level: research
this paper presents a method for constrained multi-objective optimization, applied to building stock portfolios that balance risk and return. the approach modifies the nsga-ii genetic algorithm by adding a reinforcement learning agent and a selection operator based on gray relational coefficients. the agent adjusts evolutionary parameters during the run using metrics like hypervolume, feasibility, and diversity. the gray relational tournament operator ranks candidate solutions by combining dominance rank, crowding distance, and closeness to an ideal reference point.
the combined method, called rl-nsga-ii-grc, aims to produce better pareto fronts with improved convergence and spread of solutions. the reinforcement learning component learns online which parameter settings work best as the population evolves. the gray relational coefficient provides a single score that captures multiple quality aspects of each solution, making parent selection more informed than using only pareto rank or crowding distance alone.
the framework was tested on standard benchmark problems kursawe and constr, as well as on a nasdaq portfolio optimization task. results indicate that the adaptive parameter control and unified ranking help the algorithm find more diverse and higher-quality trade-off solutions compared to the base nsga-ii. the work shows how combining learning-based control with multi-criteria decision-making techniques can address complex financial optimization problems with multiple conflicting goals.
why it matters: this method can help data scientists build more efficient portfolio optimization tools that automatically adapt to problem difficulty, leading to better investment strategies with less manual tuning.