# Reinforcement Learning-Guided NSGA-II Enhanced with Gray Relational Coefficient for Multi-Objective Optimization: Application to NASDAQ Portfolio Optimization

arXiv: https://arxiv.org/abs/2607.16194 · HTML: https://mlsanity.com/paper/2607.16194/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods.
- Builds on 5 of its 57 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Placed in

- Deep reinforcement learning methods / [Adversarial robustness and RL in finance](https://mlsanity.com/deeprl/adversarial-robustness-and-rl-in-finance/)

## Builds on (most cited first, 5 of 5)

- [RL-GA: A Reinforcement Learning-Based Genetic Algorithm for Electromagnetic Detection Satellite Scheduling Problem](https://mlsanity.com/paper/2206.05694/) (2022)
- [Reinforcement Learning-assisted Evolutionary Algorithm: A Survey and Research Opportunities](https://mlsanity.com/paper/2308.13420/) (2023)
- [Some Network Optimization Models under Diverse Uncertain Environments](https://mlsanity.com/paper/2103.08327/) (2021)
- [A Learnheuristic Approach to A Constrained Multi-Objective Portfolio Optimisation Problem](https://mlsanity.com/paper/2304.06675/) (2023)
- [Machine Learning-Assisted Surrogate Modeling with Multi-Objective Optimization and Decision-Making of a Steam Methane Reforming Reactor](https://mlsanity.com/paper/2507.07641/) (2025)

## Abstract (arXiv)

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.