A Learnheuristic Approach to A Constrained Multi-Objective Portfolio Optimisation Problem

Abstract: Multi-objective portfolio optimisation is a critical problem researched across various fields of study as it achieves the objective of maximising the expected return while minimising the risk of a given portfolio at the same time. However, many studies fail to include realistic constraints in the model, which limits practical trading strategies. This study introduces realistic constraints, such as transaction and holding costs, into an optimisation model. Due to the non-convex nature of this problem, metaheuristic algorithms, such as NSGA-II, R-NSGA-II, NSGA-III and U-NSGA-III, will play a vital role in solving the problem. Furthermore, a learnheuristic approach is taken as surrogate models enhance the metaheuristics employed. These algorithms are then compared to the baseline metaheuristic algorithms, which solve a constrained, multi-objective optimisation problem without using learnheuristics. The results of this study show that, despite taking significantly longer to run to completion, the learnheuristic algorithms outperform the baseline algorithms in terms of hypervolume and rate of convergence. Furthermore, the backtesting results indicate that utilising learnheuristics to generate weights for asset allocation leads to a lower risk percentage, higher expected return and higher Sharpe ratio than backtesting without using learnheuristics. This leads us to conclude that using learnheuristics to solve a constrained, multi-objective portfolio optimisation problem produces superior and preferable results than solving the problem without using learnheuristics.