QRL-AFOFA: Q-Learning Enhanced Self-Adaptive Fractional Order Firefly Algorithm for Large-Scale and Dynamic Multiobjective Optimization Problems

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. Extensive experiments on the 2021 IEEE Congress on Evolutionary Computation (CEC2021) benchmark functions demonstrate that QRL-AFOFA consistently outperforms other state-of-the-art algorithms across diverse problem categories. Accordingly, the proposed QRL-AFOFA demonstrated superior performance in 97.5% of test cases and outperformed the state-of-the-art algorithms in 34-40 out of 40 benchmark problems, with particularly impressive gains in dynamic and large-scale scenarios. Statistical validation using the Wilcoxon signed-rank and Friedman tests confirms the significance of the improvements. Notably, QRL-AFOFA achieves exceptional performance in high-dimensional (up to 10,000 variables) and dynamic optimization settings. Its self-adaptive design eliminates manual parameter tuning, making it a robust, scalable, and intelligent optimization framework for complex real-world applications.