Multi-Guide Set-Based Particle Swarm Optimization for Multi-Objective Portfolio Optimization

Portfolio optimization is a multi-objective optimization problem (MOOP) with risk and profit, or some form of the two, as competing objectives. Single-objective portfolio optimization requires a trade-off coefficient to be specified in order to balance the two objectives. Erwin and Engelbrecht proposed a set-based approach to single-objective portfolio optimization, namely, set-based particle swarm optimization (SBPSO). SBPSO selects a sub-set of assets that form a search space for a secondary optimization task to optimize the asset weights. The authors found that SBPSO was able to identify good solutions to portfolio optimization problems and noted the benefits of redefining the portfolio optimization problem as a set-based problem. This paper proposes the first multi-objective optimization (MOO) approach to SBPSO, and its performance is investigated for multi-objective portfolio optimization. Alongside this investigation, the performance of multi-guide particle swarm optimization (MGPSO) for multi-objective portfolio optimization is evaluated and the performance of SBPSO for portfolio optimization is compared against multi-objective algorithms. It is shown that SBPSO is as competitive as multi-objective algorithms, albeit with multiple runs. The proposed multi-objective SBPSO, i.e., multi-guide set-based particle swarm optimization (MGSBPSO), performs similarly to other multi-objective algorithms while obtaining a more diverse set of optimal solutions.