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.

翻译：多目标投资组合优化是一个跨学科研究的关键问题，其目标是在最大化预期收益的同时最小化给定投资组合的风险。然而，许多研究未能将现实约束纳入模型，这限制了实际交易策略的应用。本研究将现实约束（如交易成本和持有成本）引入优化模型。由于该问题具有非凸性，元启发式算法（如NSGA-II、R-NSGA-II、NSGA-III和U-NSGA-III）将在求解中发挥关键作用。此外，采用学习启发式方法，通过替代模型增强所采用的元启发式算法。随后，将这些算法与不使用学习启发式算法求解约束多目标优化问题的基线元启发式算法进行比较。研究结果表明，尽管学习启发式算法运行完成所需时间显著更长，但在超体积和收敛速度方面优于基线算法。此外，回测结果表明，相较于不使用学习启发式算法，使用学习启发式算法生成资产配置权重可带来更低的风险百分比、更高的预期收益和更高的夏普比率。由此我们得出结论：使用学习启发式算法求解约束多目标投资组合优化问题，能产生比不使用该算法更优且更可取的结果。