AI 中文总结
本文针对投资组合优化中的约束多目标优化问题，提出RL-NSGA-II-GRC方法，结合强化学习智能体与灰色关联系数，通过自适应控制参数及设计综合指标引导搜索，在基准测试和纳斯达克案例中提升收敛性，得到密集前沿及有效投资组合。
AI 中文摘要
在现代金融市场中，决策者越来越依赖定量方法来应对多个常常相互冲突的目标之间的复杂权衡。本文研究约束多目标优化问题，并将其应用于投资组合优化，以最小化风险并最大化回报。为弥补现有差距，我们提出了一种新颖的基于强化学习（RL）引导的非支配排序遗传算法II（NSGA-II），并通过灰色关联系数（GRC）进行增强，即RL-NSGA-II-GRC。它结合了RL智能体控制器和基于GRC的选择，以提高帕累托前沿的收敛性和多样性。智能体利用超体积、可行性和多样性指标在线调整进化参数，而GRC锦标赛算子通过考虑支配等级、拥挤距离和与理想参考的接近程度的统一分数对父代进行排序。我们在Kursawe和CONSTR基准测试以及纳斯达克投资组合应用中评估了该框架。在基准测试中，RL-NSGA-II-GRC比NSGA-II的收敛改进约为5.8%和4.4%，同时保留分布良好的非支配解。在投资组合应用中，它产生了一个平滑、密集的有效前沿，支持识别最大夏普比率投资组合（年化夏普比率=1.92）和不同风险厌恶水平的效用最优投资组合。主要贡献有三点：1）我们提出了RL-NSGA-II-GRC方法，将RL智能体集成到进化框架中，通过世代反馈自适应控制参数；2）我们设计了一种GRC增强的二元锦标赛算子，提供了一个综合指标来引导搜索向帕累托前沿；3）我们在基准多目标优化和纳斯达克案例研究中证明，该方法提供了改进的收敛性和密集的前沿，支持可操作的见解。
英文摘要
In modern financial markets, decision-makers increasingly rely on quantitative methods to navigate complex trade-offs among multiple, often conflicting objectives. This paper addresses constrained multi-objective optimization (MOO) with an application to portfolio optimization for minimizing risk and maximizing return. To address existing gaps, we propose a novel reinforcement learning (RL)-guided non-dominated sorting genetic algorithm II (NSGA-II) enhanced with gray relational coefficients (GRC), termed RL-NSGA-II-GRC, which combines an RL agent controller and GRC-based selection to improve convergence and diversity of Pareto fronts. The agent adapts evolutionary parameters online using metrics of hypervolume, feasibility, and diversity, while the GRC tournament operator ranks parents via a unified score considering dominance rank, crowding distance, and proximity to ideal reference. We evaluate the framework on the Kursawe and CONSTR benchmarks and a NASDAQ portfolio application. On the benchmarks, RL-NSGA-II-GRC achieves convergence improvements of about 5.8% and 4.4% over NSGA-II, while preserving well-distributed non-dominated solutions. In the portfolio application, it produces a smooth, densely populated efficient frontier supporting identification of the maximum Sharpe ratio portfolio (annualized Sharpe =1.92) and utility-optimal portfolios for different risk-aversion levels. The main contributions are three-fold: 1) we propose an RL-NSGA-II-GRC method integrating an RL agent into the evolutionary framework to adaptively control parameters via generational feedback; 2) we design a GRC-enhanced binary tournament operator providing a comprehensive indicator to guide the search toward the Pareto front; 3) we demonstrate, on benchmark MOO and a NASDAQ case study, that the method delivers improved convergence and well-populated frontiers supporting actionable insights.
Journal refMathematics 14(2), 296 (2026)
