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

Computer Science > Machine Learning
[Submitted on 12 Apr 2026]
Title:Reinforcement Learning-Guided NSGA-II Enhanced with Gray Relational Coefficient for Multi-Objective Optimization: Application to NASDAQ Portfolio Optimization
View PDFAbstract: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.
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* The method proposed is Reinforcement Learning-Guided NSGA-II enhanced with Gray Relational Coefficient (RL-NSGA-II-GRC).
* The application is multi-objective optimization for portfolio optimization to minimize risk and maximize return.
* An RL agent controls evolutionary parameters using hypervolume, feasibility, and diversity metrics.
* A GRC-based tournament operator ranks parents using dominance rank, crowding distance, and proximity to an ideal reference.
* Performance on Kursawe and CONSTR benchmarks showed convergence improvements of 5.8% and 4.4% over NSGA-II.
* The method was applied to a NASDAQ portfolio optimization case study.
* The application yielded an efficient frontier supporting identification of the maximum Sharpe ratio portfolio (annualized Sharpe = 1.92).

A novel method, RL-NSGA-II-GRC, is proposed for multi-objective optimization applied to NASDAQ portfolio selection, aiming to minimize risk and maximize return. The approach integrates a reinforcement learning (RL) agent controller with gray relational coefficients (GRC) enhancement within the NSGA-II evolutionary framework. The RL agent adapts evolutionary parameters based on hypervolume, feasibility, and diversity metrics generated during the process. Concurrently, the GRC is used in a binary tournament operator to rank parent solutions by considering dominance rank, crowding distance, and proximity to an ideal reference point. Evaluation on benchmark datasets (Kursawe and CONSTR) showed convergence improvements of 5.8% and 4.4% over standard NSGA-II while maintaining solution diversity. In the specific NASDAQ portfolio application, the method generated a smooth efficient frontier, identifying optimal portfolios, including one with an annualized Sharpe ratio of 1.92, across various risk-aversion levels.

This work addresses the known difficulty in navigating complex, multi-objective decision spaces by injecting adaptive intelligence from reinforcement learning into established evolutionary algorithms and refining selection mechanisms with relational metrics. The integration suggests a pattern where traditional algorithmic search methods, while robust, often struggle with the fine-grained balancing act required in high-dimensional financial scenarios. The use of GRC acts as a bridge, translating complex multi-criteria dominance into a unified, context-aware ranking system that guides exploration toward potentially superior Pareto fronts. The implication is that simply optimizing objective functions (risk vs. return) is insufficient; the process of optimization itself must be intelligently guided by dynamic feedback and relational understanding to yield actionable financial insights. The necessity for empirical validation on benchmarks alongside a real-world application suggests an acknowledgment that theoretical elegance alone does not translate into practical algorithmic superiority in volatile domains like finance. Future work must explore whether the learned RL policies generalize across different market regimes, and what specific structure in the GRC formulation most effectively captures investor risk aversion relative to market volatility outside the specified reference points.

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

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

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Executive Summary

Full Take

Sentinel — Human