suited to the problem solved using PSO. It is shown that the particle repair method outperforms traditional constraint handling methods in all tested dimensions whereas the performance of the preserving feasibility method tends to deteriorate as the dimensionality of the portfolio optimization problem is increased.