QRL-AFOFA: Q-learning enhanced self-adaptive fractional order firefly algorithm for large-scale and dynamic multiobjective optimization problems

Abstract

This paper introduces QRL-AFOFA, a Q-learning-enhanced adaptive fractional-order firefly algorithm developed to address the challenges of large-scale and dynamic multiobjective optimization problems. While fractional-order metaheuristics provide memory-driven search dynamics and reinforcement learning (RL) offers adaptive policy control, existing hybrid methods often face critical limitations such as parameter sensitivity, premature convergence, and poor diversity preservation. To overcome these challenges, QRL-AFOFA integrates five synergistic innovations: real-time adaptive tuning of fractional-order parameters, entropy-regularized Q-value updates, stagnation-aware restart strategies, reflection-based boundary handling, and dual-phase learning rate scheduling. The Q-learning framework autonomously adapts critical parameters while entropy regularization maintains the exploration-exploitation balance, and stagnation-aware mechanisms ensure the preservation of population diversity. Extensive experiments on the IEEE Congress on Evolutionary Computation (CEC2021) benchmark functions demonstrate that QRL-AFOFA consistently outperforms state-of-the-art algorithms across diverse problem categories. Statistical validation further confirmed its superior performance across multiobjective, large-scale, and dynamic optimization scenarios. The algorithm achieves exceptional performance in high-dimensional settings while eliminating manual parameter tuning requirements, positioning it as an intelligent, scalable optimization framework for complex real-world applications.